Differential calculus and equations Books
Springer Clifford Analysis and Its Applications
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Springer Semigroups in Geometrical Function Theory
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Birkhauser Boston Mathematical Analysis Functions of One Variable v 1
Book SynopsisFor more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person.Trade ReviewFrom the reviews: "Many teachers and students could benefit from thinking about its unique perspectives." ---SIAM Review "Giaquinta . . . and Modica . . . present the differential and integral calculus for real functions of a single real variable from a sophisticated point of view. Their book is far better suited as a source of unique perspectives on the logical development of calculus ideas and their physical applications . . . [so that] it will better serve the experienced calculus instructor seeking new approaches to familiar material, or the student who has already mastered the basic ideas and techniques of calculus but wishes to see it all again, 'done right,' . . . Highly recommended." ---CHOICE "This self-contained book introduces the main ideas and fundamental methods of mathematical analysis without loosing sight of the context in which it was developed and the role played in science, particularly in physics…. Each chapter has a short summary where the most important facts discussed are collected. There is also a large number of exercises inserted at various points into the text…. The book is meant principally for students in mathematics, physics, engineering, and computer science, but it can be used at technological and scientific faculties by anyone who wants to approach these topics." ---ZENTRALBLATT MATH "The presentation of the theory is clearly arranged, all theorems have rigorous proofs and every chapter closes with a summing up of the results and exericeses with different requirements. The aim of the authors was very successful[ly] realized, and this book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties." ---Journal of Analysis and its Applications "This is the first of several volumes on analysis by these authors. … It is essentially a calculus book at the advanced undergraduate level, or an analysis textbook for someone who has never seen calculus before. … I like this book … ." (Warren Johnson, The Mathematical Association of America, October, 2009)Table of ContentsNumbers, Functions and their Graphs * Limits and Continuity * The Fundamental Ideas of the Differential and Integral Calculus * The Calculus of Derivatives and Integrals * Further Developments in Calculus * Towards Differential Equations and Minimum Principles * Bibliographical Notes * Index
£44.99
Birkhauser Boston Mathematical Analysis Approximation and Discrete Processes
Book Synopsis1. Real Numbers and Natural Numbers.- 1.1 Introduction.- 1.2 The Axiomatic Approach to Real Numbers.- 1.3 Natural Numbers.- 1.4 Summing Up.- 1.5 Exercises.- 2. Sequences of Real Numbers.- 2.1 Sequences.- 2.2 Equivalent Formulations of the Continuity Axiom.- 2.3 Limits of Sequences and Continuity.- 2.4 Some Special Sequences.- 2.5 An Alternative Definition of Exponentials and Logarithms.- 2.6 Summing Up.- 2.7 Exercises.- 3. Integer Numbers: Congruences, Counting and Infinity.- 3.1 Congruences.- 3.2 Combinatorics.- 3.3 Infinity.- 3.4 Summing Up.- 3.5 Exercises.- 4. Complex Numbers.- 4.1 Complex Numbers.- 4.2 Sequences of Complex Numbers.- 4.3 Some Elementary Applications.- 4.4 Summing Up.- 4.5 Exercises.- 5. Polynomials, Rational Functions and Trigonometric Polynomials.- 5.1 Polynomials.- 5.2 Solutions of Polynomial Equations.- 5.3 Rational Functions.- 5.4 Sinusoidal Functions and Their Sums.- 5.5 Summing Up.- 5.6 Exercises.- 6. Series.- 6.1 Basic Facts.- 6.2 Taylor Series, e and ?.- 6.3 Series of Nonnegative Terms.- 6.4 Series of Terms of Arbitrary Sign.- 6.5 Series of Products.- 6.6 Products of Series.- 6.7 Rearrangements.- 6.8 Summing Up.- 6.9 Exercises.- 7. Power Series.- 7.1 Basic Theory.- 7.2 Further Results.- 7.3 Some Applications.- 7.4 Further Applications.- 7.5 Summing Up.- 7.6 Exercises.- 8. Discrete Processes.- 8.1 Recurrences.- 8.2 One-Dimensional Dynamical Systems.- 8.3 Two-Dimensional Dynamical Systems.- 8.4 Exercises.- A. Mathematicians and Other Scientists.- B. Bibliographical Notes.- C. Index.Trade Review"This self-contained book aims to introduce the main ideas for studying approximation processes, more generally discrete processes at graduate level. The use of computers induces a growing need for studying discrete processes.... A key feature this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations.... Each chapter has a short summary where the most important facts discussed are collected and described. There is also a large number of exercises inserted at various points into the text....The book is meant principally for graduate students in mathematics, physics, engineering, and computer science, but it can be used at technological and scientific faculties by anyone who wants to approach these topics. It may also be used in graduate seminars and courses or as a reference text by mathematicians, physicists, and engineers." —Zentralblatt MATH"Mathematical Analysis does contain a substantial amount of material that is unusual in terms of an introductory text in real analysis…These are all interesting topics that have gained increasing importance in modern applications of mathematics, albeit outside the traditional area of analysis. It is very nice to have these topics developed outside a specialized textbook, in, e.g., combinatorics, dynamical systems, or number theory. The authors do a very good job presenting this material…Mathematical Analysis includes substantial amounts of historical background…The book also contains a lot of examples…I can happily recommend Mathematical Analysis as a good resource for instructors of introductory analysis courses, especially in terms of providing some unusual applications of analysis and developments of some basic classic topics that are often shortchanged in standard texts." —SIAM Review“This is the second volume of a series on analysis. … a real hodgepodge that could only be the primary textbook for a course specifically based on it. … In this series Giaquinta and Modica have set themselves the formidable task of constructing from scratch an analysis sequence of several years length. … they have more regard for classical topics and arguments than most authors writing analysis books today. … I enjoyed reading this volume … .” (Warren Johnson, The Mathematical Association of America, January, 2010) Table of ContentsPreface * Real Numbers and Natural Numbers * Sequences of Real Numbers * Integer Numbers: Congruences, Counting and Infinity * Complex Numbers * Polynomials, Rational Functions and Trigonometric Polynomials * Series * Power Series * Discrete Processes * Mathematicans and Other Scientists * Bibliographical Notes * Index
£44.99
Birkhäuser Linear Partial Differential Equations for Scientists and Engineers
Book SynopsisFirst-Order, Quasi-Linear Equations and Method of Characteristics.- Mathematical Models.- Classification of Second-Order Linear Equations.- The Cauchy Problem and Wave Equations.- Fourier Series and Integrals with Applications.- Method of Separation of Variables.- Eigenvalue Problems and Special Functions.- Boundary-Value Problems and Applications.- Higher-Dimensional Boundary-Value Problems.- Green's Functions and Boundary-Value Problems.- Integral Transform Methods with Applications.- Nonlinear Partial Differential Equations with Applications.- Numerical and Approximation Methods.- Tables of Integral Transforms.Table of ContentsPreface to the Fourth Edition Preface to the Third Edition Introduction First-Order, Quasi-Linear Equations and Method of Characteristics Mathematical Models Classification of Second-Order Linear Equations The Cauchy Problem and Wave Equations Fourier Series and Integrals with Applications Method of Separation of Variables Eigenvalue Problems and Special Functions Boundary-Value Problems and Applications Higher-Dimensional Boundary-Value Problems Green's Functions and Boundary-Value Problems Integral Transform Methods with Applications Nonlinear Partial Differential Equations with Applications Numerical and Approximation Methods Tables of Integral Transforms Answers and Hints to Selected Exercises Appendix: Some Special Functions and Their Properties Bibliography Index
£104.49
Birkhauser Boston Distributions Theory and Applications Cornerstones
Book SynopsisThe treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis.Trade ReviewFrom the reviews:“This is a fantastic book…Even in this enlightened age, the theory of distributions is a highly misunderstood and undervalued business…All of this notwithstanding, learning it from the extant standard sources has always been a rather an austere affair…Distributions: Theory and Applications is laden with examples and exercises…[The book] comes equipped with a long section containing solutions to selected exercises. Distributions: Theory and Applications is much more than a textbook for a one-semester introduction to the indicated subject: the reader/student who hangs in, reads the text while filling the margins and a notebook or two (or three, or four) along the way, and wrestles with the exercises, will be more than ready for more advanced works in the area as well as the business of applying distributions in a number of nontrivial settings. Additionally he will have been exposed to a great deal of serious mathematics from, if you’ll pardon the pun, all over the spectrum.”BLL — The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition. —MAA Reviews“[Distributions: Theory and Applications] is a very useful, well-written, self contained, motivating book presenting the essentials of the theory of distributions of Schwartz, together with many applications to different areas of mathematics, like linear partial differential equations, Fourier analysis, quantum mechanics and signal analysis…One of the main features of this book is that many clarifying examples, presented with full detail, are included in the text. Moreover, a large number of problems is included at the end of each chapter…This reviewer found the book under review very stimulating, informative and inviting to further study. It is a very useful text for students who want to learn the theory of distributions, for experts in the abstract theory who want to read an application-oriented presentation with many examples and, last but not least, for mathematicians in related areas or theoretical physicists who need a self-contained, reasonable short presentation of the theory. I would strongly recommend it to all my colleagues.” —Zentralblatt MATH “The aim of this book is to present the theory of distributions of Laurent Schwartz in a rigorous, accessible way, together with applications to linear partial differential equations, Fourier analysis, quantum mechanics and signal analysis. The text of Duistermaat and Kolk emphasizes applications to natural sciences like optics, quantum field theory, signal reconstruction or computer tomography. The exposition stresses applications and interactions with other parts of mathematics...It is a useful text for students who want to learn the theory of distributions, for experts in the abstract theory who want to read an application-oriented presentation with many examples, and also for mathematicians in related areas or theoretical physicists who need a self-contained presentation of the theory. The book includes many clarifying examples, presented in full detail. Many exercises and problems, with different levels of difficulty, are included at the end of each chapter. A reader who tries to solve them will re-examine many aspects of analysis of several variables in the light of the theory of distributions. Complete solutions of 146 of the 281 problems are provided and hints are given for many others.In summary, this is a useful, well-written, self-contained book about the theory of distributions of Schwartz and applications to different areas of mathematics and physics. Although there are many good books that present an introduction to the theory of distributions of Schwartz, assuming different levels of knowledge of linear functional analysis, the text of Duistermaat and Kolk is a very welcome addition. In the opinion of this reviewer, this is a stimulating, informative book that invites further study, and I strongly recommend it to any readers interested in this topic.” —Mathematical Reviews “This is a wonderful graduate level book providing a modern introduction to distribution theory with several entrance points for deeper tours into advanced analysis and applications. The lucid discussions of the development of certain key notions and the fine careful proofs define it as a valuable text book for a corresponding university course. … even in independent self-study the reader has a fair chance to obtain a reasonable amount of working knowledge … .” (G. Hörmann, Monatshefte für Mathematik, Vol. 163 (1), May, 2011)“The authors have set out to produce a text on distribution theory accessible to undergraduate (or beginning graduate) students at the point in their studies where it could serve as an alternative to a beginning course in measure theory. … The authors discuss many fascinating results in distribution theory, with an emphasis on the use of the subject in linear PDEs … . The book succeeds both as a basic and as a rich account of results in distribution theory.” (Michael Taylor, SIAM Review, Vol. 54 (3), 2012)Table of ContentsPreface.- Standard Notation.- 1 Motivation .- Problems.- 2 Test Functions.- Problems.- 3 Distributions.- Problems.- 4 Differentiation of Distributions.- Problems.- 5 Convergence of Distributions.- Problems.- 6 Taylor Expansion in Several Variables.- Problems.- 7 Localization.- Problems.- 8 Distributions with Compact Support.- Problems.- 9 Multiplication by Functions.- Problems.- 10 Transposition: Pullback and Pushforward.- Problems.- 11 Convolution of Distributions.- Problems.- 12 Fundamental Solutions.- Problems.- 13 Fractional Integration and Differentiation .- 13.1 The Case of Dimension One.- 13.2 Wave Family.- 13.3 Appendix: Euler’s Gamma Function.- Problems.- 14 Fourier Transform.- Problems.- 15 Distribution Kernels.- Problems.- 16 Fourier Series.- Problems.- 17 Fundamental Solutions and Fourier Transform.- 17.1 Appendix: Fundamental Solution of .I?/k.- Problems.- 18 Supports and Fourier Transform.- Problems.- 19 Sobolev Spaces.- Problems.- 20 Appendix: Integration.- 21 Solutions to Selected Problems.- References.- Index of Notation.- Index.
£89.99
Birkhauser Boston Optimal Control and Viscosity Solutions of HamiltonJacobiBellman Equations Modern Birkhuser Classics
Book SynopsisOutline of the main ideas on a model problem.- Continuous viscosity solutions of Hamilton-Jacobi equations.- Optimal control problems with continuous value functions: unrestricted state space.- Optimal control problems with continuous value functions: restricted state space.- Discontinuous viscosity solutions and applications.- Approximation and perturbation problems.- Asymptotic problems.- Differential Games.Trade Review"The exposition is self-contained, clearly written and mathematically precise. The exercises and open problems…will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area. The book may be used by graduate students and researchers in control theory both as an introductory textbook, and as an up-to-date reference book." —Mathematical Reviews "The work is self-contained and is written in an accessible style with discussions of difficult questions on simplified model problems, with useful sections of bibliographical and historical notes and rich sets of proposed exercises at the end of each section. It may be easily used for graduate courses on various topics in control theory. We recommend it to both students and researchers interested in this area of applied mathematics." —Revue Roumaine de Mathématiques Pures et Appliquées "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my oppinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." —Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)... In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." —Acta Applicandae Mathematicae "The book originated from the lecture notes of courses taught by the authors, which is reflected in the style of presentation. Each chapter is enriched with a section of bibliographical and historical notes. The book can be recommended to specialists in PDEs, control theory, differential games, and related topics." —Mathematica Bohemica "As an outgrowth of lecture notes, this monograph purports to introduce and pursue the concept of viscosity solutions of the Hamilton-Jacobo-Bellman equations. It does so requiring but a relative modicum of mathematical knowledge... The book is written in a largely self-contained manner. In addition to bibliographical notes, exercises are provided as well." —Monatshefte für Mathematik "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercises exciting to self control and active collaboration. Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." —ZAATable of ContentsPreface.- Basic notations.- Outline of the main ideas on a model problem.- Continuous viscosity solutions of Hamilton-Jacobi equations.- Optimal control problems with continuous value functions: unrestricted state space.- Optimal control problems with continuous value functions: restricted state space.- Discontinuous viscosity solutions and applications.- Approximation and perturbation problems.- Asymptotic problems.- Differential Games.- Numerical solution of Dynamic Programming.- Nonlinear H-infinity control by Pierpaolo Soravia.- Bibliography.- Index
£113.99
Taylor & Francis Inc Hyperbolic Differential Operators And Related
Book SynopsisPresenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, SchrÃdinger, Einstein, and partial differential equations; complex analysis; and mathematical physics.Table of Contents1. The conference in honor of Jean Vaillant 2. Hyperbolic systems with nondegenerate characteristics 3. The Cauchy problem for hyperbolic operators dominated by the time function 4. A remark on the Cauchy problem for a model hyperbolic operator 5. Gevrey well-posedness of the Cauchy problem for systems 6. Gevrey well-posedness for pseudosymmetric systems with lower order terms 7. Le rôle des fonctions spéciales dans les problèmes de Goursat pour des équations aux dérivés partielles à coefficients constants 8. Influence of the hyperbolic part on decay rates in 1-d thermoelasticity 9. Integration and singularities of solutions for nonlinear second order hyperbolic equation 10. Causal evolution for Einsteinian gravitation 11. On the Cauchy–Kowalevskaya theorem of Nagumo type for systems 12. Differential analysis on stratified spaces 13. Edge Sobolev spaces, weakly hyperbolic equations, and branching of singularities 14. Sur les ondes superficieles de l'eau et le dévelopement de Friedrichs dans le système de coordonnées de Lagrange 15. Problème de Cauchy pour certains systèmes de Leray-Volevich du type de Schrôdinger 16. Systèmes du type de Schrôdinger à raciness caractéristiques multiples 17. Smoothing effect in Gevrey classes for Schrôdinger equations 18. Semiclassical wavefunctions and Schrôdinger equation 19. Strong uniqueness in Gevrey spaces for some elliptic operators 20. A remark on nonuniqueness in the Cauchy problem for elliptic operator having non-Lipschitz coefficients 21. Sur le prolongement analytique de la solution du problème de Cauchy 22. On the projective descriptions of the space of holomorphic germs 23. Microlocal scaling and extension of distributions 24. A lower bound for atomic Hamiltonians and Brownian motion 25. compromised arrow of time
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Taylor & Francis Inc Differential Equations and Group Methods for Scientists and Engineers
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LEGARE STREET PR A Treatise on Differential Equations
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LEGARE STREET PR A Treatise on Differential Equations
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LEGARE STREET PR Lectures on Cauchys Problem in Linear Partial Differential Equations
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LEGARE STREET PR Lectures on Cauchys Problem in Linear Partial Differential Equations
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LEGARE STREET PR Solution of Triangles
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LEGARE STREET PR A Treatise on the Analytical Dynamics of Particles and Rigid Bodies
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LEGARE STREET PR A Finite Difference Scheme for the Neumann and the Dirichlet Problem
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Legare Street Press Remarks on Strongly Elliptic Partial Differential Equations
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Legare Street Press The The Solution of a Certain Nonlinear RiemannHilbert Problem With an Application
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Legare Street Press Ordinary Differential Equations With an Introduction to Lies Theory of the Group of one Parameter
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Legare Street Press A Treatise on Linear Differential Equations
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Legare Street Press Similarity Solutions of Systems of Partial Differential Equations Using MACSYMA
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Legare Street Press Nonlinear Boundary Value Problems for the Circular Membrane
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Legare Street Press Hills Equation. Part I. General Theory
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Legare Street Press Regular Points of Linear Differential Equations of the Second Order
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Legare Street Press The The Differential Equations of Dynamics ... Volume 1
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Legare Street Press Über Die Partielle DifferentialGleichung DeltaVK V
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Legare Street Press Theorie Der Linearen Differenzengleichungen
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Legare Street Press Theory of Differential Equation
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Legare Street Press Handbuch der Theorie der Linearen Differentialgleichungen Zweiter Band
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Legare Street Press Sur Lintégration Des Équations Différentielles Linéaires
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Creative Media Partners, LLC Sammlung von mathematischen namentlich von Differential und Integral Formeln. Zweite unveränderte Ausgabe.
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Creative Media Partners, LLC Stability of two Dimensional Immiscible Flow to Viscous Fingering
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Creative Media Partners, LLC A Note on the Integral Equation of the First Kind With a Cauchy Kernel
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CRC Press Electromagnetics Through the Finite Element Method
Book SynopsisThis book presents the easiest way to learn finite element method (FEM) for electromagnetism - from static phenomena to high frequencies in a single book, based solely on Maxwell's equations. All the formalism associated with FEM is presented in detail, with simple numerical examples, duly commented to facilitate understanding of the method. Electromagnetics Through the Finite Element Method, Second Edition introduces techniques for coupling magnetic phenomena with electrical circuits and demonstrates special treatment and simulation techniques for electromagnetic problems with an open domain. This new edition includes a complete chapter on how to produce your own FEM software for electromagnetism quickly and easily. It also includes a new section on new computer programming techniques. It includes a chapter dedicated to presenting the technique for simultaneous simulation of the magnetic circuits by FEM with the analysis of electrical circuits. This technique is very useful in industrial applications where it is necessary to know not only the magnetic device, but also the converter that drives it. This new edition will not only teach the basics of this methodology, but readers will also learn about the techniques applied in industry and the computational resources to write their own FEM software, using the facilities of the Python language. The potential of this approach has been demonstrated for over 30 years with undergraduate students. The simplified approach presented in this new edition will not only benefit undergraduate students but will also be useful to practicing engineers and researchers looking to introduce themselves to these numerical methods.
£134.01
