Page 13 - Schaum's Outline of Differential Equations
P. 13
Xll CONTENTS
Chapter 20 Numerical Methods for Solving Second-Order
Differential Equations Via Systems 195
Second-Order Differential Equations 195
Euler's Method 196
Runge-Kutta Method 196
Adams-Bashford-Moulton Method 196
Chapter 21 The Laplace Transform 211
Definition 211
Properties of Laplace Transforms 211
Functions of Other Independent Variables 212
Chapter 22 Inverse Laplace Transforms 224
Definition 224
Manipulating Denominators 224
Manipulating Numerators 225
Chapter 23 Convolutions and the Unit Step Function 233
Convolutions 233
Unit Step Function 233
Translations 234
Chapter 24 Solutions of Linear Differential Equations with
Constant Coefficients by Laplace Transforms 242
Laplace Transforms of Derivatives 242
Solutions of Differential Equations 243
Chapter 25 Solutions of Linear Systems by Laplace
Transforms 249
The Method 249
Chapter 26 Solutions of Linear Differential Equations
with Constant Coefficients by Matrix Methods 254
Solution of the Initial-Value Problem 254
Solution with No Initial Conditions 255
Chapter 27 Power Series Solutions of Linear Differential
Equations with Variable Coefficients 262
Second-Order Equations 262
Analytic Functions and Ordinary Points 262
Solutions Around the Origin of Homogeneous Equations 263
