Table of Contents:

Part I Ordinary Differential Equations
Chapter 1 Introduction to Differential Equations
Chapter 2 First-Order Differential Equations
Chapter 3 Higher-Order Differential Equations
Chapter 4 The Laplace Transform
Chapter 5 Series Solutions of Linear Differential Equations
Chapter 6 Numerical Solutions of Ordinary Differential Equations

Part II Vectors, Matrices, and Vector Calculus
Chapter 7 Vectors
Chapter 8 Matrices
Chapter 9 Vector Calculus

Part III Systems of Differential Equations
Chapter 10 Systems of Linear Differential Equations
Chapter 11 Systems of Nonlinear Differential Equations

Part IV Fourier Series and Partial Differential Equations
Chapter 12 Orthogonal Functions and Fourier Series
Chapter 13 Boundary-Value Problems in Rectangular Coordinates
Chapter 14 Boundary-Value Problems in Other Coordinate Systems
Chapter 15 Integral Transform Method
Chapter 16 Numerical Solutions of Partial Differential Equations

Part V Complex Analysis
Chapter 17 Functions of a Complex Variable
Chapter 18 Integration in the Complex Plane
Chapter 19 Series and Residues
Chapter 20 Conformal Mappings and Applications