First-Order Differential Equations | |
Dynamical Systems: Modeling | p. 1 |
Solutions and Direction Fields: Qualitative Analysis | p. 11 |
Separation of Variables: Quantitative Analysis | p. 25 |
Approximation Methods: Numerical Analysis | p. 33 |
Picards Theorem: Theoretical Analysis | p. 46 |
Linearity and Nonlinearity | |
Linear Equations: The Nature of Their Solutions | p. 55 |
Solving the First-Order Linear Differential Equation | p. 63 |
Growth and Decay Phenomena | p. 73 |
Linear Models: Mixing and Cooling | p. 80 |
Nonlinear Models: Logistic Equation | p. 87 |
Systems of Differential Equations: A First Look | p. 100 |
Linear Algebra | |
Matrices: Sums and Products | p. 115 |
Systems of Linear Equations | p. 130 |
The Inverse of a Matrix | p. 146 |
Determinants and Cramers Rule | p. 156 |
Vector Spaces and Subspaces | p. 167 |
Basis and Dimension | p. 177 |
Higher-Order Linear Differential Equations | |
The Harmonic Oscillator | p. 195 |
Real Characteristic Roots | p. 210 |
Complex Characteristic Roots | p. 229 |
Undetermined Coefficients | p. 244 |
Variation of Parameters | p. 255 |
Forced Oscillations | p. 261 |
Conservation and Conversion | p. 274 |
Linear Transformations | |
Linear Transformations | p. 285 |
Properties of Linear Transformations | p. 300 |
Eigenvalues and Eigenvectors | p. 311 |
Coordinates and Diagonalization | p. 327 |
Linear Systems of Differential Equations | |
Theory of Linear DE Systems | p. 343 |
Linear Systems with Real Eigenvalues | p. 357 |
Linear Systems with Nonreal Eigenvalues | p. 372 |
Stability and Linear Classification | p. 384 |
Decoupling a Linear DE System | p. 394 |
Matrix Exponential | p. 400 |
Nonhomogeneous Linear Systems | p. 410 |
Nonlinear Systems of Differential Equations | |
Nonlinear Systems | p. 421 |
Linearization | p. 431 |
Numerical Solutions | p. 441 |
Chaos, Strange Attractors, and Period Doubling | p. 449 |
Chaos in Forced Nonlinear Systems | p. 456 |
Laplace Transforms | |
The Laplace Transform and Its Inverse | p. 467 |
Solving DEs and IVPs with Laplace Transforms | p. 475 |
The Step Function and the Delta Function | p. 485 |
The Convolution Integral and the Transfer Function | p. 499 |
Laplace Transform Solution of Linear Systems | p. 509 |
Discrete Dynamical Systems | |
Iterative Equations | p. 517 |
Linear Iterative Systems | p. 530 |
Nonlinear Iterative Equations: Chaos Again | p. 542 |
Control Theory | |
Feedback Controls | p. 557 |
Introduction to Optimal Control | p. 567 |
Pontryagin Maximum Principle | p. 579 |
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