Elementary Differential Equations and Boundary Value Problems

TABLE OF CONTENTS
 
1 Introduction
 
1.1 Some Basic Mathematical Models
 
1.2 Solutions of Some Differential Equations
 
1.3 Classification of Differential Equations
 

2 First-Order Differential Equations
 
2.1 Linear Differential Equations; Method of Integrating Factors
 
2.2 Separable Differential Equations
 
2.3 Modeling with First-Order Linear Differential Equations
 
2.4 Differences Between Linear and Nonlinear Differential Equations
 
2.5 Autonomous Differential Equations and Population Dynamics
 
2.6 Exact Differential Equations and Integrating Factors
 
2.7 Numerical Approximations: Euler's Method
 
2.8 The Existence and Uniqueness Theorem
 
2.9 First-Order Difference Equations
 

3 Second-Order Linear Differential Equations
 
3.1 Homogeneous Differential Equations with Constant Coefficients
 
3.2 Solutions of Linear Homogeneous Equations; the Wronskian
 
3.3 Complex Roots of the Characteristic Equation
 
3.4 Repeated Roots; Reduction of Order
 
3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
 
3.6 Variation of Parameters
 
3.7 Mechanical and Electrical Vibrations
 
3.8 Forced Periodic Vibrations
 
3.9 Central Gravitational Forces and Kepler's Laws
 

4 Higher-Order Linear Differential Equations
 
4.1 General Theory of nth Order Linear Differential Equations
 
4.2 Homogeneous Differential Equations with Constant Coefficients
 
4.3 The Method of Undetermined Coefficients
 
4.4 The Method of Variation of Parameters
 

5 Series Solutions of First-Order and Second-Order Linear Equations
 
5.1 Review of Power Series
 
5.2 Series Solution of First Order Equations
 
5.3 Series Solutions Near an Ordinary Point, Part I
 
5.4 Series Solutions Near an Ordinary Point, Part II
 
5.5 Euler Equations; Regular