Differential Equations and Boundary Value Problems Computing and Modeling

ISBN-10: 0130797707

ISBN-13: 9780130797704

Edition: 2nd 2000

List price: $110.00
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Description:

For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course while maintaining the solid foundation of algebraic techniques that are still essential to science and engineering students. It reflects the new excitement in differential equations as the availability of technical computing environments likeMaple, Mathematica, and MATLAB reshape the role and applications of the discipline. New technology has motivated a shift in emphasis from traditional, manual methods to both qualitative and computer-based methods that render accessible a wider range of realistic applications. With this in mind, the text augments core skills with conceptual perspectives that students will need for the effective use of differential equations in their subsequent work and study.
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Book details

List price: $110.00
Edition: 2nd
Copyright year: 2000
Publisher: Prentice Hall PTR
Publication date: 6/11/1999
Binding: Hardcover
Pages: 787
Size: 8.50" wide x 10.00" long x 1.25" tall
Weight: 3.190
Language: English

First-Order Differential Equations
Differential Equations and Mathematical Models
Integrals as General and Particular Solutions
Direction Fields and Solutions Curves
Separable Equations and Applications
Linear First-Order Equations
Substitution Methods and Exact Equations
Mathematical Models and Numerical Methods
Population Models
Equilibrium Solutions and Stability
Acceleration-Velocity Models
Numerical Approximation: Euler's Method
A Closer Look at the Euler Method
The Runge-Kutta Method
Linear Equations of Higher Order
Introduction: Second-Order Linear Equations
General Solutions of Linear Equations
Homogeneous Equations with Constant Coefficients
Mechanical Vibrations
Nonhomogeneous Equations and the Method of Undetermined Coefficients
Forced Oscillations and Resonance
Electrical Circuits
Endpoint Problems and Eigenvalues
Introduction to Systems of Differential Equations
First-Order Systems and Applications
The Method of Elimination
Numerical Methods for Systems
Linear Systems of Differential Equations
Linear Systems and Matrices
The Eigenvalue Method for Homogeneous Systems
Second Order Systems and Mechanical Applications
Multiple Eignvalue Solutions
Matrix Exponentials and Linear Systems
Nonhomogeneous Linear Systems
Nonlinear Systems and Phenomena
Stability and the Phase Plane
Linear and Almost Linear Systems
Ecological Models: Predators and Competitors
Nonlinear Mechanical Systems
Chaos in Dynamical Systems
Laplace Transform Methods
Laplace Transforms and Inverse Transforms
Transformation of Initial Value Problems
Translation and Partial Fractions
Derivatives, Integrals, and Products of Transforms
Periodic and Piecewise Continuous Forcing Functions
Impulses and Delta Functions
Power Series Methods
Introduction and Review of Power Series
Series Solutions Near Ordinary Points
Regular Singular Points
Method of Frobenius: The Exceptional Cases
Bessel's Equation
Applications of Bessel Functions
Fourier Series Methods
Periodic Functions and Trigonometric Series
General Fourier Series and Convergence
Fourier Sine and Cosine Series
Applications of Fourier Series
Heat Conduction and Separation of Variables
Vibrating Strings and the One-Dimensional Wave Equation
Steady-State Temperature and Laplace's Equation
Eigenvalues and Boundary Value Problems
Strum-Liouville Problems and Eigenfunction Expansions
Applications of Eigenfunction Series
Steady Periodic Solutions and Natural Frequencies
Cylindrical Coordinate Problems
Higher-Dimensional Phenomena
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