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| Prologue | |
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| Goals | |
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| A modeling example | |
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| Differential equations and solutions | |
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| Models from Conservation Laws | |
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| Simple population growth | |
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| Emigration and competition | |
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| Heat flow | |
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| Multiple species | |
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| Numerical and Graphical Tools | |
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| Numerical methods | |
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| Graphs, direction fields, and phase lines | |
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| Steady states, stability, and local linearization | |
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| Analytic Tools for One Dimension | |
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| Basic definitions | |
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| Separation of variables | |
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| Characteristic equations | |
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| Undetermined coefficients | |
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| Variation of parameters | |
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| Existence and uniqueness | |
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| Two-Dimensional Models: Oscillating Systems. Overviewpopulations, position, and velocity | |
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| Spring-mass systems | |
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| Pendulum | |
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| RLC circuits | |
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| Analytic Tools for Two Dimensions: Basic definitions | |
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| The Wronskian and linear independence | |
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| Characteristic equations: real roots | |
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| Characteristic equations: complex roots | |
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| Unforced spring-mass systems | |
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| Undetermined coefficients | |
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| Forced spring-mass systems | |
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| Linear vs. nonlinear | |
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| Graphical Tools for Two Dimensions | |
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| Back to the phase plane | |
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| More phase plane: nullclines, steady states, stability | |
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| Limit cycles | |
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| Analytic Tools for Higher Dimensions: Systems | |
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| Motivation and review | |
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| Basic definitions | |
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| Homogeneous systems | |
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| Connections with the phase plane | |
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| Nonhomogeneous systems: undetermined coefficients | |
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| Diffusion Models and Boundary-Value Problems | |
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| Diffusion models | |
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| Boundary-value problems | |
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| Buckling | |
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| Time-dependent diffusion | |
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| Fourier methods. Numerical tools: time-dependent diffusion | |
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| Finite difference approximations to steady states | |
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| Laplace Transform | |
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| The transform idea: jumps and filters | |
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| Inverse transforms. Other properties of Laplace transforms | |
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| Ramps and jumps | |
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| The unit impulse function | |
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| Control applications | |
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| More Analytic Tools for Two Dimensions | |
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| Variation of parameters for systems | |
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| Variation of parameters for second-order equations | |
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| Reduction of order. Cauchy-Euler equations | |
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| Power series methods | |
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| Regular singular points | |
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| Solution method summary | |
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| Appendicies | |
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| Bibliography | |
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| Solutions to Selected Exercises | |
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| Index | |
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| Matlab tutorial | |
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| Calculus review | |