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What is included with this book?
Introduction | |
Mathematical Models, Solutions, and Direction Fields | |
Linear Equations: Method of Integrating Factors | |
Numerical Approximations: Euler's Method | |
Classification of Differential Equations | |
First Order Differential Equations | |
Separable Equations | |
Modeling with First Order Equations | |
Differences between Linear and Nonlinear Equations | |
Autonomous Equations and Population Dynamics | |
Exact Equations and Integrating Factors | |
Accuracy of Numerical Methods | |
Improved Euler and Runge-Kutta Methods | |
Projects | |
Harvesting a Renewable Resource | |
Designing a Drip Dispenser for a Hydrology Experiment | |
A Mathematical Model of a Groundwater Contaminant Source | |
Monte-Carlo Option Pricing: Pricing Financial Options by Flipping a Coin | |
Systems of Two First Order Equations | |
Systems of Two Linear Algebraic Equations | |
Systems of Two First Order Linear Differential Equations | |
Homogeneous Linear Systems with Constant Coefficients | |
Complex Eigenvalues | |
Repeated Eigenvalues | |
A Brief Introduction to Nonlinear Systems | |
Numerical Methods for Systems of First Order Equations | |
Projects | |
Eigenvalue Placement Design of a Satellite Attitude Control System | |
Estimating Rate Constants for an Open Two-Compartment Model | |
The Ray Theory of Wave Propagation | |
A Blood-Brain Pharmacokinetic Model | |
Second Order Linear Equations | |
Definitions and Examples | |
Theory of Second Order Linear Homogeneous Equations | |
Linear Homogeneous Equations with Constant Coefficients | |
Mechanical and Electrical Vibrations | |
Nonhomogeneous Equations: Method of Undetermined Coefficients | |
Forced Vibrations, Frequency Response, and Resonance | |
Variation of Parameters | |
Projects | |
A Vibration Insulation Problem | |
Linearization of a Nonlinear Mechanical System | |
A Spring-Mass Event Problem | |
Uniformly Distributing Points on a Sphere | |
Euler-Lagrange Equations | |
The Laplace Transform | |
Definition of the Laplace Transform | |
Properties of the Laplace Transform | |
The Inverse Laplace Transform | |
Solving Differential Equations with Laplace Transforms | |
Discontinuous Functions and Periodic Functions | |
Differential Equations with Discontinuous Forcing Functions | |
Impulse Functions | |
Convolution Integrals and Their Applications | |
Linear Systems and Feedback Control | |
Projects | |
An Electric Circuit Problem | |
Effects of Pole Locations on Step Responses of Second Order Systems | |
The Watt Governor, Feedback Control, and Stability | |
Systems of First Order Linear Equations | |
Definitions and Examples | |
Basic Theory of First Order Linear Systems | |
Homogeneous Linear Systems with Constant Coefficients | |
Complex Eigenvalues | |
Fundamental Matrices and the Exponential of a Matrix | |
Nonhomogeneous Linear Systems | |
Defective Matrices | |
Projects | |
A Compartment Model of Heat Flow in a Rod | |
Earthquakes and Tall Buildings | |
Controlling a Spring-Mass System to Equilibrium | |
Nonlinear Differential Equations and Stability | |
Almost Linear Systems | |
Competing Species | |
Predator-Prey Equations | |
Periodic Solutions and Limit Cycles | |
Chaos and Strange Attractors: The Lorenz Equations | |
Projects | |
Modeling of Epidemics | |
Harvesting in a Competitive Environment | |
The Rossler System | |
[Chapters 8-10 in Boundary Value Problems version only] | |
Series Solutions of Second Order Equations | |
Review of Power Systems | |
Series Solutions Near an Ordinary Point, Part I | |
Series Solutions Near an Ordinary Point, Part II | |
Regular Singular Points | |
Series Solutions Near a Regular Singular Point, Part I | |
Series Solutions Near a Regular Singular Point, Part II | |
Bessel's Equation | |
Projects | |
Distraction Through a Circular Aperture | |
Hermite Polynomials and the Quantum Mechanical Harmonic Oscillator | |
Perturbation Methods | |
Partial Differential Equations and Fourier Series | |
Two-Point Boundary Value Problems | |
Fourier Series | |
The Fourier Convergence Theorem | |
Even and Odd Functions | |
Separation of Variables, Heat Conduction in a Rod | |
Other Heat Conduction Problems | |
The Wave Equation, Vibrations of an Elastic String | |
Laplace's Equation | |
Projects | |
Estimating the Diffusion Coefficient in the Heat Equation | |
The Transmission Line Problem | |
Solving Poisson's Equation by Finite Differences | |
Boundary Value Problems and Sturm-Liouville Theory | |
The Occurrence of Two-Point Boundary Value Problems | |
Sturm-Liouville Boundary Value Problems | |
Nonhomogeneous Boundary Value Problems | |
Singular Sturm-Liouville Problems | |
Further Remarks on the Method of Separation of Variables: A Bessel Series | |
Expansion | |
Series of Orthogonal Functions: Mean Convergence | |
Projects | |
Dynamic Behavior of a Hanging Cable | |
Advection-Dispersion: A Model for Solute Transport in Saturated Porous | |
Media | |
Fisher's Equation for Population Growth and Dispersion | |
Matrices and Linear Algebra | |
Matrices | |
Systems of Linear Algebraic Equations, Linear Independence, and Rank | |
Determinants and Inverses | |
The Eigenvalue Problem | |
Complex Variables | |
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