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Differential Equations Modeling with MATLAB

ISBN-10: 013736539X
ISBN-13: 9780137365395
Edition: 1999
Authors: Paul W. Davis
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Description: For undergraduate engineering and science courses in Differential Equations. This progressive text on differential equations utilizes MATLAB's state-of-the-art computational and graphical tools right from the start to help students probe a variety  More...

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Book details

List price: $111.00
Copyright year: 1999
Publisher: Prentice Hall PTR
Publication date: 4/2/1999
Binding: Hardcover
Pages: 641
Size: 8.50" wide x 9.50" long x 1.00" tall
Weight: 2.948
Language: English

For undergraduate engineering and science courses in Differential Equations. This progressive text on differential equations utilizes MATLAB's state-of-the-art computational and graphical tools right from the start to help students probe a variety of mathematical models. Ideas are examined from four perspectives: geometric, analytic, numeric, and physical. Students are encouraged to develop problem-solving skills and independent judgment as they derive models, select approaches to their analysis, and find answers to the original, physical questions. Both qualitative and algebraic tools are stressed.

Prologue
Goals
A modeling example
Differential equations and solutions
Models from Conservation Laws
Simple population growth
Emigration and competition
Heat flow
Multiple species
Numerical and Graphical Tools
Numerical methods
Graphs, direction fields, and phase lines
Steady states, stability, and local linearization
Analytic Tools for One Dimension
Basic definitions
Separation of variables
Characteristic equations
Undetermined coefficients
Variation of parameters
Existence and uniqueness
Two-Dimensional Models: Oscillating Systems. Overviewpopulations, position, and velocity
Spring-mass systems
Pendulum
RLC circuits
Analytic Tools for Two Dimensions: Basic definitions
The Wronskian and linear independence
Characteristic equations: real roots
Characteristic equations: complex roots
Unforced spring-mass systems
Undetermined coefficients
Forced spring-mass systems
Linear vs. nonlinear
Graphical Tools for Two Dimensions
Back to the phase plane
More phase plane: nullclines, steady states, stability
Limit cycles
Analytic Tools for Higher Dimensions: Systems
Motivation and review
Basic definitions
Homogeneous systems
Connections with the phase plane
Nonhomogeneous systems: undetermined coefficients
Diffusion Models and Boundary-Value Problems
Diffusion models
Boundary-value problems
Buckling
Time-dependent diffusion
Fourier methods. Numerical tools: time-dependent diffusion
Finite difference approximations to steady states
Laplace Transform
The transform idea: jumps and filters
Inverse transforms. Other properties of Laplace transforms
Ramps and jumps
The unit impulse function
Control applications
More Analytic Tools for Two Dimensions
Variation of parameters for systems
Variation of parameters for second-order equations
Reduction of order. Cauchy-Euler equations
Power series methods
Regular singular points
Solution method summary
Appendicies
Bibliography
Solutions to Selected Exercises
Index
Matlab tutorial
Calculus review

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