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Introduction Background Solutions and Initial Value Problems | |
Direction Fields | |
The Approximation Method of Euler Chapter | |
Summary Technical Writing | |
Exercises Group | |
Projects for Chapter 1 | |
Taylor Series Method | |
Picard's Method | |
Magnetic Dipole | |
The Phase Line | |
First-Order Differential Equations | |
Introduction: Motion of a Falling Body | |
Separable Equations Linear Equations | |
Exact Equations Special Integrating Factors | |
Substitutions and Transformations | |
Chapter Summary Technical Writing | |
Exercises Group | |
Projects for Chapter 2 | |
Differential Equations in Clinical Medicine | |
Torricelli's Law of Fluid Flow | |
The Snowplow Problem | |
Two Snowplows | |
Clairaut Equations and Singular Solutions | |
Multiple Solutions of a First-Order Initial Value Problem | |
Designing a Solar Collector | |
Asymptotic Behavior of Solutions to Linear Equations | |
Utility Functions and Risk Aversion | |
Mathematical Models and Numerical Methods | |
Involving First Order Equations | |
Mathematical Modeling Compartmental Analysis | |
Heating and Cooling of Buildings | |
Newtonian Mechanics Electrical Circuits | |
Improved Euler's Method Higher-Order | |
Numerical Methods: Taylor and Runge-Kutta | |
Chapter Summary Technical Writing | |
Exercises Group | |
Projects for Chapter 3 | |
Dynamics of HIV Infection | |
Aquaculture | |
Curve of Pursuit | |
Aircraft Guidance in a Crosswind | |
Feedback and the Op Amp | |
Bang-Bang Controls | |
Market Equilibrium: Stability and Time Paths | |
Stability of Numerical Methods | |
Period Doubling and Chaos | |
Linear Second-Order Equations | |
Introduction: The Mass-Spring Oscillator | |
Homogeneous Linear Equations | |
The General Solution Auxiliary | |
Equations with Complex Roots | |
Nonhomogeneous Equations: The Method of Undetermined Coefficients | |
The Superposition Principle and Undetermined Coefficients | |
Revisited Variation of Parameters Variable-Coefficient | |
Equations Qualitative Considerations for Variable-Coefficient and Nonlinear Equations | |
A Closer Look at Free Mechanical Vibrations | |
A Closer Look at Forced Mechanical Vibrations | |
Chapter Summary Technical | |
Writing Exercises | |
Group Projects for Chapter 4 | |
Nonlinear Equations Solvable by First-Order Techniques | |
Apollo Reentry | |
Simple Pendulum | |
Linearization of Nonlinear Problems | |
Convolution Method | |
Undetermined Coefficients Using Complex Arithmetic | |
An Alternative to the Method of Undetermined Coefficients | |
Asymptotic Behavior of Solutions | |
Introduction to Systems and Phase Plane Analysis | |
Interconnected Fluid Tanks Elimination | |
Method for Systems with Constant Coefficients | |
Solving Systems and Higher-Order Equations | |
Numerically Introduction to the Phase Plane | |
Applications to Biomathematics: Epidemic and Tumor | |
Growth Models Coupled Mass-Spring Systems | |
Electrical Systems Dynamical Systems, Poincare Maps, and Chaos Chapter | |
Summary Technical Writing | |
Exercises Group | |
Projects for Chapter 5 | |
Designing a Landing System for Interplanetary Travel | |
Things That Bob | |
Hamiltonian Systems | |
Strange Behavior of Competing Species - Part 1 | |
Cleaning Up the Great Lakes | |
Theory of Higher-Order Linear | |
Differential Equations Basic | |
Theory of Linear Differential | |
Equations Homogeneous Linear | |
Equations with Constant Coefficients | |
Undetermined Coefficients and the Annihilator Method | |
Method of Variation of Parameters Chapter Summary Technic | |
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