Copyright
Preface
Projects
Project for Section 2.2 When Differential Equations Invaded Geometry: Inverse Tangent Problems in the 17th Century
Project for Section 2.5 Two Properties of the Sphere
Project for Section 2.7 Potassium-Argon Dating
Project for Section 2.8 Tricky Timing: The Isochrones of Huygens and Leibniz
Project for Section 3.8 Vibration Control: Vibration Isolation
Project for Section 3.11 Vibration Control: Vibration Absorbers
Project for Section 9.16 Minimal Surfaces
Project for Section 13.4 Making Waves: Convection, Diffusion, and Traffi c Flow
Project for Section 15.4 The Uncertainty Inequality in Signal Processing
Part 1 Ordinary Differential Equations
1 Introduction to Differential Equations
2 First-Order Differential Equations
3 Higher-Order Differential Equations
The Laplace Transform
5 Series Solutions of Linear Differential Equations
6 Numerical Solutions of Ordinary Differential Equations
Part 2 Vectors, Matrices, and Vector Calculus
7 Vectors
8 Matrices
9 Vector Calculus
Part 3 Systems of Differential Equations
10 Systems of Linear Differential Equations
11 Systems of Nonlinear Differential Equations
Part 4 Partial Differential Equations
12 Orthogonal Functions and Fourier Series
13 Boundary-Value Problems in Rectangular Coordinates
14 Boundary-Value Problems in Other Coordinate Systems
Integral Transform Method
16 Numerical Solutions of Partial Differential Equations
Part 5 Complex Analysis
17 Functions of a Complex Variable
18 Integration in the Complex Plane
19 Series and Residues
Conformal Mappings
Appendix I Derivative and Integral Formulas
Appendix II Gamma Function
Appendix III Table of Laplace Transforms
Appendix IV Conformal Mappings
Answers for Selected Odd–Numbered Problems
Index
Endpapers
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