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Ordinary Differential Equations - Table of Contents
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Overview
Preface
Table of Contents
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Offering: Ordinary Differential Equations
Titles: Ordinary Differential Equations
By Dr. Henry van Roessel
1. Introduction
1.1 - Modelling with Differential Equations
1.2 - Basic Definitions
2. First Order Equations
2.1 - Direction Fields
2.2 - Separable Equations
2.3 - Existence and Uniqueness
2.4 - Exact Equations
2.5 - Integrating Factors
2.6 - Linear Equations
2.7 - Special Equations
3. Second Order Equations
3.1 - Linear Differential Operators
3.2 - Homogeneous Equations
3.3 - Reduction of Order
3.4 - Constant Coefficient Equations
3.5 - Cauchy--Euler Equation
3.6 - Nonhomogeneous Equations
3.7 - Undetermined Coefficients
3.8 - Variation of Parameters
3.9 - Applications
4. Higher Order Equations
4.1 - Basic Theory
4.2 - Constant Coefficient Equations
4.3 - Undetermined Coefficients
4.4 - Variation of Parameters
5. Series Solutions
5.1 - Review of Power Series
5.2 - Solution Near Ordinary Points
5.3 - Solution Near Singular Points
5.4 - Special Functions
6. Laplace Transforms
6.1 - Introduction
6.2 - Properties of Laplace Transforms
6.3 - Inverse Laplace Transforms
6.4 - Applications to Differential Equations
6.5 - Convolution
6.6 - The Delta Function