### Table of contents:

Part One: 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 Two: Vectors, Matrices, and Vector Calculus

Chapter 7: Vectors

Chapter 8: Matrices

Chapter 9: Vector Calculus

Part Three: Systems of Differential Equations

Chapter 10: Systems of Linear Differential Equations

Chapter 11: Systems of Nonlinear Differential Equations

Part Four: 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 Five: 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

Appendices

I Some Derivative and Integral Formulas

II Gamma Function

III Table of Laplace Transforms

IV Conformal Mappings

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