Chapter 1: Introduction
1.1 Foundations
1.2 Classes of Differential Equations
1.3 A Few Other Things
Chapter Summary
Solved Problems
Problems to Solve
Word Problems
Challenge Problems
Chapter 2: First-Order Linear Ordinary Differential Equations
2.1 First Order Linear Homogeneous ODEs
2.2 First Order Linear Nonhomogeneous ODEs
2.3 System Stability
Chapter Summary
Solved Problems
Problems to Solve
Word Problems
Challenge Problems
Chapter 3: First-Order Nonlinear Ordinary Differential Equations
3.1 Nonlinear Separable ODEs
3.2 The Possibility of Transforming Nonlinear Equations into Linear Ones
3.3 Successive Approximations for Almost Linear Systems
Chapter Summary
Solved Problems
Problems to Solve
Word Problems
Challenge Problems
Computing Projects: Phase 1
Chapter 4: Existence, Uniqueness, and Qualitative Analysis
4.1 Motivation
4.2 Successive Approximations (General Form)
4.3 Existence and Uniqueness Theorem
4.4 Qualitative Analysis
4.5 Stability Revisited
4.6 Local Solutions
Chapter Summary
Solved Problems
Problems to Solve
Word Problems
Challenge Problems
Chapter 5: Second-Order Linear Ordinary Differential Equations
5.1 Second Order Linear Time-Invariant Homogeneous ODEs
5.2 Fundamental Solutions
5.3 Second Order Linear Nonhomogeneous ODEs
5.4 Existence and Uniqueness of Solutions to Second-Order Linear ODEs
Chapter Summary
Solved Problems
Problems to Solve
Word Problems
Challenge Problems
Chapter 6: Higher-Order Linear Ordinary Differential Equations
6.1 Example: Satellite Orbit Decay
6.2 Higher Order Homogeneous Linear Equations
6.3 Higher Order Nonhomogeneous Linear Equations
6.4 Existence and Uniqueness
6.5 Stability of Higher Order Systems
Chapter Summary
Solved Problems
Problems to Solve
Word Problems
Challenge Problems
Computing Projects: Phase 2
Chapter 7: Laplace Transforms
7.1 Preliminaries
7.2 Introducing the Laplace Transform
7.3 Laplace Transforms of Some Common Functions
7.4 Laplace Transforms of Derivatives
7.5 Laplace Transforms in Homogeneous ODEs
7.6 Laplace Transforms in Nonhomogeneous ODEs
Chapter Summary
Solved Problems
Problems to Solve
Word Problems
Challenge Problems
Chapter 8: Systems of First-Order Ordinary Differential Equations
8.1 Preliminaries
8.2 Existence and Uniqueness
8.3 Numerical Integration Methods
8.4 Review of Matrix Algebra
8.5 Linear Systems in State Space Format
8.6 A Brief Look at N-Dimensional Nonlinear Systems
Chapter Summary
Solved Problems
Problems to Solve
Word Problems
Challenge Problems
Chapter 9: Partial Differential Equations
9.1 The Heat Equation
9.2 The Wave Equation
9.3 Laplace’s Equation
9.4 The Beam Equation
Chapter Summary
Solved Problems
Problems to Solve
Word Problems
Challenge Problems
Biography
David V. Kalbaugh received his B.S. from the Johns Hopkins University in 1967; M.S. from Stanford University in 1968; and doctorate from University of Maryland in 1974. He was exposed to many practical problems across engineering and physics at Johns Hopkins University Applied Physics Laboratory, where he eventually retired as Assistant Director in 2005. Dr. Kalbaugh developed this text while teaching both engineering courses and differential equations as an adjunct Assistant Professor in the Mathematics and Computer Science Department at the University of Maryland Eastern Shore from 2008-2014. UMES achieved ABET accreditation of its engineering program in August 2013.
