Fundamentals of Differential Equations with Boundary Value Problems with IDE CD (Saleable Package)

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  • Edition: 5th
  • Format: Hardcover w/CD
  • Copyright: 2008-01-01
  • Publisher: Addison Wesley
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Key Message:Fundamentals of Differential Equationspresents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software. Topics: Introduction, First-Order Differential Equations, Mathematical Models and Numerical Methods Involving First Order Equations, Linear Second-Order Equations, Introduction to Systems and Phase Plane Analysis, Theory of Higher-Order Linear Differential Equations, Laplace Transforms, Series Solutions of Differential Equations, Matrix Methods for Linear Systems, Partial Differential Equations, Eigenvalue Problems and Sturm-Liouville Equations, Stability of Autonomous Systems, Existence and Uniqueness Theory Market: For all readers interested in Differential Equations.

Table of Contents

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
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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