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E-raamat: Partial Differential Equations and Boundary Value Problems with Maple

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(Rutgers University, New Brunswick, NJ, USA)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 23-Mar-2009
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780080885063
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Partial Differential Equations and Boundary Value Problems with MapleSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 23-Mar-2009
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780080885063
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Partial Differential Equations and Boundary Value Problems with Maple, Second Edition, presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple.

The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours - an investment that provides substantial returns. Maple's animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations.

This updated edition provides a quick overview of the software w/simple commands needed to get started. It includes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equations. It also incorporates an early introduction to Sturm-Liouville boundary problems and generalized eigenfunction expansions. Numerous example problems and end of each chapter exercises are provided.

  • Provides a quick overview of the software w/simple commands needed to get started
  • Includes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equations
  • Incorporates an early introduction to Sturm-Liouville boundary problems and generalized eigenfunction expansions
  • Numerous example problems and end of each chapter exercises


Partial Differential Equations and Boundary Value Problems with Maple presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple's animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations. Maple files can be found on the books website.

Ancillary list: Maple files- http://www.elsevierdirect.com/companion.jsp ISBN=9780123747327

  • Provides a quick overview of the software w/simple commands needed to get started
  • Includes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equations
  • Incorporates an early introduction to Sturm-Liouville boundary problems and generalized eigenfunction expansions
  • Numerous example problems and end of each chapter exercises

Arvustused

Review of the previous edition:"Integrating Maple V animation software and traditional topics of partial differential equations, this text discusses first and second-order differential equations, Sturm-Liouville eigenvalue problems, generalized Fourier series, the diffusion or heat equation and the wave equation in one and two spatial dimensions, the Laplace equation in two spatial dimensions, nonhomogenous versions of the diffusion and wave equations, and Laplace transform methods of solution. The CD-ROM contains real-time animations of solutions of partial differential equations using Maple V." --Book News

Muu info

Offers a unique approach to learning the mathematics first, then use Maple graphics capabilities to visualize both static and animated behavior of the solution
Preface ix
Chapter 0: Basic Review 1
0.1 Preparation for Maple Worksheets
1
0.2 Preparation for Linear Algebra
4
0.3 Preparation for Ordinary Differential Equations
8
0.4 Preparation for Partial Differential Equations
10
Chapter 1: Ordinary Linear Differential Equations 13
1.1 Introduction
13
1.2 First-Order Linear Differential Equations
14
1.3 First-Order Initial-Value Problem
19
1.4 Second-Order Linear Differential Equations with Constant Coefficients
23
1.5 Second-Order Linear Differential Equations with Variable Coefficients
28
1.6 Finding a Second Basis Vector by the Method of Reduction of Order
32
1.7 The Method of Variation of Parameters Second-Order Green's Function
36
1.8 Initial-Value Problem for Second-Order Differential Equations
45
1.9 Frobenius Method of Series Solutions to Ordinary Differential Equations
49
1.10 Series Sine and Cosine Solutions to the Euler Differential Equation
51
1.11 Frobenius Series Solution to the Besse' Differential Equation
56
Chapter Summary
63
Exercises
65
Chapter 2: Sturm-Liouville Eigenvalue Problems and Generalized Fourier Series 73
2.1 Introduction
73
2.2 The Regular Sturm-Liouville Eigenvalue Problem
73
2.3 Green's Formula and the Statement of Orthonormality
75
2.4 The Generalized Fourier Series Expansion
81
2.5 Examples of Regular Sturm-Liouville Eigenvalue Problems
86
2.6 Nonregular or Singular Sturm-Liouville Eigenvalue Problems
129
Chapter Summary
146
Exercises
147
Chapter 3: The Diffusion or Heat Partial Differential Equation 161
3.1 Introduction
161
3.2 One-Dimensional Diffusion Operator in Rectangular Coordinates
161
3.3 Method of Separation of Variables for the Diffusion Equation
163
3.4 Sturm-Liouville Problem for the Diffusion Equation
165
3.5 Initial Conditions for the Diffusion Equation in Rectangular Coordinates
168
3.6 Example Diffusion Problems in Rectangular Coordinates
170
3.7 Verification of Solutions—Three-Step Verification Procedure
186
3.8 Diffusion Equation in the Cylindrical Coordinate System
190
3.9 Initial Conditions for the Diffusion Equation in Cylindrical Coordinates
194
3.10 Example Diffusion Problems in Cylindrical Coordinates
196
Chapter Summary
205
Exercises
206
Chapter 4: The Wave Partial Differential Equation 217
4.1 Introduction
217
4.2 One-Dimensional Wave Operator in Rectangular Coordinates
217
4.3 Method of Separation of Variables for the Wave Equation
219
4.4 Sturm-Liouville Problem for the Wave Equation
221
4.5 Initial Conditions for the Wave Equation in Rectangular Coordinates
224
4.6 Example Wave Equation Problems in Rectangular Coordinates
228
4.7 Wave Equation in the Cylindrical Coordinate System
244
4.8 Initial Conditions for the Wave Equation in Cylindrical Coordinates
249
4.9 Example Wave Equation Problems in Cylindrical Coordinates
251
Chapter Summary
261
Exercises
262
Chapter 5: The Laplace Partial Differential Equation 275
5.1 Introduction
275
5.2 Laplace Equation in the Rectangular Coordinate System
276
5.3 Sturm-Liouville Problem for the Laplace Equation in Rectangular Coordinates
278
5.4 Example Laplace Problems in the Rectangular Coordinate System
284
5.5 Laplace Equation in Cylindrical Coordinates
299
5.6 Sturm-Liouville Problem for the Laplace Equation in Cylindrical Coordinates
301
5.7 Example Laplace Problems in the Cylindrical Coordniate System
307
Chapter Summary
325
Exercises
327
Chapter 6: The Diffusion Equation in Two Spatial Dimensions 339
6.1 Introduction
339
6.2 Two-Dimensional Diffusion Operator in Rectangular Coordinates
339
6.3 Method of Separation of Variables for the Diffusion Equation in Two Dimensions
341
6.4 Sturm-Liouville Problem for the Diffusion Equation in Two Dimensions
342
6.5 Initial Conditions for the Diffusion Equation in Rectangular Coordinates
347
6.6 Example Diffusion Problems in Rectangular Coordinates
351
6.7 Diffusion Equation in the Cylindrical Coordinate System
365
6.8 Initial Conditions for the Diffusion Equation in Cylindrical Coordinates
371
6.9 Example Diffusion Problems in Cylindrical Coordinates
374
Chapter Summary
394
Exercises
395
Chapter 7: The Wave Equation in Two Spatial Dimensions 409
7.1 Introduction
409
7.2 Two-Dimensional Wave Operator in Rectangular Coordinates
409
7.3 Method of Separation of Variables for the Wave Equation
411
7.4 Sturm-Liouville Problem for the Wave Equation in Two Dimensions
412
7.5 Initial Conditions for the Wave Equation in Rectangular Coordinates
417
7.6 Example Wave Equation Problems in Rectangular Coordinates
420
7.7 Wave Equation in the Cylindrical Coordinate System
437
7.8 Initial Conditions for the Wave Equation in Cylindrical Coordinates
443
7.9 Example Wave Equation Problems in Cylindrical Coordinates
447
Chapter Summary
466
Exercises
467
Chapter 8: Nonhomogeneous Partial Differential Equations 477
8.1 Introduction
477
8.2 Nonhomogeneous Diffusion or Heat Equation
477
8.3 Initial Condition Considerations for the Nonhomogeneous Heat Equation
488
8.4 Example Nonhomogeneous Problems for the Diffusion Equation
490
8.5 Nonhomogeneous Wave Equation
510
8.6 Initial Condition Considerations for the Nonhomogeneous Wave Equation
520
8.7 Example Nonhomogeneous Problems for the Wave Equation
523
Chapter Summary
546
Exercises
547
Chapter 9: Infinite and Semi-infinite Spatial Domains 557
9.1 Introduction
557
9.2 Fourier Integral
557
9.3 Fourier Sine and Cosine Integrals
561
9.4 Nonhomogeneous Diffusion Equation over Infinite Domains
564
9.5 Convolution Integral Solution for the Diffusion Equation
568
9.6 Nonhomogeneous Diffusion Equation over Semi-infinite Domains
570
9.7 Example Diffusion Problems over Infinite and Semi-infinite Domains
573
9.8 Nonhomogeneous Wave Equation over Infinite Domains
586
9.9 Wave Equation over Semi-infinite Domains
588
9.10 Example Wave Equation Problems over Infinite and Semi-infinite Domains
594
9.11 Laplace Equation over Infinite and Semi-infinite Domains
606
9.12 Example Laplace Equation over Infinite and Semi-infinite Domains
612
Chapter Summary
619
Exercises
621
Chapter 10: Laplace Transform Methods for Partial Differential Equations 639
10.1 Introduction
639
10.2 Laplace Transform Operator
639
10.3 Inverse Transform and Convolution Integral
641
10.4 Laplace Transform Procedures on the Diffusion Equation
642
10.5 Example Laplace Transform Problems for the Diffusion Equation
646
10.6 Laplace Transform Procedures on the Wave Equation
666
10.7 Example Laplace Transform Problems for the Wave Equation
671
Chapter Summary
693
Exercises
694
References 709
Index 711
Dr. George A. Articolo has 35 years of teaching experience in physics and applied mathematics at Rutgers University, and has been a consultant for several government research laboratories and aerospace corporations. He has a Ph.D. in mathematical physics with degrees from Temple University and Rensselaer Polytechnic Institute.
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