ordinary_differential_equation
常微分方程
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常微分方程式
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linear ordinary differential equation
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ordinary difference differential equation
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&&&&&&&&&&&&Ordinary Differential Equations
Ordinary Differential Equations
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ＩＳＢＮ：8
字　　数：107153
正文语种：英文
文件大小：3.82M
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Cover image
Title page
Table of Contents
Inside Front Cover
Dedication
Series Preface
Acknowledgements
Chapter 1: Introduction and a Look Ahead
1.1 Getting an overview
1.2 Notation, terminology and analytical aspects
1.3 Direct methods of solution
1.4 Transform methods
1.5 Solution in series
1.6 Systems of equations
1.7 Qualitative methods
1.8 Numerical methods
1.9 Modelling with differential equations
FURTHER EXERCISES
Chapter 2: First-order Differential Equations C Methods and Models
2.1 Introduction and a quick review
2.2 Complementary function plus particular integral
2.3 Exact equations and more integrating factors
2.4 Transforming an equation C new from old
2.5 Modelling with first-order differential equations
Chapter 3: First-order Differential Equations C Analysis and Approximation
3.1 Introduction - solution of a differential equation
3.2 Existence and uniqueness for the linear first-order equation
3.3 The Peano existence theorem
3.4 Uniqueness theorems - the Lipschitz condition
3.5 Higher-order equations
3.6 Picard’s method
3.7 Numerical methods for first-order equations
Chapter 4: Second- and Higher-order Homogenous Linear Differential Equations
4.1 Introduction
4.2 Linear second-order equations
4.3 Linearly dependent and independent functions
4.4 Fundamental solution sets and the general solution
4.5 Second-order linear homogeneous equations with constant coefficients
FURTHER EXERCISES
Chapter 5: Inhomogeneous Linear Differential Equations
5.1 Second-order inhomogeneous equations with constant coefficients. Undetermined coefficients
5.2 Variation of parameters
5.3 Higher-order equations C project
5.4 D-operator methods
5.5 A note on numerical methods for higher-order differential equations
5.6 Modelling with second-order equations C project
FURTHER EXERCISES
Chapter 6: Laplace Transform Methods for Solving Initial Value Problems
6.1 Introduction
6.2 The Laplace transform
6.3 Laplace transforms of the elementary functions
6.4 Properties of the Laplace transform
6.5 The inverse Laplace transform
6.6 Solution of initial value problems by Laplace transform
6.7 The convolution theorem
6.8 Heaviside and Dirac functions’
Chapter 7: Systems of Linear Differential Equations
7.1 Introduction
7.2 An obvious approach for homogeneous systems
7.3 Solution of systems by diagonalization
7.4 Undetermined coefficients and variation of parameters for inhomogeneous systems
7.5 The exponential matrix
7.6 Use of Laplace transforms in solving initial value problems for systems of differential equations
7.7 D-operator methods. Elimination
7.8 Higher-order systems
7.9 Mathematical modelling with systems of differential equations
Chapter 8: Series Solution of Linear Differential Equations
8.1 Introduction
8.2 Singular points
8.3 Legendre’s equation C Taylor series solution
8.4 Legend re polynomials
8.5 Frobenius’ method
8.6 Bessel′s equation - project
8.7 More ‘special’ functions
FURTHER EXERCISES
Chapter 9: Special Functions and Orthogonal Expansions
9.1 Why are ‘special functions’ special?
9.2 The Fourier series expansion
9.3 Sturm-Liouville systems
9.4 The Legendre Sturm-Liouville system -project
9.5 Orthogonal functions with respect to a weight function - project
FURTHER EXERCISES
Chapter 10: An Introduction to Nonlinear Systems
10.1 Introduction
10.2 Linearization of nonlinear systems. Phase plane and state space
10.3 The general linear homogeneous second-order system - project
10.4 Putting it all together - the linearization theorem
10.5 The route to chaos
Appendix C Chapter Summaries
Answers to Exercises
Bibliography
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