Calculus and mathematical analysis Books

This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.

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Book SynopsisWith a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus.  Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse''s lemma and the Poincaré lemma.  The ideas behind most topics can be understood with just two or three variables.  The book incorporates modern computational tools to give visualization real power.  Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps.  The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books.  This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics.  Prerequisites are an introduction to linear algebra and multivariable calculus.  There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry.  The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.Trade ReviewFrom the reviews:“Many concepts in calculus and linear algebra have obvious geometric interpretations. … This book differs from other advanced calculus works … it can serve as a useful reference for professors. … it is the adopted course resource, its inclusion in a college library’s collection should be determined by the size and interests of the mathematics faculty. Summing Up … . Upper-division undergraduate through professional collections.” (C. Bauer, Choice, Vol. 48 (8), April, 2011)“The author of this book sees an opportunity to bring back a more geometric, visual and physically-motivated approach to the subject. … The author makes exceptionally good use of two and three-dimensional graphics. Drawings and figures are abundant and strongly support his exposition. Exercises are plentiful and they cover a range from routine computational work to proofs and extensions of results from the text. … Strong students … are likely to be attracted by the approach and the serious meaty content.” (William J. Satzer, The Mathematical Association of America, January, 2011)“A new geometric and visual approach to advanced calculus is presented. … The book can be useful a textbook for beginners as well as a source of supplementary material for university teachers in calculus and analysis. … the book meets a wide auditorium among undergraduate and graduate students in mathematics, physics, economics and in other fields which essentially use mathematical models. It is also very interesting for teachers and instructors in Calculus and Mathematical Analysis.” (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1205, 2011)Table of Contents1 Starting Points.-1.1 Substitution.- Exercises.- 1.2 Work and path integrals.- Exercises.- 1.3 Polar coordinates.- Exercises.- 2 Geometry of Linear Maps.- 2.1 Maps from R2 to R2.- Exercises.- 2.2 Maps from Rn to Rn.- Exercises.- 2.3 Maps from Rn to Rp, n 6= p.- Exercises.- 3 Approximations.- 3.1 Mean-value theorems.- Exercises.- 3.2 Taylor polynomials in one variable.- Exercises.- 3.3 Taylor polynomials in several variables.- Exercises.- 4 The Derivative.- 4.1 Differentiability.- Exercises.- 4.2 Maps of the plane.- Exercises.- 4.3 Parametrized surfaces.- Exercises.- 4.4 The chain rule.- Exercises.- 5 Inverses.- 5.1 Solving equations.- Exercises.- 5.2 Coordinate Changes.- Exercises.- 5.3 The Inverse Function Theorem.- Exercises.- 6 Implicit Functions.- 6.1 A single equation.- Exercises.- 6.2 A pair of equations.- Exercises.- 6.3 The general case.- Exercises.- 7 Critical Points.- 7.1 Functions of one variable.- Exercises.- 7.2 Functions of two variables.- Exercises.- 7.3 Morse’s lemma.- Exercises.- 8 Double Integrals.- 8.1 Example: gravitational attraction.- Exercises.- 8.2 Area and Jordan content.- Exercises.- 8.3 Riemann and Darboux integrals.- Exercises.- 9 Evaluating Double Integrals.- 9.1 Iterated integrals.- Exercises.- 9.2 Improper integrals.- Exercises.- 9.3 The change of variables formula.- 9.4 Orientation.- Exercises.- 9.5 Green’s Theorem.- Exercises.- 10 Surface Integrals.- 10.1 Measuring flux.- Exercises.- 10.2 Surface area and scalar integrals.- Exercises.- 10.3 Differential forms.- Exercises.- 11 Stokes’ Theorem.- 11.1 Divergence.- Exercises.- 11.2 Circulation and Vorticity.- Exercises.- 11.3 Stokes’ Theorem.- 11.4 Closed and Exact Forms.- Exercises

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Book SynopsisManifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory.Trade ReviewFrom the reviews of the second edition:“This book could be called a prequel to the book ‘Differential forms in algebraic topology’ by R. Bott and the author. Assuming only basic background in analysis and algebra, the book offers a rather gentle introduction to smooth manifolds and differential forms offering the necessary background to understand and compute deRham cohomology. … The text also contains many exercises … for the ambitious reader.” (A. Cap, Monatshefte für Mathematik, Vol. 161 (3), October, 2010)Table of ContentsPreface to the Second Edition.- Preface to the First Edition.-Chapter 1. Eudlidean Spaces. 1. Smooth Functions on a Euclidean Space.- 2. Tangent Vectors in R(N) as Derivativations.- 3. The Exterior Algebra of Multicovectors.- 4. Differential Forms on R(N).- Chapter 2. Manifolds.- 5. Manifolds.- 6. Smooth Maps on a Manifold.- 7. Quotients.- Chapter 3. The Tangent Space.- 8. The Tangent Space.- 9. Submanifolds.- 10. Categories and Functors.- 11. The Rank of a Smooth Map.- 12. The Tangent Bundle.- 13. Bump Functions and Partitions of Unity.- 14. Vector Fields.-Chapter 4. Lie Groups and Lie Algebras.- 15. Lie Groups.- 16. Lie Algebras.- Chapter 5. Differential Forms.- 17. Differential 1-Forms.- 18. Differential k-Forms.- 19. The Exterior Derivative.- 20. The Lie Derivative and Interior Multiplication.- Chapter 6. Integration.- 21. Orientations.- 22. Manifolds with Boundary.- 23. Integration on Manifolds.- Chapter 7. De Rham Theory.- 24. De Rham Cohomology.- 25. The Long Exact Sequence in Cohomology.- 26. The Mayer –Vietoris Sequence.- 27. Homotopy Invariance.- 28. Computation of de Rham Cohomology.- 29. Proof of Homotopy Invariance.-Appendices.- A. Point-Set Topology.- B. The Inverse Function Theorem on R(N) and Related Results.- C. Existence of a Partition of Unity in General.- D. Linear Algebra.- E. Quaternions and the Symplectic Group.- Solutions to Selected Exercises.- Hints and Solutions to Selected End-of-Section Problems.- List of Symbols.- References.- Index.

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Book Synopsis1 The Spectrum of Linear Operators and Hilbert Spaces.- 2 The Geometry of a Hilbert Space and Its Subspaces.- 3 Exponential Decay of Eigenfunctions.- 4 Operators on Hilbert Spaces.- 5 Self-Adjoint Operators.- 6 Riesz Projections and Isolated Points of the Spectrum.- 7 The Essential Spectrum: Weyl's Criterion.- 8 Self-Adjointness: Part 1. The Kato Inequality.- 9 Compact Operators.- 10 Locally Compact Operators and Their Application to Schrödinger Operators.- 11 Semiclassical Analysis of Schrödinger Operators I: The Harmonic Approximation.- 12 Semiclassical Analysis of Schrödinger Operators II: The Splitting of Eigenvalues.- 13 Self-Adjointness: Part 2. The Kato-Rellich Theorem 131.- 14 Relatively Compact Operators and the Weyl Theorem.- 15 Perturbation Theory: Relatively Bounded Perturbations.- 16 Theory of Quantum Resonances I: The Aguilar-Balslev-Combes-Simon Theorem.- 17 Spectral Deformation Theory.- 18 Spectral Deformation of Schrödinger Operators.- 19 The General Theory of Spectral Stability.- 20 Theory of Quantum Resonances II: The Shape Resonance Model.- 21 Quantum Nontrapping Estimates.- 22 Theory of Quantum Resonances III: Resonance Width.- 23 Other Topics in the Theory of Quantum Resonances.- Appendix 1. Introduction to Banach Spaces.- A1.1 Linear Vector Spaces and Norms.- A1.2 Elementary Topology in Normed Vector Spaces.- A1.3 Banach Spaces.- A1.4 Compactness.- 1. Density results.- 2. The Hölder Inequality.- 3. The Minkowski Inequality.- 4. Lebesgue Dominated Convergence.- Appendix 3. Linear Operators on Banach Spaces.- A3.1 Linear Operators.- A3.2 Continuity and Boundedness of Linear Operators.- A3.3 The Graph of an Operator and Closure.- A3.4 Inverses of Linear Operators.- A3.5 Different Topologies on L(X).- Appendix 4. The Fourier Transform, SobolevSpaces, and Convolutions.- A4.1 Fourier Transform.- A4.2 Sobolev Spaces.- A4.3 Convolutions.- References.Table of Contents1 The Spectrum of Linear Operators and Hilbert Spaces.- 2 The Geometry of a Hilbert Space and Its Subspaces.- 3 Exponential Decay of Eigenfunctions.- 4 Operators on Hilbert Spaces.- 5 Self-Adjoint Operators.- 6 Riesz Projections and Isolated Points of the Spectrum.- 7 The Essential Spectrum: Weyl’s Criterion.- 8 Self-Adjointness: Part 1. The Kato Inequality.- 9 Compact Operators.- 10 Locally Compact Operators and Their Application to Schrödinger Operators.- 11 Semiclassical Analysis of Schrödinger Operators I: The Harmonic Approximation.- 12 Semiclassical Analysis of Schrödinger Operators II: The Splitting of Eigenvalues.- 13 Self-Adjointness: Part 2. The Kato-Rellich Theorem 131.- 14 Relatively Compact Operators and the Weyl Theorem.- 15 Perturbation Theory: Relatively Bounded Perturbations.- 16 Theory of Quantum Resonances I: The Aguilar-Balslev-Combes-Simon Theorem.- 17 Spectral Deformation Theory.- 18 Spectral Deformation of Schrödinger Operators.- 19 The General Theory of Spectral Stability.- 20 Theory of Quantum Resonances II: The Shape Resonance Model.- 21 Quantum Nontrapping Estimates.- 22 Theory of Quantum Resonances III: Resonance Width.- 23 Other Topics in the Theory of Quantum Resonances.- Appendix 1. Introduction to Banach Spaces.- A1.1 Linear Vector Spaces and Norms.- A1.2 Elementary Topology in Normed Vector Spaces.- A1.3 Banach Spaces.- A1.4 Compactness.- 1. Density results.- 2. The Hölder Inequality.- 3. The Minkowski Inequality.- 4. Lebesgue Dominated Convergence.- Appendix 3. Linear Operators on Banach Spaces.- A3.1 Linear Operators.- A3.2 Continuity and Boundedness of Linear Operators.- A3.3 The Graph of an Operator and Closure.- A3.4 Inverses of Linear Operators.- A3.5 Different Topologies on L(X).- Appendix 4. The Fourier Transform, Sobolev Spaces, and Convolutions.- A4.1 Fourier Transform.- A4.2 Sobolev Spaces.- A4.3 Convolutions.- References.

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Book SynopsisFundamental Fixed-Point Principles.- 1 The Banach Fixed-Point Theorem and Iterative Methods.- 2 The Schauder Fixed-Point Theorem and Compactness.- Applications of the Fundamental Fixed-Point Principles.- 3 Ordinary Differential Equations in B-spaces.- 4 Differential Calculus and the Implicit Function Theorem.- 5 Newton's Method.- 6 Continuation with Respect to a Parameter.- 7 Positive Operators.- 8 Analytic Bifurcation Theory.- 9 Fixed Points of Multivalued Maps.- 10 Nonexpansive Operators and Iterative Methods.- 11 Condensing Maps and the BourbakiKneser Fixed-Point Theorem.- The Mapping Degree and the Fixed-Point Index.- 12 The Leray-Schauder Fixed-Point Index.- 13 Applications of the Fixed-Point Index.- 14 The Fixed-Point Index of Differentiable and Analytic Maps.- 15 Topological Bifurcation Theory.- 16 Essential Mappings and the Borsuk Antipodal Theorem.- 17 Asymptotic Fixed-Point Theorems.- References.- Additional References to the Second Printing.- List of Symbols.- List of TheoreTable of ContentsFundamental Fixed-Point Principles.- 1 The Banach Fixed-Point Theorem and Iterative Methods.- §1.1. The Banach Fixed-Point Theorem.- §1.2. Continuous Dependence on a Parameter.- §1.3. The Significance of the Banach Fixed-Point Theorem.- §1.4. Applications to Nonlinear Equations.- §1.5. Accelerated Convergence and Newton’s Method.- § 1.6. The Picard-Lindelof Theorem.- §1.7. The Main Theorem for Iterative Methods for Linear Operator Equations.- §1.8. Applications to Systems of Linear Equations.- §1.9. Applications to Linear Integral Equations.- 2 The Schauder Fixed-Point Theorem and Compactness.- §2.1. Extension Theorem.- §2.2. Retracts.- §2.3. The Brouwer Fixed-Point Theorem.- §2.4. Existence Principle for Systems of Equations.- §2.5. Compact Operators.- §2.6. The Schauder Fixed-Point Theorem.- §2.7. Peano’s Theorem.- §2.8. Integral Equations with Small Parameters.- §2.9. Systems of Integral Equations and Semilinear Differential Equations.- §2.10. A General Strategy.- §2.11. Existence Principle for Systems of Inequalities.- Applications of the Fundamental Fixed-Point Principles.- 3 Ordinary Differential Equations in B-spaces.- §3.1. Integration of Vector Functions of One Real Variable t.- §3.2. Differentiation of Vector Functions of One Real Variable t.- §3.3. Generalized Picard-Lindelöf Theorem.- §3.4. Generalized Peano Theorem.- §3.5. Gronwall’s Lemma.- §3.6. Stability of Solutions and Existence of Periodic Solutions.- §3.7. Stability Theory and Plane Vector Fields, Electrical Circuits, Limit Cycles.- §3.8. Perspectives.- 4 Differential Calculus and the Implicit Function Theorem.- §4.1. Formal Differential Calculus.- §4.2. The Derivatives of Fréchet and Gâteaux.- §4.3. Sum Rule, Chain Rule, and Product Rule.- §4.4. Partial Derivatives.- §4.5. Higher Differentials and Higher Derivatives.- §4.6. Generalized Taylor’s Theorem.- §4.7. The Implicit Function Theorem.- §4.8. Applications of the Implicit Function Theorem.- §4.9. Attracting and Repelling Fixed Points and Stability.- §4.10. Applications to Biological Equilibria.- §4.11. The Continuously Differentiable Dependence of the Solutions of Ordinary Differential Equations in B-spaces on the Initial Values and on the Parameters.- §4.12. The Generalized Frobenius Theorem and Total Differential Equations.- §4.13. Diffeomorphisms and the Local Inverse Mapping Theorem.- §4.14. Proper Maps and the Global Inverse Mapping Theorem.- §4.15. The Suijective Implicit Function Theorem.- §4.16. Nonlinear Systems of Equations, Subimmersions, and the Rank Theorem.- §4.17. A Look at Manifolds.- §4.18. Submersions and a Look at the Sard-Smale Theorem.- §4.19. The Parametrized Sard Theorem and Constructive Fixed-Point Theory.- 5 Newton’s Method.- §5.1. A Theorem on Local Convergence.- §5.2. The Kantorovi? Semi-Local Convergence Theorem.- 6 Continuation with Respect to a Parameter.- §6.1. The Continuation Method for Linear Operators.- §6.2. B-spaces of Hölder Continuous Functions.- §6.3. Applications to Linear Partial Differential Equations.- §6.4. Functional-Analytic Interpretation of the Existence Theorem and its Generalizations.- §6.5. Applications to Semi-linear Differential Equations.- §6.6. The Implicit Function Theorem and the Continuation Method.- §6.7. Ordinary Differential Equations in B-spaces and the Continuation Method.- §6.8. The Leray—Schauder Principle.- §6.9. Applications to Quasi-linear Elliptic Differential Equations.- 7 Positive Operators.- §7.1. Ordered B-spaces.- §7.2. Monotone Increasing Operators.- §7.3. The Abstract Gronwall Lemma and its Applications to Integral Inequalities.- §7.4. Supersolutions, Subsolutions, Iterative Methods, and Stability.- §7.5. Applications.- §7.6. Minorant Methods and Positive Eigensolutions.- §7.7. Applications.- §7.8. The Krein-Rutman Theorem and its Applications.- §7.9. Asymptotic Linear Operators.- §7.10. Main Theorem for Operators of Monotone Type.- §7.11. Application to a Heat Conduction Problem.- §7.12. Existence of Three Solutions.- §7.13. Main Theorem for Abstract Hammerstein Equations in Ordered B-spaces.- §7.14. Eigensolutions of Abstract Hammerstein Equations, Bifurcation, Stability, and the Nonlinear Krein-Rutman Theorem.- §7.15. Applications to Hammerstein Integral Equations.- §7.16. Applications to Semi-linear Elliptic Boundary-Value Problems.- §7.17. Application to Elliptic Equations with Nonlinear Boundary Conditions.- §7.18. Applications to Boundary Initial-Value Problems for Parabolic Differential Equations and Stability.- 8 Analytic Bifurcation Theory.- §8.1. A Necessary Condition for Existence of a Bifurcation Point.- §8.2. Analytic Operators.- §8.3. An Analytic Majorant Method.- §8.4. Fredholm Operators.- §8.5. The Spectrum of Compact Linear Operators (Riesz—Schauder Theory).- §8.6. The Branching Equations of Ljapunov—Schmidt.- §8.7. The Main Theorem on the Generic Bifurcation From Simple Zeros.- §8.8. Applications to Eigenvalue Problems.- §8.9. Applications to Integral Equations.- §8.10. Application to Differential Equations.- §8.11. The Main Theorem on Generic Bifurcation for Multiparametric Operator Equations—The Bunch Theorem.- §8.12. Main Theorem for Regular Semi-linear Equations.- §8.13. Parameter-Induced Oscillation.- §8.14. Self-Induced Oscillations and Limit Cycles.- §8.15. Hopf Bifurcation.- §8.16. The Main Theorem on Generic Bifurcation from Multiple Zeros.- §8.17. Stability of Bifurcation Solutions.- §8.18. Generic Point Bifurcation.- 9 Fixed Points of Multivalued Maps.- §9.1. Generalized Banach Fixed-Point Theorem.- §9.2. Upper and Lower Semi-continuity of Multivalued Maps.- §9.3. Generalized Schauder Fixed-Point Theorem.- §9.4. Variational Inequalities and the Browder Fixed-Point Theorem.- §9.5. An Extremal Principle.- §9.6. The Minimax Theorem and Saddle Points.- §9.7. Applications in Game Theory.- §9.8. Selections and the Marriage Theorem.- §9.9. Michael’s Selection Theorem.- §9.10. Application to the Generalized Peano Theorem for Differential Inclusions.- 10 Nonexpansive Operators and Iterative Methods.- §10.1. Uniformly Convex B-spaces.- §10.2. Demiclosed Operators.- §10.3. The Fixed-Point Theorem of Browder, Göhde, and Kirk.- §10.4. Demicompact Operators.- §10.5. Convergence Principles in B-spaces.- §10.6. Modified Successive Approximations.- §10.7. Application to Periodic Solutions.- 11 Condensing Maps and the Bourbaki—Kneser Fixed-Point Theorem.- §11.1. A Noncompactness Measure.- §11.2. Applications to Generalized Interval Nesting.- §11.3. Condensing Maps.- §11.4. Operators with Closed Range and an Approximation Technique for Constructing Fixed Points.- §11.5. Sadovskii’s Fixed-Point Theorem for Condensing Maps.- §11.6. Fixed-Point Theorems for Perturbed Operators.- §11.7. Application to Differential Equations in B-spaces.- §11.8. The Bourbaki-Kneser Fixed-Point Theorem.- § 11.9. The Fixed-Point Theorems of Amann and Tarski.- §11.10. Application to Interval Arithmetic.- §11.11. Application to Formal Languages.- The Mapping Degree and the Fixed-Point Index.- 12 The Leray-Schauder Fixed-Point Index.- §12.1. Intuitive Background and Basic Concepts.- §12.2. Homotopy.- §12.3. The System of Axioms.- §12.4. An Approximation Theorem.- §12.5. Existence and Uniqueness of the Fixed-Point Index in ?N.- §12.6. Proof of Theorem 12.A..- §12.7. Existence and Uniqueness of the Fixed-Point Index in B-spaces.- §12.8. Product Theorem and Reduction Theorem.- 13 Applications of the Fixed-Point Index.- §13.1. A General Fixed-Point Principle.- §13.2. A General Eigenvalue Principle.- §13.3. Existence of Multiple Solutions.- §13.4. A Continuum of Fixed Points.- §13.5. Applications to Differential Equations.- §13.6. Properties of the Mapping Degree.- §13.7. The Leray Product Theorem and Homeomorphisms.- §13.8. The Jordan-Brouwer Separation Theorem and Brouwer’s Invariance of Dimension Theorem.- §13.9. A Brief Glance at the History of Mathematics.- §13.10. Topology and Intuition.- §13.11. Generalization of the Mapping Degree.- 14 The Fixed-Point Index of Differentiable and Analytic Maps.- §14.1. The Fixed-Point Index of Classical Analytic Functions.- §14.2. The Leray—Schauder Index Theorem.- §14.3. The Fixed-Point Index of Analytic Mappings on Complex B-spaces.- §14.4. The Schauder Fixed-Point Theorem with Uniqueness.- §14.5. Solution of Analytic Operator Equations.- §14.6. The Global Continuation Principle of Leray—Schauder.- §14.7. Unbounded Solution Components.- §14.8. Applications to Systems of Equations.- §14.9. Applications to Integral Equations.- §14.10. Applications to Boundary-Value Problems.- §14.11. Applications to Integral Power Series.- 15 Topological Bifurcation Theory.- §15.1. The Index Jump Principle.- §15.2. Applications to Systems of Equations.- §15.3. Duality Between the Index Jump Principle and the Leray—Schauder Continuation Principle.- §15.4. The Geometric Heart of the Continuation Method.- §15.5. Stability Change and Bifurcation.- §15.6. Local Bifurcation.- §15.7. Global Bifurcation.- §15.8. Application to Systems of Equations.- §15.9. Application to Integral Equations.- §15.10. Application to Differential Equations.- §15.11. Application to Bifurcation at Infinity.- §15.12. Proof of the Main Theorem.- §15.13. Preventing Secondary Bifurcation.- 16 Essential Mappings and the Borsuk Antipodal Theorem.- §16.1. Intuitive Introduction.- §16.2. Essential Mappings and their Homotopy Invariance.- §16.3. The Antipodal Theorem.- §16.4. The Invariance of Domain Theorem and Global Homeomorphisms.- §16.5. The Borsuk—Ulam Theorem and its Applications.- §16.6. The Mapping Degree and Essential Maps.- §16.7. The Hopf Theorem.- §16.8. A Glance at Homotopy Theory.- 17 Asymptotic Fixed-Point Theorems.- §17.1. The Generalized Banach Fixed-Point Theorem.- §17.2. The Fixed-Point Index of Iterated Mappings.- §17.3. The Generalized Schauder Fixed-Point Theorem.- §17.4. Application to Dissipati ve Dynamical Systems.- §17.5. Perspectives.- References.- Additional References to the Second Printing.- List of Symbols.- List of Theorems.- List of the Most Important Definitions.- Schematic Overviews.- General References to the Literature.- List of Important Principles.- of the Other Parts.

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Book SynopsisIts discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.This volume is the fourth of five volumes that the authors plan to write on Ramanujan’s lost notebook.​ In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series.Table of ContentsPreface.- ​​​1 Introduction.- 2 Double Series of Bessel Functions and the Circle and Divisor Problems.- 3 Koshliakov's Formula and Guinand's Formula.- 4 Theorems Featuring the Gamma Function.- 5 Hypergeometric Series.- 6 Euler's Constant.- 7 Problems in Diophantine Approximation.- 8 Number Theory.- 9 Divisor Sums.- 10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions.- 11 Two Partial Unpublished Manuscripts on Sums Involving Primes.- 12 Infinite Series.- 13 A Partial Manuscript on Fourier and Laplace Transforms.- 14 Integral Analogues of Theta Functions adn Gauss Sums.- 15 Functional Equations for Products of Mellin Transforms.- 16 Infinite Products.- 17 A Preliminary Version of Ramanujan's Paper, On the Integral ∫_0^x tan^(-1)t)/t dt.- 18 A Partial Manuscript Connected with Ramanujan's Paper, Some Definite Integrals.- 19 Miscellaneous Results in Analysis.- 20 Elementary Results.- 21 A Strange, Enigmatic Partial Manuscript.- Location Guide.- Provenance.- References.- Index.

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Book SynopsisPreface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.Trade ReviewFrom the reviews of the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."—MATHEMATICAL REVIEWS"This book occupies a niche between a calculus course and a full-blown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails." —Allen Stenger (The Mathematical Association of America, June, 2008)Table of ContentsPreface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.

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Book SynopsisFeaturing over 180 exercises, this text for a one-semester course in Lebesgue's theory takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students.Trade ReviewFrom the reviews:“It is accessible to upper-undergraduate and lower graduate level students, and the only prerequisite is a course in elementary real analysis. … The book proposes 187 exercises where almost always the reader is proposed to prove a statement. … this book is a very helpful tool to get into Lebesgue’s theory in an easy manner.” (Daniel Cárdenas-Morales, zbMATH, Vol. 1277, 2014)“This is a brief … but enjoyable book on Lebesgue measure and Lebesgue integration at the advanced undergraduate level. … The presentation is clear, and detailed proofs of all results are given. … The book is certainly well suited for a one-semester undergraduate course in Lebesgue measure and Lebesgue integration. In addition, the long list of exercises provides the instructor with a useful collection of homework problems. Alternatively, the book could be used for self-study by the serious undergraduate student.” (Lars Olsen, Mathematical Reviews, December, 2013)Table of Contents1 Preliminaries.- 2 Lebesgue Measure.- 3 ​Lebesgue Integration.- 4 Differentiation and Integration.- A Measure and Integral over Unbounded Sets.- Index.

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Book SynopsisBasic Objects and Notation.- Linear Algebra Essentials.- Advanced Calculus.- Differential Forms and Tensors.- Riemannian Geometry.- Contact Geometry.- Symplectic Geometry.- References.- Index.Trade ReviewFrom the book reviews:“This books presents an alternative route, aiming to provide the student with an introduction not only to Riemannian geometry, but also to contact and symplectic geometry. … the book is leavened with an excellent collection of illustrative examples, and a wealth of exercises on which students can hone their skills. Each chapter also includes a short guide to further reading on the topic with a helpful brief commentary on the suggestions.” (Robert J. Low, Mathematical Reviews, May, 2014)“This book is a distinctive and ambitious effort to bring modern notions of differential geometry to undergraduates. … Mclnerney’s writing is well constructed and very clear … . Summing Up: Recommended. Upper-division undergraduates and graduate students.” (S. J. Colley, Choice, Vol. 51 (8), April, 2014)“The author does make a considerable effort to keep things as accessible as possible, with fairly detailed explanations, extensive motivational discussions and homework problems … . this book provides a different way of looking at the subject of differential geometry, one that is more modern and sophisticated than is provided by many of the standard undergraduate texts and which will certainly do a good job of preparing the student for additional work in this area down the road.” (Mark Hunacek, MAA Reviews, January, 2014)“This text provides an early and broad view of geometry to mathematical students … . Altogether, this book is easy to read because there are plenty of figures, examples and exercises which make it intuitive and perfect for undergraduate students.” (Teresa Arias-Marco, zbMATH, Vol. 1283, 2014)Table of ContentsBasic Objects and Notation.- Linear Algebra Essentials.- Advanced Calculus.- Differential Forms and Tensors.- Riemannian Geometry.- Contact Geometry.- Symplectic Geometry.- References.- Index.

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Book Synopsis1 Euclidean spaces.- 1.1 The real number system.- 1.2 Euclidean En.- 1.3 Elementary geometry of En.- 1.4 Basic topological notions in En.- *1.5 Convex sets.- 2 Elementary topology of En.- 2.1 Functions.- 2.2 Limits and continuity of transformations.- 2.3 Sequences in En.- 2.4 Bolzano-Weierstrass theorem.- 2.5 Relative neighborhoods, continuous transformations.- 2.6 Topological spaces.- 2.7 Connectedness.- 2.8 Compactness.- 2.9 Metric spaces.- 2.10 Spaces of continuous functions.- *2.11 Noneuclidean norms on En.- 3 Differentiation of real-valued functions.- 3.1 Directional and partial derivatives.- 3.2 Linear functions.- **3.3 Difierentiable functions.- 3.4 Functions of class C(q).- 3.5 Relative extrema.- *3.6 Convex and concave functions.- 4 Vector-valued functions of several variables.- 4.1 Linear transformations.- 4.2 Affine transformations.- 4.3 Differentiable transformations.- 4.4 Composition.- 4.5 The inverse function theorem.- 4.6 The implicit function theorem.- 4.7 Manifolds.- 4Table of Contents1 Euclidean spaces.- 1.1 The real number system.- 1.2 Euclidean En.- 1.3 Elementary geometry of En.- 1.4 Basic topological notions in En.- *1.5 Convex sets.- 2 Elementary topology of En.- 2.1 Functions.- 2.2 Limits and continuity of transformations.- 2.3 Sequences in En.- 2.4 Bolzano-Weierstrass theorem.- 2.5 Relative neighborhoods, continuous transformations.- 2.6 Topological spaces.- 2.7 Connectedness.- 2.8 Compactness.- 2.9 Metric spaces.- 2.10 Spaces of continuous functions.- *2.11 Noneuclidean norms on En.- 3 Differentiation of real-valued functions.- 3.1 Directional and partial derivatives.- 3.2 Linear functions.- **3.3 Difierentiable functions.- 3.4 Functions of class C(q).- 3.5 Relative extrema.- *3.6 Convex and concave functions.- 4 Vector-valued functions of several variables.- 4.1 Linear transformations.- 4.2 Affine transformations.- 4.3 Differentiable transformations.- 4.4 Composition.- 4.5 The inverse function theorem.- 4.6 The implicit function theorem.- 4.7 Manifolds.- 4.8 The multiplier rule.- 5 Integration.- 5.1 Intervals.- 5.2 Measure.- 5.3 Integrals over En.- 5.4 Integrals over bounded sets.- 5.5 Iterated integrals.- 5.6 Integrals of continuous functions.- 5.7 Change of measure under affine transformations.- 5.8 Transformation of integrals.- 5.9 Coordinate systems in En.- 5.10 Measurable sets and functions; further properties.- 5.11 Integrals: general definition, convergence theorems.- 5.12 Differentiation under the integral sign.- 5.13 Lp-spaces.- 6 Curves and line integrals.- 6.1 Derivatives.- 6.2 Curves in En.- 6.3 Differential 1-forms.- 6.4 Line integrals.- *6.5 Gradient method.- *6.6 Integrating factors; thermal systems.- 7 Exterior algebra and differential calculus.- 7.1 Covectors and differential forms of degree 2.- 7.2 Alternating multilinear functions.- 7.3 Multicovectors.- 7.4 Differential forms.- 7.5 Multivectors.- 7.6 Induced linear transformations.- 7.7 Transformation law for differential forms.- 7.8 The adjoint and codifferential.- *7.9 Special results for n = 3.- *7.10 Integrating factors (continued).- 8 Integration on manifolds.- 8.1 Regular transformations.- 8.2 Coordinate systems on manifolds.- 8.3 Measure and integration on manifolds.- 8.4 The divergence theorem.- *8.5 Fluid flow.- 8.6 Orientations.- 8.7 Integrals of r-forms.- 8.8 Stokes’s formula.- 8.9 Regular transformations on submanifolds.- 8.10 Closed and exact differential forms.- 8.11 Motion of a particle.- 8.12 Motion of several particles.- Axioms for a vector space.- Mean value theorem; Taylor’s theorem.- Review of Riemann integration.- Monotone functions.- References.- Answers to problems.

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Book SynopsisTrade ReviewMany journal articles have been devoted to various aspects of mathematics in Lvov or to biographies of Lvov mathematicians, but Duda's book is the first comprehensive exposition...In summary, I conclude that Duda's book is a must for everyone interested in the history of functional analysis or in the history of mathematics in Poland." - Lech Maligranda, Mathematical Intelligencer"This eagerly awaited translation of the book Pearls describes a world-class Polish school of mathematics at Lvov (now the Ukrainian Lviv) that thrived during the interwar period and has left an enduring legacy that remains part of the folklore today. Published in English translation after a somewhat protracted period of negotiation, this important work fills a niche in the history of science and should become a standard source of mathematics in Poland, especially the genesis of functional analysis during its Golden Age, 1918-1939. Moreover, the translator, Oxford's Daniel Davies, explains material that is unlikely to be familiar to readers outside Poland." - Isis, A Journal of the History of Science Society"Many journal articles have been devoted to various aspects of mathematics in Lwów or to biographies of Lwów mathematicians, but Duda's book is the first comprehensive exposition. It is a must-read for everyone interested in the history of functional analysis or of mathematics in Poland, where the original Polish edition from 2007 ... has been highly successful. There is good reason to assume that the English version will be likewise successful." - Dirk Werner, ZMATH"This book gives the history of Lvov as a mathematical center, from pre-WWI to Soviet and Ukrainian times, looking especially at the interwar golden age and the special favorable environment for mathematical scholarship. The author also describes the ways in which the Soviets and Germans destroyed this rich environment. The book includes a list, with biographical sketches, of mathematicians associated with Lvov, and a Lvov biography. It was a special time and place for mathematics, disrupted by war and politics and oppression and murder, and one wonders what more could have been achieved in a peaceful environment." - CHOICE Reviews"The book under review is well and carefully written. The translation from Polish into English is polished and lively... I highly recommend the book for all university libraries, and I recommend it to those interested in the history of mathematics. The general mathematical reader will find it an entertaining and informative story about mathematicians and a truly extraordinary mathematical community." - Henry Heatherly, MAA ReviewsTable of Contents Background The University and the Polytechnic in Lvov Polish mathematics at the turn of the twentieth century Sierpiski's stay at the University of Lvov (1908-1914) The University in Warsaw and Janiszewski's program (1915-1920) World mathematics (active fields in Poland) around 1920 The golden age: Individuals and community The mathematical community in Lvov after World War I Mathematical studies and students Journals, monographs, and congresses The popularization of mathematics Social life (the Scottish Café, the Scottish Book) The Polish Mathematical Society Collaboration with other centers In the eyes of others The golden age: Achievements Stefan Banach's doctoral thesis and priority claims Probability theory Measure theory Game theory: A revelation without follow-up Operator theory in the 1920s Methodological audacity Banach's monograph: Polishing the pearls Operator theory in the 1930s: The dazzle of pearls New perspectives for which time did not allow On the periphery Oblivion Ukrainization the Soviet way (1939-1941) The German occupation (1941-1944) The expulsion of Poles (1945-1946) Historical significance Chronological overview Chronology of events as perceived elsewhere Influence on mathematics of the Lvov school A tentative summary Mathematics in Lvov after 1945 List of Lvov mathematicians Mathematicians associated with Lvov Bibliographies List of illustrations Index of names

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Book SynopsisTrade ReviewThis book introduces the reader to some basic concepts of hyperbolic theory of dynamical systems with emphasis on structural stability. It is well written, the proofs are presented with great attention to details, and every chapter ends with a good collection of exercises. It is suitable for a semester-long course on the basics of dynamical systems"". - Yakov Pesin, Penn State University""Lan Wen's book is a thorough introduction to the ``classical'' theory of (uniformly) hyperbolic dynamics, updated in light of progress since Smale's seminal 1967 Bulletin article. The exposition is aimed at newcomers to the field and is clearly informed by the author's extensive experience teaching this material. A thorough discussion of some canonical examples and basic technical results culminates in the proof of the Omega-stability theorem and a discussion of structural stability. A fine basic text for an introductory dynamical systems course at the graduate level"". - Zbigniew Nitecki, Tufts University"...[T]he introductory parts of the book are quite suitable for graduate students, and the more advanced sections can be useful even for experts in the field." - S. Yu. Pilyugin, Mathematical ReviewsTable of Contents Basics of dynamical systems Hyperbolic fixed points Horseshoes, toral automorphisms, and solenoids Hyperbolic sets Axiom A, no-cycle condition, and Ω-stability Quasi-hyperbolicity and linear transversality Bibliography Index

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Book SynopsisConsiders models that are described by systems of partial differential equations, focusing on modelling rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing.Table of Contents Introductory biology Introduction to modeling Models of population dynamics Cancer and the immune system Parameters estimation Mathematical analysis inspired by cancer models Mathematical model of artherosclerosis: Risk of high cholesterol Mathematical analysis inspired by the atherosclerosis model Mathematical models of chronic wounds Mathematical analysis inspired by the chronic wound model Introduction to PDEs Bibliography Index

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Book SynopsisThis volume contains the proceedings of the “Arizona School of Analysis and Mathematical Physics”, held in March 2018, at the University of Arizona. The articles in this volume reflect recent progress and innovative techniques developed within mathematical physics.Table of Contents H. Abdul-Rahman, M. Lemm, A. Lucia, B. Nachtergaele, and A. Young, A class of two-dimensional AKLT models with a gap S. Bachmann, A. Bols, W. De Roeck, and M. Fraas, Note on linear response for interacting Hall insulators S. Bachmann, W. De Roeck, and M. Fraas, The adiabatic theoerm in a quantum many-body setting R. DeMuse and M. Yin, Perspectives on exponential random graphs C. Fischbacher, A Schrodinger operator approach to higher spin XXZ systems on general graphs Y. Latushkin and S. Sukhtaiev, An index theorem for Schrodinger operators on metric graphs M. Lemm, Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems A. Saenz, The KPZ universality class and related topics G. Stolz, Aspects of the mathematical theory of disordered quantum spin chains.

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Book SynopsisPresents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients.Table of Contents Introduction Differential equations in Hilbert space Linear parabolic systems: Basic theory Elliptic systems: Higher order regularity Parabolic systems: Higher order regularity Applications to quasilinear systems Selected topics in analysis Bibliography Index

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Book SynopsisProvides a concise and rigorous introduction to the theory of functions of a complex variable. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. The book is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation.Trade ReviewFrom a review of the previous edition: ""The exposition is clear, rigorous, and friendly."" —Zentralblatt MATHTable of Contents Complex numbers Complex differentiation Linear-fractional transformations Elementary functions Power series Complex integration Core versions of Cauchy's theorem, and consequences Laurent series and isolated singularities Cauchy's theorem Further development of basic complex function theory Appendix 1: Sufficient condition for differentiability Appendix 2: Two instances of the chain rule Appendix 3: Groups, and linear-fractional transformations Appendix 4: Differentiation under the integral sign References Index

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Book SynopsisPresents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes.Table of Contents Review of elementary number theory Arithmetic functions I The floor function Summation formulas Arithmetic functions II Elementary results on the distribution of primes Characters and Dirichlet's theorem The Riemann zeta function Prime number theorem and some extensions Introduction to other topics Hints for selected exercises Bibliography Subject index Name Index

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Book SynopsisPresents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events).Trade ReviewThis book strikes a nice balance between mathematical formalism and intuitive arguments; a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation."" —Peter Rabinovitch, MAA Reviews Table of Contents Fundamentals: Random variables Limit theorems Markov chains Monte Carlo methods Stochastic processes Wiener process Stochastic differential equations Fokker-Planck equation Advanced topics: Path integral Random fields Introduction to statistical mechanics Rare events Introduction to chemical reaction kinetics Appendix Bibliography Index

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Book SynopsisCovers recent advances in the study of formal and analytic solutions of different kinds of equations such as ordinary differential equations, difference equations, $q$-difference equations, partial differential equations, and moment differential equations.Table of Contents A. D. Bruno, Normal forms of a polynomial ODE A. B. Batkhin, Computation of homological equations for Hamiltonian normal form E. Ciechanowicz, A note on value distribution of solutions of certain second order ODEs G. Filipuk, A. Ligeza, and A. Stokes, Relations between different Hamiltonian forms of the third Painleve equation T. Aoki and S. Uchida, Degeneration structures of the Voros coefficients of the generalized hypergeometric differential equations with a large parameter T. Oshima, Riemann-Liouville transform and linear differential equations on the Riemann sphere M. Cafasso and S. Tarricone, The Riemann-Hilbert approach to the generating function of the higher order Airy point processes Y. Chen, G. Filipuk, and M. N. R. Rebocho, A system of nonlinear difference equations for recurrence relation coefficients of a modified Jacobi weight S. Sasaki, S. Takagi, and K. Takemura, $q$-Heun equation and initial-value space of $q$-Painleve equation H. Ogawara, Differential transcendence of solutions for $q$-difference equation of Ramanujan function C. Zhang, On the positive powers of $q$-analogs of Euler series M. Suwinska, Summability of formal solutions for a family of linear moment integro-differential equations H. Tahara, Uniqueness of the solution of some nonlinear singular partial differential equations of the second order M. Yoshino, Solution with movable singular points of some Hamiltonian system A. Lastra, S. Michalik, and M. Suwinska, Some notes on moment partial differential equations. Application to fractional functional equations.

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Book Synopsis

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Book SynopsisThe subjects explored in the book are dimensional analysis and scaling, dynamical systems, perturbation methods, and calculus of variations. These are immense subjects of wide applicability and a fertile ground for critical thinking and quantitative reasoning, in which every student of mathematics should have some experience.Table of Contents Dimensional analysis Scaling One-dimensional dynamics Two-dimensional dynamics Perturbation methods Calculus of variations Bibliography Index

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Book SynopsisFoundations of Analysis covers the basics of real analysis for a one- or two-semester course. In a straightforward and concise way, it helps students understand the key ideas and apply the theorems. The bookâs accessible approach will appeal to a wide range of students and instructors.Each section begins with a boxed introduction that familiarizes students with the upcoming topics and sets the stage for the work to be done. Each section ends with several questions that ask students to review what they have just learned. The text is also scattered with notes pointing out places where different pieces of terminology seem to conflict with each other or where different ideas appear not to fit together properly. In addition, many remarks throughout help put the material in perspective.As with any real analysis text, exercises are powerful and effective learning tools. This book is no exception. Each chapter generally contains at least 50 exercises that builTrade Review"… there is a good set of exercises in each section … . If real analysis is to be dealt with in a one-semester course, this book appears to provide a reasonable text for the course."—Mathematical Reviews, April 2015Table of ContentsNumber Systems. Sequences. Series of Numbers. Basic Topology. Limits and Continuity of Functions. Differentiation of Functions. The Integral. Sequences and Series of Functions. Elementary Transcendental Functions. Appendices. Table of Notation. Glossary. Bibliography. Index.

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Book SynopsisBlow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book first studies the particular self-similar singularity solutions (patterns) of the equations. This approach allows four different classes of nonlinear PDEs to be treated simultaneously to establish their striking common features. The book describes many properties of the equations and examines traditional questions of existence/nonexistence, uniqueness/nonuniqueness, global asymptotics, regularizations, shock-wave theory, and various blow-up singularities.Preparing readers for more advanced mathematical PDE analysis, the book demonstrates that quasilinear degenerate higher-order PDEs, even exoticTrade Review"This volume gives a collection of results on self-similar singular solutions for nonlinear partial differential equations (PDEs), with special emphasis on ‘exotic’ equations of higher order …"—Zentralblatt MATH 1320Table of ContentsIntroduction. Complicated Self-Similar Blow-Up, Compacton, and Standing Wave Patterns for Four Nonlinear PDEs: A Unified Variational Approach to Elliptic Equations. Classification of Global Sign-Changing Solutions of Semilinear Heat Equations in the Subcritical Fujita Range: Second- and Higher-Order Diffusion. Global and Blow-Up Solutions for Kuramoto–Sivashinsky, Navier–Stokes, and Burnett Equations. Regional, Single-Point, and Global Blow-Up for a Fourth-Order Porous Medium-Type Equation with Source. Semilinear Fourth-Order Hyperbolic Equation: Two Types of Blow-Up Patterns. Quasilinear Fourth-Order Hyperbolic Boussinesq Equation: Shock, Rarefaction, and Fundamental Solutions. Blow-Up and Global Solutions for Korteweg–de Vries-Type Equations. Higher-Order Nonlinear Dispersion PDEs: Shock, Rarefaction, and Blow-Up Waves. Higher-Order Schrödinger Equations: From "Blow-Up" Zero Structures to Quasilinear Operators. References.

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Book SynopsisGet creative and optimize your SAP SuccessFactors Recruiting implementation with this guide, which examines a variety of integration and automation opportunities throughout the recruiting process outside of the standard integrations. Innovative SAP SuccessFactors Recruiting walks you through the end-to-end recruiting process and highlights opportunities to create interfaces and automation at each stage using a variety of methods and tools. After a brief overview of the market demands driving growth in this area and an introduction to OData, Anand Athanur, Mark Ingram and Michael A. Wellens detail each step in the recruiting process, starting with automating and integrating requisition creation using APIs and middleware. They then explore ways of enhancing candidate attraction and experience for the initial application process. After that, they jump into automation for overall candidate selection and processing, including automation using Robotic Process Automation, Integration centerTable of ContentsChapter 1: OData Overview Chapter Goal: Introduce the reader to basic OData concepts that are needed to understand the remainder of the book. No of pages: 20 Sub - Topics 1. What is OData 2. How to execute simple Odata calls 3. Example: Reading a requisition using Postman 4. Setting up required users and permissions 5. Executing 6. End result 7. Closing remarks Chapter 2: Automatic Requisition creation Chapter Goal: Walk the reader through the tools and steps needed to automatically create requisitions in SAP SuccessFactors No of pages: 25 Sub - Topics: 1. Introduction / Business Scenario 2. Architectural Overview 3. Review of Relevant Odata API objects and functions 4. End User Experience 5. Closing Remarks Chapter 3: Preparing Requisitions Automatically Using Middleware Chapter Goal: Introduce to the reader another tool available for integration (middleware) while taking on the next logical step in the recruiting process (preparing the requisition for posting) No of pages: 40 Sub - Topics: 1. Introduction 2. What is middleware / when would it be used? (e.g. when 2 systems house data, but don’t have the capability to actively make requests to one another, also data mapping scenarios, also mention CPI) 3. Case Study: Automatic question creation on a requisition 4. Conclusions Chapter 4: Expanding Posting Capabilities to expand Candidate Attraction Chapter Goal: Continuing on to the next step in the recruiting process, explore how SAP SuccessFactors makes posting information available on the internet and describe how to use that information to expand its posting capabilities using an example case study. No of pages: 25 Sub - Topics: 1. Introduction / What is candidate attraction 2. Strategies for increasing candidate attraction vs. simple out-of-box funcitonality 3. How SAP SuccessFactors exposes posting information 4. Case Study: Re-posting using Wodpress 5. Conclusions Chapter 5: Enhancing Candidate Engagement Chapter Goal: After candidates are attracted, we need to keep them engaged! This chapter explores a creative ways to expand SAP SuccessFactors candidate engagement capabilities through a case study. No of pages: 25 Sub - Topics: 1. Introduction / What is Candidate Engagement? 2. Strategies and tools for Increasing Candidate Engagement 3. Review of Relevant OData API objects and functions 4. Case Study: Chatbots 5. Conclusions Chapter 6: Using Robotic Process Automation to Streamline Candidate Selection Chapter Goal: In this chapter we see how bots can help automate tasks for recruiters to streamline the recruiting selection process. No of pages: 20 Sub - Topics: 1. Introduction 2. Pros and Cons of RPA technology 3. Review of Relevant OData API objects and functions 4. Case Study: Chatbots 5. Conclusions Chapter 7: Candidate Selection Automation using Integration Center Chapter Goal: In this chapter we see the integration center can help automate tasks for recruiters to streamline the recruiting selection process. No of pages: 20 Sub - Topics: 1. Introduction 2. Using the integration center 3. Review of Relevant OData API objects and functions 4. Case Study: Advancing candidates based on attributes 5. Conclusions Chapter 8: Assessment Integration Framework Chapter Goal: In this chapter we explore the functionality of SAP SuccessFactors that allows 3rd party assessment vendors to integrate directly into the SAP SuccessFactors candidate selection process. No of pages: 20 Sub - Topics: 1. Introduction 2. What is the assessment integration framework? 3. How does the assessment integration framework work? 4. Case Study 5. Conclusions Chapter 9: Custom OData Integrations Chapter Goal: Here we explore how Odata can also be used to help with the candidate selection process by allowing vendors (such as assessment vendors or others) another method to access and update SAP SuccessFactors recruiting. No of pages: 25 Sub - Topics: 1. Introduction 2. Odata API Review 3. Sample business Scenarios using available Odata API objects 4. Case Study: Assessing Candidates using AI 5. Conclusions Chapter 10: Background Check Integration Framework Chapter Goal: In this chapter we explore the functionality of SAP SuccessFactors that allows 3rd party background vendors to integrate directly into the SAP SuccessFactors candidate selection process. No of pages: 30 Sub - Topics: 1. Introduction 2. What is the background integration framework? 3. How does the background integration framework work? 4. Case Study 5. Conclusions Chapter 11: Candidate Offer Automation Using Business Rules Chapter Goal: This chapter shows the reader how the offer process can be streamlined using business rules. No of pages: 20 Sub - Topics: 1. Introduction 2. How to configure business rules 3. Case Study: Calculating a recommended offer amount 4. Conclusions Chapter 12: Using Intelligent Services to Ease the Onboarding Process Chapter Goal: In this chapter we No of pages: 30 Sub - Topics: 1. Introduction 2. What are Intelligent services 3. Example use case scenarios 4. Case Study: Pushing Candidate Data to ServiceNow using Intelligent Services 5. Conclusions Chapter 13: Hiring Integration with Non-SAP Systems Chapter Goal:This chapter shows the reader how the SAP SuccessFactors Recruiting OData APIs can be used to integrate with 3rd party systems to complete the hiring process. No of pages: 25 Sub - Topics: 1. Introduction 2. Example systems integrations 3. Review of relevant OData API objects and functions 4. Case Study 5. Conclusions Chapter 14: Conclusion Chapter Goal: In this chapter we review the concepts we have covered across the book. The reader should leave understanding the integration and automation opportunities at each step of the recruiting process and the variety of methods and tools available for making these possible. No of pages: 5 Sub - Topics: 1. Introduction 2. Review of concepts across chapters 3. Realizing business value 4. More Concepts / ideas for integrations and automations not covered 5. Final Conclusions

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Book SynopsisIntended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups.Trade ReviewFrom the book reviews:“This textbook provides a comprehensive and consistent introduction to measure and integration theory. … The book can be recommended to anyone having basic knowledge of calculus and point-set topology. It is very self-contained, and can thus serve as an excellent reference book as well.” (Ville Suomala, Mathematical Reviews, July, 2014)“In this second edition, Cohn has updated his excellent introduction to measure theory … and has made this great textbook even better. Those readers unfamiliar with Cohn’s style will discover that his writing is lucid. … this is a wonderful text to learn measure theory from and I strongly recommend it.” (Tushar Das, MAA Reviews, June, 2014)Table of Contents1. Measures.- Algebras and sigma-algebras.- Measures.- Outer measures.- Lebesgue measure.- Completeness and regularity.- Dynkin classes.- 2. Functions and Integrals.- Measurable functions.- Properties that hold almost everywhere.- The integral.- Limit theorems.- The Riemann integral.- Measurable functions again, complex-valued functions, and image measures.- 3. Convergence.- Modes of Convergence.- Normed spaces.- Definition of L^p and L^p.- Properties of L^p and L-p.- Dual spaces.- 4. Signed and Complex Measures.- Signed and complex measures.- Absolute continuity.- Singularity.- Functions of bounded variation.- The duals of the L^p spaces.- 5. Product Measures.- Constructions.- Fubini’s theorem.- Applications.- 6. Differentiation.- Change of variable in R^d.- Differentiation of measures.- Differentiation of functions.- 7. Measures on Locally Compact Spaces.- Locally compact spaces.- The Riesz representation theorem.- Signed and complex measures; duality.- Additional properties of regular measures.- The µ^*-measurable sets and the dual of L^1.- Products of locally compact spaces.- 8. Polish Spaces and Analytic Sets.- Polish spaces.- Analytic sets.- The separation theorem and its consequences.- The measurability of analytic sets.- Cross sections.- Standard, analytic, Lusin, and Souslin spaces.- 9. Haar Measure.- Topological groups.- The existence and uniqueness of Haar measure.- The algebras L^1 (G) and M (G).- Appendices.- A. Notation and set theory.- B. Algebra.- C. Calculus and topology in R^d.- D. Topological spaces and metric spaces.- E. The Bochner integral.- F Liftings.- G The Banach-Tarski paradox.- H The Henstock-Kurzweil and McShane integralsBibliography.- Index of notation.- Index.

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Book SynopsisPreface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.Trade ReviewFrom the reviews of the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."—MATHEMATICAL REVIEWS"This book occupies a niche between a calculus course and a full-blown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails." —Allen Stenger (The Mathematical Association of America, June, 2008)Table of ContentsPreface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.

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Book SynopsisImplicit Functions and Solution MappingsTrade Review“The book represents the state of the art of the modern theory of inverse and implicit functions and provides an important source for studies of numerical methods and applications in this area. It can be warmly recommended to all specialists and advanced students working in optimization, analysis, numerical mathematics, and other mathematical fields, as well as to all those who apply variational analysis in engineering, physics, operations research, economics, finance, and more.” (Diethard Klatte, SIAM Review, Vol. 57 (2), June, 2015)“The book commences with a helpful context-setting preface followed by six chapters. Each chapter starts with a useful preamble and concludes with a careful and instructive commentary, while a good set of references, a notation guide and a somewhat brief index complete this study. … I unreservedly recommended this book to all practitioners and graduate students interested in modern optimization theory or control theory or to those just engaged by beautiful analysis cleanly described.” (Jonathan Michael Browein, IEEE Control Systems Magazine, February, 2012).“This book is devoted to the theory of inverse and implicit functions and some of its modifications for solution mappings in variational problems. … The book is targeted to a broad audience of researchers, teachers and graduate students. It can be used as well as a textbook as a reference book on the topic. Undoubtedly, it will be used by mathematicians dealing with functional and numerical analysis, optimization, adjacent branches and also by specialists in mechanics, physics, engineering, economics and so on.” (Peter Zabreiko, Zentralblatt MATH, Vol. 1178, 2010).“The present monograph will be a most welcome and valuable addition. … This book will save much time and effort, both for those doing research in variational analysis and for students learning the field. This important contribution fills a gap in the existing literature.” (Stephen M. Robinson, Mathematical Reviews, Issue 2010).Table of ContentsIntroduction and equation-solving background.- Solution mappings for variational problems.- Set-valued analysis of solution mappings.- Regularity properties through generalized derivatives.- Metric regularity in infinite dimensions.- Applications in numerical variational analysis.

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