Introduction to Differential Equations with Dynamical Systems / Edition 1

Introduction to Differential Equations with Dynamical Systems / Edition 1

1.0 1
by Stephen L. Campbell
     
 

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ISBN-10: 0691124744

ISBN-13: 2900691124741

Pub. Date: 04/01/2008

Publisher: Princeton University Press

Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on

Overview

Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman-using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs-have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length. A student solutions manual is available at press.princeton.edu.

About the Author:
Stephen L. Campbell is professor of mathematics and director of the graduate program in mathematics at North Carolina State University

About the Author:
Richard Haberman is professor of mathematics at Southern Methodist University. Campbell and Haberman are prolific researchers in applied mathematics and the authors of a number of textbooks

Product Details

ISBN-13:
2900691124741
Publisher:
Princeton University Press
Publication date:
04/01/2008
Edition description:
New Edition
Pages:
444

Table of Contents


Preface     ix
First-Order Differential Equations and Their Applications     1
Introduction to Ordinary Differential Equations     1
The Definite Integral and the Initial Value Problem     4
The Initial Value Problem and the Indefinite Integral     5
The Initial Value Problem and the Definite Integral     6
Mechanics I: Elementary Motion of a Particle with Gravity Only     8
First-Order Separable Differential Equations     13
Using Definite Integrals for Separable Differential Equations     16
Direction Fields     19
Existence and Uniqueness     25
Euler's Numerical Method (optional)     31
First-Order Linear Differential Equations     37
Form of the General Solution     37
Solutions of Homogeneous First-Order Linear Differential Equations     39
Integrating Factors for First-Order Linear Differential Equations     42
Linear First-Order Differential Equations with Constant Coefficients and Constant Input     48
Homogeneous Linear Differential Equations with Constant Coefficients     48
Constant Coefficient Linear Differential Equations with Constant Input     50
Constant Coefficient Differential Equations with Exponential Input     52
Constant Coefficient Differential Equations with Discontinuous Input     52
Growth and Decay Problems     59
A First Model of Population Growth     59
Radioactive Decay     65
Thermal Cooling     68
Mixture Problems     74
Mixture Problems with a Fixed Volume     74
Mixture Problems with Variable Volumes     77
Electronic Circuits     82
Mechanics II: Including Air Resistance     88
Orthogonal Trajectories (optional)     92
Linear Second- and Higher-Order Differential Equations     96
General Solution of Second-Order Linear Differential Equations     96
Initial Value Problem (for Homogeneous Equations)     100
Reduction of Order     107
Homogeneous Linear Constant Coefficient Differential Equations (Second Order)     112
Homogeneous Linear Constant Coefficient Differential Equations (nth-Order)     122
Mechanical Vibrations I: Formulation and Free Response     124
Formulation of Equations     124
Simple Harmonic Motion (No Damping, [delta] = 0)     128
Free Response with Friction ([delta] > 0)     135
The Method of Undetermined Coefficients     142
Mechanical Vibrations II: Forced Response     159
Friction is Absent ([delta] = 0)     159
Friction is Present ([delta] > 0) (Damped Forced Oscillations)     168
Linear Electric Circuits     174
Euler Equation     179
Variation of Parameters (Second-Order)     185
Variation of Parameters (nth-Order)     193
The Laplace Transform     197
Definition and Basic Properties     197
The Shifting Theorem (Multiplying by an Exponential)     205
Derivative Theorem (Multiplying by t)     210
Inverse Laplace Transforms (Roots, Quadratics, and Partial Fractions)     213
Initial Value Problems for Differential Equations     225
Discontinuous Forcing Functions     234
Solution of Differential Equations     239
Periodic Functions     248
Integrals and the Convolution Theorem     253
Derivation of the Convolution Theorem (optional)     256
Impulses and Distributions     260
An Introduction to Linear Systems of Differential Equations and Their Phase Plane     265
Introduction     265
Introduction to Linear Systems of Differential Equations     268
Solving Linear Systems Using Eigenvalues and Eigenvectors of the Matrix      269
Solving Linear Systems if the Eigenvalues are Real and Unequal     272
Finding General Solutions of Linear Systems in the Case of Complex Eigenvalues     276
Special Systems with Complex Eigenvalues (optional)     279
General Solution of a Linear System if the Two Real Eigenvalues are Equal (Repeated) Roots     281
Eigenvalues and Trace and Determinant (optional)     283
The Phase Plane for Linear Systems of Differential Equations     287
Introduction to the Phase Plane for Linear Systems of Differential Equations     287
Phase Plane for Linear Systems of Differential Equations     295
Real Eigenvalues     296
Complex Eigenvalues     304
General Theorems     310
Mostly Nonlinear First-Order Differential Equations     315
First-Order Differential Equations     315
Equilibria and Stability     316
Equilibrium     316
Stability     317
Review of Linearization     318
Linear Stability Analysis     318
One-Dimensional Phase Lines     322
Application to Population Dynamics: The Logistic Equation     327
Nonlinear Systems of Differential Equations in the Plane     332
Introduction      332
Equilibria of Nonlinear Systems, Linear Stability Analysis of Equilibrium, and the Phase Plane     335
Linear Stability Analysis and the Phase Plane     336
Nonlinear Systems: Summary, Philosophy, Phase Plane, Direction Field, Nullclines     341
Population Models     349
Two Competing Species     350
Predator-Prey Population Models     356
Mechanical Systems     363
Nonlinear Pendulum     363
Linearized Pendulum     364
Conservative Systems and the Energy Integral     364
The Phase Plane and the Potential     367
Answers to Odd-Numbered Exercises     379
Index     429

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Introduction to Differential Equations with Dynamical Systems 1 out of 5 based on 0 ratings. 1 reviews.
Anonymous More than 1 year ago
Cant get past the table of contents. Dont buy on nook.