Differential Equations Theory, Technique, and Practice

Name: Differential Equations Theory, Technique, and Practice
Price: 14.54 USD
Availability: InStock
ISBN: 9780072863154

ISBN-10: 0072863153

ISBN-13: 9780072863154

Edition: 2007

Authors: George F. Simmons, Steven G. Krantz

List price: $157.50

30 day, 100% satisfaction guarantee!

Marketplace

2 new & used from $14.54

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

Book details

List price: $157.50
Copyright year: 2007
Publisher: McGraw-Hill Higher Education
Publication date: 1/4/2006
Binding: Hardcover
Pages: 544
Size: 6.50" wide x 9.25" long x 1.00" tall
Weight: 1.848
Language: English

Preface	p. VII
What is a Differential Equation?	p. 1
Introductory Remarks	p. 2
The Nature of Solutions	p. 4
Separable Equations	p. 10
First-Order Linear Equations	p. 13
Exact Equations	p. 17
Orthogonal Trajectories and Families of Curves	p. 22
Homogeneous Equations	p. 26
Integrating Factors	p. 29
Reduction of Order	p. 33
Dependent Variable Missing	p. 33
Independent Variable Missing	p. 35
The Hanging Chain and Pursuit Curves	p. 38
The Hanging Chain	p. 38
Pursuit Curves	p. 42
Electrical Circuits	p. 45
Anatomy of an Application: The Design of a Dialysis Machine	p. 49
Problems for Review and Discovery	p. 53
Second-Order Linear Equations	p. 57
Second-Order Linear Equations with Constant Coefficients	p. 58
The Method of Undetermined Coefficients	p. 63
The Method of Variation of Parameters	p. 67
The Use of a Known Solution to Find Another	p. 71
Vibrations and Oscillations	p. 75
Undamped Simple Harmonic Motion	p. 75
Damped Vibrations	p. 77
Forced Vibrations	p. 80
A Few Remarks about Electricity	p. 82
Newton's Law of Gravitation and Kepler's Laws	p. 84
Kepler's Second Law	p. 86
Kepler's First Law	p. 87
Kepler's Third Law	p. 89
Higher Order Linear Equations, Coupled Harmonic Oscillators	p. 93
Historical Note: Euler	p. 99
Anatomy of an Application: Bessel Functions and the Vibrating Membrane	p. 101
Problems for Review and Discovery	p. 105
Qualitative Properties and Theoretical Aspects	p. 109
Review of Linear Algebra	p. 110
Vector Spaces	p. 110
The Concept of Linear Independence	p. 111
Bases	p. 113
Inner Product Spaces	p. 114
Linear Transformations and Matrices	p. 115
Eigenvalues and Eigenvectors	p. 117
A Bit of Theory	p. 119
Picard's Existence and Uniqueness Theorem	p. 125
The Form of a Differential Equation	p. 125
Picard's Iteration Technique	p. 126
Some Illustrative Examples	p. 127
Estimation of the Picard Iterates	p. 129
Oscillations and the Sturm Separation Theorem	p. 130
The Sturm Comparison Theorem	p. 138
Anatomy of an Application: The Green's Function	p. 142
Problems for Review and Discovery	p. 146
Power Series Solutions and Special Functions	p. 149
Introduction and Review of Power Series	p. 150
Review of Power Series	p. 150
Series Solutions of First-Order Differential Equations	p. 159
Second-Order Linear Equations: Ordinary Points	p. 164
Regular Singular Points	p. 171
More on Regular Singular Points	p. 177
Gauss's Hypergeometric Equation	p. 184
Historical Note: Gauss	p. 189
Historical Note: Abel	p. 190
Anatomy of an Application: Steady-State Temperature in a Ball	p. 192
Problems for Review and Discovery	p. 194
Fourier Series: Basic Concepts	p. 197
Fourier Coefficients	p. 198
Some Remarks about Convergence	p. 207
Even and Odd Functions: Cosine and Sine Series	p. 211
Fourier Series on Arbitrary Intervals	p. 218
Orthogonal Functions	p. 221
Historical Note: Riemann	p. 225
Anatomy of an Application: Introduction to the Fourier Transform	p. 227
Problems for Review and Discovery	p. 236
Partial Differential Equations and Boundary Value Problems	p. 239
Introduction and Historical Remarks	p. 240
Eigenvalues, Eigenfunctions, and the Vibrating String	p. 243
Boundary Value Problems	p. 243
Derivation of the Wave Equation	p. 244
Solution of the Wave Equation	p. 246
The Heat Equation	p. 251
The Dirichlet Problem for a Disc	p. 256
The Poisson Integral	p. 259
Sturm-Liouville Problems	p. 262
Historical Note: Fourier	p. 267
Historical Note: Dirichlet	p. 268
Anatomy of an Application: Some Ideas from Quantum Mechanics	p. 270
Problems for Review and Discovery	p. 273
Laplace Transforms	p. 277
Introduction	p. 278
Applications to Differential Equations	p. 280
Derivatives and Integrals of Laplace Transforms	p. 285
Convolutions	p. 291
Abel's Mechanical Problem	p. 293
The Unit Step and Impulse Functions	p. 298
Historical Note: Laplace	p. 305
Anatomy of an Application: Flow Initiated by an Impulsively Started Flat Plate	p. 306
Problems for Review and Discovery	p. 309
The Calculus of Variations	p. 315
Introductory Remarks	p. 316
Euler's Equation	p. 319
Isoperimetric Problems and the Like	p. 327
Lagrange Multipliers	p. 328
Integral Side Conditions	p. 329
Finite Side Conditions	p. 333
Historical Note: Newton	p. 338
Anatomy of an Application: Hamilton's Principle and its Implications	p. 340
Problems for Review and Discovery	p. 344
Numerical Methods	p. 347
Introductory Remarks	p. 348
The Method of Euler	p. 349
The Error Term	p. 353
An Improved Euler Method	p. 357
The Runge-Kutta Method	p. 360
Anatomy of an Application: A Constant Perturbation Method for Linear, Second-Order Equations	p. 365
Problems for Review and Discovery	p. 368
Systems of First-Order Equations	p. 371
Introductory Remarks	p. 372
Linear Systems	p. 374
Homogeneous Linear Systems with Constant Coefficients	p. 382
Nonlinear Systems: Volterra's Predator-Prey Equations	p. 389
Anatomy of an Application: Solution of Systems with Matrices and Exponentials	p. 395
Problems for Review and Discovery	p. 400
The Nonlinear Theory	p. 403
Some Motivating Examples	p. 404
Specializing Down	p. 404
Types of Critical Points: Stability	p. 409
Critical Points and Stability for Linear Systems	p. 417
Stability by Liapunov's Direct Method	p. 427
Simple Critical Points of Nonlinear Systems	p. 432
Nonlinear Mechanics: Conservative Systems	p. 439
Periodic Solutions: The Poincare-Bendixson Theorem	p. 444
Historical Note: Poincare	p. 452
Anatomy of an Application: Mechanical Analysis of a Block on a Spring	p. 454
Problems for Review and Discovery	p. 457
Dynamical Systems	p. 461
Flows	p. 462
Dynamical Systems	p. 464
Stable and Unstable Fixed Points	p. 466
Linear Dynamics in the Plane	p. 468
Some Ideas from Topology	p. 475
Open and Closed Sets	p. 475
The Idea of Connectedness	p. 476
Closed Curves in the Plane	p. 478
Planar Autonomous Systems	p. 480
Ingredients of the Proof of Poincare-Bendixson	p. 480
Anatomy of an Application: Lagrange's Equations	p. 489
Problems for Review and Discovery	p. 493
Bibliography	p. 495
Answers to Odd-Numbered Exercises	p. 497
Index	p. 525
Table of Contents provided by Ingram. All Rights Reserved.