| Dr.Clay Ross Taught mathematics at the university level from 1967through his retirement in may of 2003,he continues to pursue his interests in mathematics,travel,and nature pho-tography;still plays in the university orchestra;and serves as organist at his church.those activities and much reading keep him productively occupied. |
| Preface About Differential Equations 1.0 Introduction 1.1 Numerical Methods 1.2 Uniqueness considerations 1.3 Differential Inclusions （Optional） 2 Linear Atgehca 2.0 [atxoduction 2.1 Familiar Linear Spaces 2.2 Abstract Linear Spaces 2.3 Differential Equations from Solutions 2.4 Characteristic Value Problems 3 First-Order Differential Equations 3.0 Introduction 3.I First-order Linear Differential Equations 3.2 Lineax Equations by mathematica 3.3 Exact Equations 3.4 Variables Separable 3.5 Homogeneous Nonlinear Differential Equations 3.6 Bernoulli and Riccati Differential Equations (Optional) 3.7 Clairaut Differential Equations (Optional) 4 Applications of First-Order Equations 4.0 Introduction 4.1 Orthogonal Trajectories 4.2 Linear Applications 4.3 Nonlinear Applications 5 Higher-Order Linear Differential Equations 5.0 Introduction 5.1 The Fundamental Theorem 5.2 Homogeneous Second-Order Linear Constant Coefficients 5.3 Higher-Order Constant Coefficients (Homogeneous) 5.4 The Method of Undetermined Coefficients 5.5 Variation of Parameters 6 Applications of Second-Order Equations 6.0 Introduction 6.1 Simple Harmonic Motion 6.2 Damped Harmonic Motion 6.3 Forced Oscillation 6.4 Simple Electronic Circuits 6.5 Two Nonlinear Examples (Optional) 7 The Laplace Transform 7.0 Introduction 7.1 The Laplace Transform 7.2 Properties of the Laplace Transform 7.3 The Inverse Laplace Transform 7.4 Discontinous Functions and Their Transforms 8 Higher-Order Differential Equations with Variable Coefficients 8.0 Introduction 8.1 Cauchy-Euler Differential Equations 8.2 Obtaining a Second Solution 8.3 Sums, Products and Recursion Relations 8.4 Series Solutions of Differential Equations 8.5 Series Solutions About Ordinary Points 8.6 Series Solution About Regular Singular Points 8.7 Important Classical Differential Equations and Functions 9 Differential Systems: Theory 9.0 Introduction 9.1 Reduction to First-Order Systems 9.2 Theory of First-Order Systems 9.3 First-Order Constant Coefficients Systems 9.4 Repeated and complex roots 9.5 Nonhomogeneous Equations and Boundary-value problems 9.6 Cauchy-Euler Systems 10 Differential Systems:Applications References Index |
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