Differential Equations with Boundary-Value Problems

ISBN-10: 0534418872

ISBN-13: 9780534418878

Edition: 6th 2005

List price: $284.95
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Description: Now enhanced with the innovative DE Tools CD-ROM and the iLrn teaching and learning system, this proven text explains the "how" behind the material and strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This accessible text speaks to students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. This book was written with the student's understanding firmly in mind. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

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Book details

List price: $284.95
Edition: 6th
Copyright year: 2005
Publisher: Brooks/Cole
Publication date: 10/19/2004
Binding: Hardcover
Pages: 760
Size: 8.75" wide x 11.00" long x 1.25" tall
Weight: 3.432
Language: English

Preface
Acknowledgments
Introduction to Differential Equations
Definitions and Terminology
Initial-Value Problems
Differential Equations as Mathematical Models
Chapter 1 in Review
First-Order Differential Equations
Solution Curves Without the Solution
Separable Variables
Linear Equations
Exact Equations
Solutions by Substitutions
A Numerical Solution
Chapter 2 in Review
Modeling with First-Order Differential Equations
Linear Equations
Nonlinear Equations
Systems of Linear and Nonlinear Differential Equations
Chapter 3 in Review
Project Module: Harvesting of Renewable Natural Resources
Higher-Order Differential Equations
Preliminary Theory: Linear Equations
Initial-Value and Boundary-Value Problems
Homogeneous Equations
Nonhomogeneous Equations
Reduction of Order
Homogeneous Linear Equations with Constant Coefficients
Undetermined Coefficients--Superposition Approach
Undetermined Coefficients--Annihilator Approach
Variation of Parameters
Cauchy-Euler Equation
Solving Systems of Linear Equations by Elimination
Nonlinear Equations
Chapter 4 in Review
Modeling with Higher-Order Differential Equations
Linear Equations: Initial-Value Problems
Spring/Mass Systems: Free Undamped Motion
Spring/Mass Systems: Free Damped Motion
Spring/Mass Systems: Driven Motion
Series Circuit Analogue
Linear Equations: Boundary-Value Problems
Nonlinear Equations
Chapter 5 in Review
Project Module: The Collapse of the Tacoma Narrows Suspension Bridge
Series Solutions of Linear Equations
Solutions About Ordinary Points
Review of Power Series
Power Series Solutions
Solutions About Singular Points
Two Special Equations
Chapter 6 in Review
The Laplace Transform
Definition of the Laplace Transform
Inverse Transform and Transforms of Derivatives
Translation Theorems
Translation on the s-Axis
Translation on the t-Axis
Additional Operational Properties
Dirac Delta Function
Systems of Linear Equations
Chapter 7 in Review
Systems of Linear First-Order Differential Equations
Preliminary Theory
Homogeneous Linear Systems with Constant Coefficients
Distinct Real Eigenvalues
Repeated Eigenvalues
Complex Eigenvalues
Variation of Parameters
Matrix Exponential
Chapter 8 in Review
Project Module: Earthquake Shaking of Multistory Buildings
Numerical Solutions of Ordinary Differential Equations
Euler Methods and Error Analysis
Runge-Kutta Methods
Multistep Methods
Higher-Order Equations and Systems
Second-Order Boundary-Value Problems
Chapter 9 in Review
Plane Autonomous Systems and Stability
Autonomous Systems, Critical Points, and Periodic Solutions
Stability of Linear Systems
Linearization and Local Stability
Modeling Using Autonomous Systems
Chapter 10 in Review
Orthogonal Functions and Fourier Series
Orthogonal Functions
Fourier Series
Fourier Cosine and Sine Series
Sturm-Liouville Problem
Bessel and Legendre Series
Fourier-Bessel Series
Fourier-Legendre Series
Chapter 11 in Review
Partial Differential Equations and Boundary-Value Problems in Rectangular Coordinates
Separable Partial Differential Equations
Classical Equations and Boundary-Value Problems
Heat Equation
Wave Equation
Laplace's Equation
Nonhomogeneous Equations and Boundary Conditions
Orthogonal Series Expansions
Boundary-Value Problems Involving Fourier Series in Two Variables
Chapter 12 in Review
Boundary-Value Problems in other Coordinate Systems
Problems Involving Laplace's Equation in Polar Coordinates
Problems in Polar and Cylindrical Coordinates: Bessel Functions
Problems in Spherical Coordinates: Legendre Polynomials
Chapter 13 in Review
Integral Transform Method
Error Function
Applications of the Laplace Transform
Fourier Integral
Fourier Transforms
Chapter 14 in Review
Numerical Solutions of Partial Differential Equations
Elliptic Equations
Parabolic Equations
Hyperbolic Equations
Chapter 15 in Review
Appendixes
Gamma Function
Introduction to Matrices
Laplace Transforms
Selected Answers for Odd-Numbered Problems
Index
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