Search results for ""Author Amol Sasane""
John Wiley & Sons Inc The How and Why of One Variable Calculus
Book SynopsisFirst course calculus texts have traditionally been either engineering/science-oriented with too little rigor, or have thrown students in the deep end with a rigorous analysis text.Table of ContentsPreface ix Introduction xi Preliminary notation xv 1 The real numbers 1 1.1 Intuitive picture of R as points on the number line 2 1.2 The field axioms 6 1.3 Order axioms 8 1.4 The Least Upper Bound Property of R 9 1.5 Rational powers of real numbers 20 1.6 Intervals 21 1.7 Absolute value |·|and distance in R 23 1.8 (∗) Remark on the construction of R 26 1.9 Functions 28 1.10 (∗) Cardinality 40 Notes 43 2 Sequences 44 2.1 Limit of a convergent sequence 46 2.2 Bounded and monotone sequences 54 2.3 Algebra of limits 59 2.4 Sandwich theorem 64 2.5 Subsequences 68 2.6 Cauchy sequences and completeness of R 74 2.7 (∗) Pointwise versus uniform convergence 78 Notes 85 3 Continuity 86 3.1 Definition of continuity 86 3.2 Continuous functions preserve convergence 91 3.3 Intermediate Value Theorem 99 3.4 Extreme Value Theorem 106 3.5 Uniform convergence and continuity 111 3.6 Uniform continuity 111 3.7 Limits 115 Notes 124 4 Differentiation 125 4.1 Differentiable Inverse Theorem 136 4.2 The Chain Rule 140 4.3 Higher order derivatives and derivatives at boundary points 144 4.4 Equations of tangent and normal lines to a curve 148 4.5 Local minimisers and derivatives 157 4.6 Mean Value, Rolle’s, Cauchy’s Theorem 159 4.7 Taylor’s Formula 167 4.8 Convexity 172 4.9 0/0 form of l’Hôpital’s Rule 180 Notes 182 5 Integration 183 5.1 Towards a definition of the integral 183 5.2 Properties of the Riemann integral 198 5.3 Fundamental Theorem of Calculus 210 5.4 Riemann sums 226 5.5 Improper integrals 232 5.6 Elementary transcendental functions 245 5.7 Applications of Riemann Integration 278 Notes 296 6 Series 297 6.1 Series 297 6.2 Absolute convergence 305 6.3 Power series 320 Appendix 335 Notes 337 Solutions 338 Solutions to the exercises from Chapter 1 338 Solutions to the exercises from Chapter 2 353 Solutions to the exercises from Chapter 3 369 Solutions to the exercises from Chapter 4 388 Solutions to the exercises from Chapter 5 422 Solutions to the exercises from Chapter 6 475 Bibliography 493 Index 495
£47.45
World Scientific Publishing Co Pte Ltd Axiomatic Arithmetic An Introduction To Number Systems
£42.75
World Scientific Publishing Co Pte Ltd Mathematical Introduction To General Relativity A
Book Synopsis
£130.50
World Scientific Publishing Co Pte Ltd Mathematical Introduction To General Relativity,
Book SynopsisThe book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.
£130.50
World Scientific Europe Ltd Friendly Approach To Functional Analysis, A
Book Synopsis'The book is unusual among functional analysis books in devoting a lot of space to the derivative. The ‘friendly’ aspect promised in the title is not explained, but there are three things I think would strike most students as friendly: the slow pace, the enormous number of examples, and complete solutions to all the exercises.'MAA ReviewsThis book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study.A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics.
£93.10
World Scientific Publishing Co Pte Ltd Axiomatic Arithmetic An Introduction To Number Systems
£76.00
World Scientific Europe Ltd Friendly Approach To Functional Analysis, A
Book Synopsis'The book is unusual among functional analysis books in devoting a lot of space to the derivative. The ‘friendly’ aspect promised in the title is not explained, but there are three things I think would strike most students as friendly: the slow pace, the enormous number of examples, and complete solutions to all the exercises.'MAA ReviewsThis book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study.A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics.
£53.20
World Scientific Publishing Co Pte Ltd Mathematical Introduction To General Relativity A
Book Synopsis
£76.00
World Scientific Publishing Co Pte Ltd Plain Plane Geometry
Book SynopsisThe book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also for students participating in mathematics circles and in mathematics olympiads.Each section contains several problems, which are not purely drill exercises, but are intended to introduce a sense of 'play' in mathematics, and inculcate appreciation of the elegance and beauty of geometric results. There is an abundance of colour pictures illustrating results and their proofs. A section on hints and a further section on detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.Table of ContentsGeometric Figures; Congruent Triangles; Quadrilaterals; Similar Triangles; Circles;
£38.00
World Scientific Publishing Co Pte Ltd Plain Plane Geometry
Book SynopsisThe book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also for students participating in mathematics circles and in mathematics olympiads.Each section contains several problems, which are not purely drill exercises, but are intended to introduce a sense of 'play' in mathematics, and inculcate appreciation of the elegance and beauty of geometric results. There is an abundance of colour pictures illustrating results and their proofs. A section on hints and a further section on detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.Table of ContentsGeometric Figures; Congruent Triangles; Quadrilaterals; Similar Triangles; Circles;
£75.05
World Scientific Publishing Co Pte Ltd Friendly Approach To Complex Analysis, A
Book SynopsisThe book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text.The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained.
£42.75
World Scientific Publishing Co Pte Ltd Friendly Approach To Complex Analysis, A
Book SynopsisThe book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series expansions.Each section contains several problems, which are not purely drill exercises, but are rather meant to reinforce the fundamental concepts. Detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study. There are many figures illustrating the text.Table of ContentsComplex Numbers; Elementary Functions; Complex Differentiability and the Cauchy - Riemann Equations; Contour Integration; Cauchy Integral Theorem and Its Consequences; Taylor and Laurent Series; Harmonic Functions.
£33.25
World Scientific Publishing Co Pte Ltd Friendly Approach To Complex Analysis, A
Book SynopsisThe book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text.The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained.
£76.00
World Scientific Publishing Co Pte Ltd Friendly Approach To Complex Analysis, A
Book SynopsisThe book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series expansions.Each section contains several problems, which are not purely drill exercises, but are rather meant to reinforce the fundamental concepts. Detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study. There are many figures illustrating the text.Table of ContentsComplex Numbers; Elementary Functions; Complex Differentiability and the Cauchy - Riemann Equations; Contour Integration; Cauchy Integral Theorem and Its Consequences; Taylor and Laurent Series; Harmonic Functions.
£62.70
Jaypee Brothers Medical Publishers Textbook of Radiology Physics
Book SynopsisThis book provides a concise overview of the field of radiology physics and its application in everyday practice. Beginning with an introduction to the fundamental concepts and the basics of radiation, the following sections review different techniques, from X-Ray production and ultrasound, to Doppler, mammography, computed tomography, and nuclear medicine procedures. Further topics include complex magnetic resonance concepts, radiation exposure monitoring, single-photon emission computed tomography, and positron emission tomography. Enhanced by radiological images and illustrations, each chapter explains the principles, function, application and limitations of the radiological technique in question. Key points Concise review of the field of radiology physics Covers complete range of radiology techniques, from basic to more complex Principles, function, application and limitations of each technique explained in detail Includes radiological images and illustrations to enhance learning Table of Contents Electromagnetic Radiations Production of X-ray X-ray Interactions Grids, Collimators, Filters X-ray Films Fluoroscopic Imaging Image Quality Radiation Hazards and Protection Ultrasound Physics Doppler Recent Advances in Ultrasound Mammography Computed Tomography Magnetic Resonance Imaging Computed Tomography Contrast Media Artifacts Computed Radiography and Digital Radiography Positron Emission Tomography-Computed Tomography Magnetic Resonance-Positron Emission Tomography Single-photon Emission Computed Tomography Picture Archiving and Communication System Planning of Radiology Department Molecular Imaging Nuclear Medicine Physics Miscellaneous Index
£19.00
