Differential Equations : Linear, Nonlinear, Ordinary, Partial
A. C. King
Bok Engelsk 2003 · Electronic books.
| Utgitt | Cambridge : Cambridge University Press , 2003
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| Omfang | 1 online resource (555 p.)
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| Opplysninger | Description based upon print version of record.. - Cover; Half-title; Title; Copyright; Contents; Preface; CHAPTER ONE Variable Coefficient, Second Order, Linear, Ordinary Differential Equations; CHAPTER TWO Legendre Functions; CHAPTER THREE Bessel Functions; CHAPTER FOUR Boundary Value Problems, Green's Functions and Sturm-Liouville Theory; CHAPTER FIVE Fourier Series and the Fourier Transform; CHAPTER SIX Laplace Transforms; CHAPTER SEVEN Classification, Properties and Complex Variable Methods for Second Order Partial Differential Equations. - A1.3 Linear Transformations and MatricesA1.4 The Eigenvalues and Eigenvectors of a Matrix; APPENDIX 2 Continuity and Differentiability; APPENDIX 3 Power Series; A3.1 Maclaurin Series; A3.2 Taylor Series; A3.3 Convergence of Power Series; A3.4 Taylor Series for Functions of Two Variables; APPENDIX 4 Sequences of Functions; APPENDIX 5 Ordinary Differential Equations; A5.1 Variables Separable; A5.2 Integrating Factors; A5.3 Second Order Equations with Constant Coefficients; APPENDIX 6 Complex Variables; A6.1 Analyticity and the Cauchy-Riemann Equations. - A6.2 Cauchy's Theorem, Cauchy's Integral Formula and Taylor's TheoremA6.3 The Laurent Series and Residue Calculus; A6.4 Jordan's Lemma; A6.5 Linear Ordinary Differential Equations in the Complex Plane; APPENDIX 7 A Short Introduction to MATLAB; A7.1 Getting Started; A7.2 Variables, Vectors and Matrices; A7.3 User-Defined Functions; A7.4 Graphics; A7.5 Programming in MATLAB; Bibliography; Index. - CHAPTER EIGHT Existence, Uniqueness, Continuity and Comparison of Solutions of Ordinary Differential EquationsCHAPTER NINE Nonlinear Ordinary Differential Equations: Phase Plane Methods; CHAPTER TEN Group Theoretical Methods; CHAPTER ELEVEN Asymptotic Methods: Basic Ideas; CHAPTER TWELVE Asymptotic Methods: Differential Equations; CHAPTER THIRTEEN Stability, Instability and Bifurcations; CHAPTER FOURTEEN Time-Optimal Control in the Phase Plane; CHAPTER FIFTEEN An Introduction to Chaotic Systems; APPENDIX 1 Linear Algebra; A1.1 Vector Spaces Over the Real Numbers; A1.2 Inner Product Spaces. - The authors focus on constructing solutions analytically, and interpreting their meaning; MATLAB is used extensively to illustrate the material. The many worked examples, based on interesting real world problems, the large selection of exercises, including several lengthier projects, the broad coverage, and clear and concise presentation will appeal to undergraduates.
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| ISBN | 0521016878. - 0521816580
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