Page 12 - Schaum's Outline of Differential Equations
P. 12
CONTENTS XI
Chapter 14 Applications of Second-Order Linear
Differential Equations 114
Spring Problems 114
Electrical Circuit Problems 115
Buoyancy Problems 116
Classifying Solutions 117
Chapter 15 Matrices 131
Matrices and Vectors 131
Matrix Addition 131
Scalar and Matrix Multiplication 132
Powers of a Square Matrix 132
Differentiation and Integration of Matrices 132
The Characteristic Equation 133
Chapter 16 eat 140
Definition 140
Computation of eAt 140
Chapter 17 Reduction of Linear Differential Equations
to a System of First-Order Equations 148
An Example 148
th
Reduction of an n Order Equation 149
Reduction of a System 150
Chapter 18 Graphical and Numerical Methods for Solving
First-Order Differential Equations 157
Qualitative Methods 157
Direction Fields 157
Euler's Method 158
Stability 158
Chapter 19 Further Numerical Methods for Solving
First-Order Differential Equations 176
General Remarks 176
Modified Euler's Method 177
Runge-Kutta Method 177
Adams-Bashford-Moulton Method 177
Milne's Method 177
Starting Values 178
Order of a Numerical Method 178
