Front
Contents
Preface
To the Reader
Prologue
Ch 1: first-order ODE
1.1
1.2 Qualitative
1.3 Quantitative
1.4 Numerical
1.5 Theoretical
Ch 2: linearity and nonlinearity
2.1 linear equations
2.2 solving first-order linear ODE
2.3 growth and decay
2.4 mixing and cooling
2.5 nonlinear and logistic eq
2.6 systems, first look
Ch 3: linear algebra
3.1 matrices
3.2 systems of eqn
3.3 inverse of a matrix
3.4 determinants and Cramer's rule
3.5 vector spaces
3.6 basis and dimension
Ch 4: higher-order linear ODE
4.1 harmonic oscillator
4.2 real characteristic roots
4.3 complex characteristic roots
4.4 undetermined coefficients
4.5 variation of parameters
4.6 forced oscillations
4.7 conservation and conversion
Ch 5: linear transformations
5.1 linear transformations
5.2 properties of linear transformations
5.3 eigenvalues
5.4 coordinates and diagonalization
Ch 6: linear systems of ODE
6.1 theory of linear DE systems
6.2 linear systems with real eigenvalues
6.3 linear systems with nonreal eigenvalues
6.4 stability and linear classification
6.5 decoupling a linear DE system
6.6 matrix exponential
6.7 nonhomogeneous linear systems
Ch 7: nonlinear systems of ODE
7.1 nonlinear systems
7.2 lineariziation
7.3 numerical solutions
7.4 chaos, strange attractors, period doubling
7.5 chaos in forced nonlinear systems
Ch 8: Laplace transforms
8.1 Laplace transform and its inverse
8.2 solving DEs with Laplace transform
8.3 step function and delta function
8.4 convolution and transfer function
8.5 Laplace transform for systems
Ch 9: discrete dynamical systems
9.1 iterative equation
9.2 linear iterative systems
9.3 nonlinear iterative equations, chaos
Ch 10: control theory
10.1 feedback controls
10.2 optimal control
10.3 Pontryagin maximum principle
Appendix CN: complex numbers
Appendix LT: linear transformations
Appendix PF: partial fractions
Appendix SS: spreadsheets for systems
Bibliography
Answers
ch 1
ch 2
ch 3
ch 4
ch 5
ch 6
ch 7
ch 8
ch 9
ch 10
Index
Table of Integrals
Table of Laplace Transforms