1CHAPTER 1 Introduction to Ordinary Differential Equations
315.5 Applications and Examples
21.1 Definition and Basic Concepts
32CHAPTER 6 Numerical Methods for Ordinary Differential Equations
31.2 Classification of Differential Equations
336.1 Euler’s Method
41.3 Historical Overview
346.2 Runge-Kutta Methods
5CHAPTER 2 First-Order Differential Equations
356.3 Multistep Methods
62.1 Separable Equations
366.4 Stability and Convergence
72.2 Linear Equations
376.5 Error Analysis
82.3 Exact Equations
386.6 Applications and Examples
92.4 Integrating Factors
39CHAPTER 7 Boundary Value Problems
102.5 Applications and Examples
407.1 Definition and Formulation
11CHAPTER 3 Higher-Order Differential Equations
417.2 Shooting Method
123.1 Second-Order Linear Equations
427.3 Finite Difference Methods
133.2 Reduction of Order
437.4 Green’s Functions
143.3 Homogeneous Linear Equations with Constant Coefficients
447.5 Sturm-Liouville Theory
153.4 Nonhomogeneous Linear Equations
457.6 Applications and Examples
163.5 Undetermined Coefficients
46CHAPTER 8 Special Topics in Ordinary Differential Equations
173.6 Variation of Parameters
478.1 Bifurcation Theory
183.7 Applications and Examples
488.2 Chaos Theory
19CHAPTER 4 bSystems of Differential Equations
498.3 Hamiltonian Systems
204.1 Introduction to Systems
508.4 Singular Perturbation Methods
214.2 First-Order Linear Systems
518.5 Delay Differential Equations
224.3 Higher-Order Linear Systems
528.6 Applications and Examples
234.4 Nonlinear Systems
53CHAPTER 9 Advanced Applications and Case Studies
244.5 Stability and Phase Portraits
549.1 Fluid Dynamics and Heat Transfer
254.6 Applications and Examples
559.2 Population Dynamics and Epidemiology
26CHAPTER 5 Laplace Transform Methods
569.3 Control Theory and Electrical Circuits
275.1 Definition and Properties of the Laplace Transform
579.4 Mechanical Vibrations and Oscillations
285.2 Solving Initial Value Problems
589.5 Biological Models and Pharmacokinetics
295.3 Systems of Differential Equations
59Glossaries
305.4 Convolution Integrals
60Index
