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Partial Differential Equations & Boundary Value Problems with Maple V [Kõva köide]

(Rutgers University, New Brunswick, NJ, USA)
  • Formaat: Hardback, 628 pages, kõrgus x laius: 235x191 mm, kaal: 1100 g
  • Ilmumisaeg: 07-May-1998
  • Kirjastus: Academic Press Inc
  • ISBN-10: 0120644754
  • ISBN-13: 9780120644759
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Partial Differential Equations & Boundary Value Problems with Maple VSuurem pilt
  • Formaat: Hardback, 628 pages, kõrgus x laius: 235x191 mm, kaal: 1100 g
  • Ilmumisaeg: 07-May-1998
  • Kirjastus: Academic Press Inc
  • ISBN-10: 0120644754
  • ISBN-13: 9780120644759
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780120644759.html
Märksõnad:
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. Annotation c. by Book News, Inc., Portland, Or.

George Articulo covers all the material found in traditional partial differentiation equations and boundary value courses in this textbook. Its unique approach allows students to learn the mathematics first, then use Maple graphics capabilities to visualize both static and animated behavior of the solution. The book provides many example problems using commands that render two- or three-dimensional animated graphics. The author focuses on the natural union between partial differential equations and a powerful computational language such as Maple.
* Assumes no previous experience with Maple V; provides a quick review of the language with some simple commands needed to get started and a quick review of linear algebra
* Includes a review material in linear algebra and ordinary differential equations, and their contribution in solving partial differential equations
* Includes an early introduction to Sturm-Liouille boundary problems and generalized eigenfuction expansions
* Numerous example problems in both one and two spatial dimensions, in both the rectangular and cylindrical coordinate systems; an abundant array of exercises problems at the end of each chapter
* CD-ROM enclosed allows for rapid reader involvement, through interaction with real-time animation's of solutions of partial differential equations.

George Articulo covers all the material found in traditional partial differentiation equations and boundary value courses in this textbook. Its unique approach allows students to learn the mathematics first, then use Maple graphics capabilities to visualize both static and animated behavior of the solution. The book provides many example problems using commands that render two- or three-dimensional animated graphics. The author focuses on the natural union between partial differential equations and a powerful computational language such as Maple.
  • Assumes no previous experience with Maple V; provides a quick review of the language with some simple commands needed to get started and a quick review of linear algebra
  • Includes a review material in linear algebra and ordinary differential equations, and their contribution in solving partial differential equations
  • Includes an early introduction to Sturm-Liouille boundary problems and generalized eigenfuction expansions
  • Numerous example problems in both one and two spatial dimensions, in both the rectangular and cylindrical coordinate systems; an abundant array of exercises problems at the end of each chapter

Arvustused

From Book News, Inc. "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, Inc.®, Portland, OR

Muu info

* Assumes no previous experience with Maple V; provides a quick review of the language with some simple commands needed to get started and a quick review of linear algebra * Includes a review material in linear algebra and ordinary differential equations, and their contribution in solving partial differential equations * Includes an early introduction to Sturm-Liouille boundary problems and generalized eigenfuction expansions * Numerous example problems in both one and two spatial dimensions, in both the rectangular and cylindrical coordinate systems; an abundant array of exercises problems at the end of each chapter * CD-ROM enclosed allows for rapid reader involvement, through interaction with real-time animation's of solutions of partial differential equations.
Preface xi
Chapter 0 Basic Review
1(10)
0.1 Preparation for Maple V Worksheets
1(3)
0.2 Preparation for Linear Algebra
4(3)
0.3 Preparation for Ordinary Differential Equations
7(2)
0.4 Preparation for Partial Differential Equations
9(2)
Chapter 1 Ordinary Linear Differential Equations
11(54)
1.1 Introduction
11(1)
1.2 First-Order Linear Differential Equations
12(5)
1.3 First-Order Initial Value Problem
17(2)
1.4 Second-Order Linear Differential Equations with Constant Coefficients
19(5)
1.5 Second-Order Linear Differential Equations with Variable Coefficients
24(3)
1.6 Finding a Second Basis Vector by the Method of Reduction of Order
27(4)
1.7 The Particular Solution by the Method of Variation of Parameters
31(7)
1.8 Initial Value Problem for Second-Order Differential Equations
38(3)
1.9 Frobenius Method of Series Solutions to Ordinary Differential Equations
41(2)
1.10 Series Sine and Cosine Solutions to the Euler Differential Equation
43(5)
1.11 Frobenius Series Solution to the Bessel Differential Equation
48(8)
Chapter Summary
56(2)
Exercises
58(7)
Chapter 2 Sturm-Liouville Eigenvalue Problems and Generalized Fourier Series
65(78)
2.1 Introduction
65(1)
2.2 The Regular Sturm-Liouville Eigenvalue Problem
65(2)
2.3 Green's Formula and the Statement of Orthonormality
67(5)
2.4 The Generalized Fourier Series Expansion
72(4)
2.5 Examples of Regular Sturm-Liouville Eigenvalue Problems
76(39)
2.6 Nonregular or Singular Sturm-Liouville Eigenvalue Problems
115(15)
Chapter Summary
130(1)
Exercises
131(12)
Chapter 3 The Diffusion or Heat Partial Differential Equation
143(50)
3.1 Introduction
143(1)
3.2 One-Dimensional Diffusion Operator in Rectangular Coordinates
143(2)
3.3 Method of Separation of Variables for the Diffusion Equation
145(1)
3.4 Sturm-Liouville Problem for the Diffusion Equation
146(3)
3.5 Initial Conditions for the Diffusion Equation in Rectangular Coordinates
149(2)
3.6 Example Diffusion Problems in Rectangular Coordinates
151(14)
3.7 Verification of Solutions -- Three-Step Verification Procedure
165(4)
3.8 Diffusion Equation in the Cylindrical Coordinate System
169(4)
3.9 Initial Conditions for the Diffusion Equation in Cylindrical Coordinates
173(1)
3.10 Example Diffusion Problems in Cylindrical Coordinates
174(8)
Chapter Summary
182(1)
Exercises
183(10)
Chapter 4 The Wave Partial Differential Equation
193(54)
4.1 Introduction
193(1)
4.2 One-Dimensional Wave Operator in Rectangular Coordinates
193(2)
4.3 Method of Separation of Variables for the Wave Equation
195(2)
4.4 Sturm-Liouville Problem for the Wave Equation
197(3)
4.5 Initial Conditions for the Wave Equation in Rectangular Coordinates
200(3)
4.6 Example Wave Equation Problems in Rectangular Coordinates
203(14)
4.7 Wave Equation in the Cylindrical Coordinate System
217(5)
4.8 Initial Conditions for the Wave Equation in Cylindrical Coordinates
222(2)
4.9 Example Wave Equation Problems in Cylindrical Coordinates
224(9)
Chapter Summary
233(1)
Exercises
234(13)
Chapter 5 The Laplace Partial Differential Equation
247(54)
5.1 Introduction
247(1)
5.2 Laplace Equation in the Rectangular Coordinate System
248(1)
5.3 Sturm-Liouville Problem for the Laplace Equation in Rectangular Coordinates
249(6)
5.4 Example Laplace Problems in the Rectangular Coordinate System
255(13)
5.5 Laplace Equation in Cylindrical Coordinates
268(1)
5.6 Sturm-Liouville Problem for the Laplace Equation in Cylindrical Coordinates
269(5)
5.7 Example Laplace Problems in the Cylindrical Coordinate System
274(15)
Chapter Summary
289(1)
Exercises
290(11)
Chapter 6 The Diffusion Equation in Two Spatial Dimensions
301(60)
6.1 Introduction
301(1)
6.2 Two-Dimensional Diffusion Operator in Rectangular Coordinates
301(2)
6.3 Method of Separation of Variables for the Diffusion Equation in Two Dimensions
303(1)
6.4 Sturm-Liouville Problem for the Diffusion Equation in Two Dimensions
304(4)
6.5 Initial Conditions for the Diffusion Equation in Rectangular Coordinates
308(3)
6.6 Example Diffusion Problems in Rectangular Coordinates
311(13)
6.7 Diffusion Equation in the Cylindrical Coordinate System
324(5)
6.8 Initial Conditions for the Diffusion Equation in Cylindrical Coordinates
329(3)
6.9 Example Diffusion Problems in Cylindrical Coordinates
332(16)
Chapter Summary
348(2)
Exercises
350(11)
Chapter 7 The Wave Equation in Two Spatial Dimensions
361(58)
7.1 Introduction
361(1)
7.2 Two-Dimensional Wave Operator in Rectangular Coordinates
361(2)
7.3 Method of Separation of Variables for the Wave Equation
363(1)
7.4 Sturm-Liouville Problem for the Wave Equation in Two Dimensions
364(5)
7.5 Initial Conditions for the Wave Equation in Rectangular Coordinates
369(2)
7.6 Example Wave Equation Problems in Rectangular Coordinates
371(13)
7.7 Wave Equation in the Cylindrical Coordinate System
384(6)
7.8 Initial Conditions for the Wave Equation in Cylindrical Coordinates
390(3)
7.9 Example Wave Equation Problems in Cylindrical Coordinates
393(15)
Chapter Summary
408(2)
Exercises
410(9)
Chapter 8 Nonhomogeneous Partial Differential Equations
419(70)
8.1 Introduction
419(1)
8.2 Nonhomogeneous Diffusion or Heat Equation
419(9)
8.3 Initial Condition Considerations for the Nonhomogeneous Heat Equation
428(2)
8.4 Example Nonhomogeneous Problems for the Diffusion Equation
430(17)
8.5 Nonhomogeneous Wave Equation
447(9)
8.6 Initial Condition Considerations for the Nonhomogeneous Wave Equation
456(2)
8.7 Example Nonhomogeneous Problems for the Wave Equation
458(20)
Chapter Summary
478(2)
Exercises
480(9)
Chapter 9 Infinite and Semi-Infinite Spatial Domains
489(68)
9.1 Introduction
489(1)
9.2 Fourier Integral
489(3)
9.3 Fourier Sine and Cosine Integrals
492(3)
9.4 Nonhomogeneous Diffusion Equation over Infinite Domains
495(3)
9.5 Convolution Integral Solution for the Diffusion Equation
498(2)
9.6 Nonhomogeneous Diffusion Equation over Semi-Infinite Domains
500(3)
9.7 Example Diffusion Problems over Infinite and Semi-Infinite Domains
503(11)
9.8 Nonhomogeneous Wave Equation over Infinite Domains
514(2)
9.9 Wave Equation over Semi-Infinite Domains
516(4)
9.10 Example Wave Equation Problems over Infinite and Semi-Infinite Domains
520(10)
9.11 Laplace Equation over Infinite and Semi-Infinite Domains
530(5)
9.12 Example Laplace Equation over Infinite and Semi-Infinite Domains
535(6)
Chapter Summary
541(1)
Exercises
542(15)
Chapter 10 Laplace Transform Methods for Partial Differential Equations
557(64)
10.1 Introduction
557(1)
10.2 Laplace Transform Operator
557(2)
10.3 Inverse Transform and Convolution Integral
559(1)
10.4 Laplace Transform Procedures on the Diffusion Equation
560(4)
10.5 Example Laplace Transform Problems for the Diffusion Equation
564(18)
10.6 Laplace Transform Procedures on the Wave Equation
582(4)
10.7 Example Laplace Transform Problems for the Wave Equation
586(20)
Chapter Summary
606(2)
Exercises
608(13)
Selected References on Partial Differential Equations 621(2)
Selected References on Maple V 623(2)
Index 625
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.