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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