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E-raamat: Introduction to Partial Differential Equations for Scientists and Engineers Using Mathematica [Taylor & Francis e-raamat]

(Sharda University, Greater Noida, India), (South Carolina State University, Orangeburg, USA)
  • Formaat: 648 pages, 37 Tables, black and white; 146 Illustrations, black and white
  • Ilmumisaeg: 23-Oct-2013
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9780429096303
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  • Taylor & Francis e-raamat
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Introduction to Partial Differential Equations for Scientists and Engineers Using MathematicaSuurem pilt
  • Formaat: 648 pages, 37 Tables, black and white; 146 Illustrations, black and white
  • Ilmumisaeg: 23-Oct-2013
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9780429096303
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9780429096303
With special emphasis on engineering and science applications, this textbook provides a mathematical introduction to the field of partial differential equations (PDEs). The text represents a new approach to PDEs at the undergraduate level by presenting computation as an integral part of the study of differential equations. The authors use the computer software Mathematica® along with graphics to improve understanding and interpretation of concepts. The book also presents solutions to selected examples as well as exercises in each chapter. Topics include Laplace and Fourier transforms as well as Sturm-Liuville Boundary Value Problems.
Preface ix
Acknowledgments xiii
1 Fourier Series 1(82)
1.1 Fourier Series of Periodic Functions
2(17)
1.2 Convergence of Fourier Series
19(18)
1.3 Integration and Differentiation of Fourier Series
37(24)
1.4 Fourier Sine and Cosine Series
61(13)
1.5 Projects Using Mathematica
74(9)
2 Integral Transforms 83(62)
2.1 The Laplace Transform
84(32)
2.1.1 Definition and Properties of the Laplace Transform
84(12)
2.1.2 Step and Impulse Functions
96(6)
2.1.3 Initial-Value Problems and the Laplace Transform
102(7)
2.1.4 The Convolution Theorem
109(7)
2.2 Fourier Transforms
116(23)
2.2.1 Definition of Fourier Transforms
116(11)
2.2.2 Properties of Fourier Transforms
127(12)
2.3 Projects Using Mathematica
139(6)
3 Sturm-Liouville Problems 145(59)
3.1 Regular Sturm-Liouville Problems
145(14)
3.2 Eigenfunction Expansions
159(9)
3.3 Singular Sturm-Liouville Problems
168(31)
3.3.1 Definition of Singular Sturm-Liouville Problems
168(2)
3.3.2 Legendre's Differential Equation
170(12)
3.3.3 Bessel's Differential Equation
182(17)
3.4 Projects Using Mathematica
199(5)
4 Partial Differential Equations 204(39)
4.1 Basic Concepts and Terminology
204(5)
4.2 Partial Differential Equations of the First Order
209(12)
4.3 Linear Partial Differential Equations of the Second Order
221(17)
4.3.1 Important Equations of Mathematical Physics
222(8)
4.3.2 Classification of Linear PDEs of the Second Order
230(8)
4.4 Boundary and Initial Conditions
238(2)
4.5 Projects Using Mathematica
240(3)
5 The Wave Equation 243(83)
5.1 d'Alembert's Method
243(16)
5.2 Separation of Variables Method for the Wave Equation
259(17)
5.3 The Wave Equation on Rectangular Domains
276(12)
5.3.1 Homogeneous Wave Equation on a Rectangle
276(5)
5.3.2 Nonhomogeneous Wave Equation on a Rectangle
281(3)
5.3.3 The Wave Equation on a Rectangular Solid
284(4)
5.4 The Wave Equation on Circular Domains
288(17)
5.4.1 The Wave Equation in Polar Coordinates
288(9)
5.4.2 The Wave Equation in Spherical Coordinates
297(8)
5.5 Integral Transform Methods for the Wave Equation
305(16)
5.5.1 The Laplace Transform Method for the Wave Equation
305(5)
5.5.2 The Fourier Transform Method for the Wave Equation
310(11)
5.6 Projects Using Mathematica
321(5)
6 The Heat Equation 326(57)
6.1 The Fundamental Solution of the Heat Equation
326(8)
6.2 Separation of Variables Method for the Heat Equation
334(15)
6.3 The Heat Equation in Higher Dimensions
349(17)
6.3.1 Green Function of the Higher Dimensional Heat Equation
349(2)
6.3.2 The Heat Equation on a Rectangle
351(4)
6.3.3 The Heat Equation in Polar Coordinates
355(4)
6.3.4 The Heat Equation in Cylindrical Coordinates
359(2)
6.3.5 The Heat Equation in Spherical Coordinates
361(5)
6.4 Integral Transform Methods for the Heat Equation
366(11)
6.4.1 The Laplace Transform Method for the Heat Equation
366(5)
6.4.2 The Fourier Transform Method for the Heat Equation
371(6)
6.5 Projects Using Mathematica
377(6)
7 Laplace and Poisson Equations 383(68)
7.1 The Fundamental Solution of the Laplace Equation
383(14)
7.2 Laplace and Poisson Equations on Rectangular Domains
397(16)
7.3 Laplace and Poisson Equations on Circular Domains
413(19)
7.3.1 Laplace Equation in Polar Coordinates
413(7)
7.3.2 Poisson Equation in Polar Coordinates
420(2)
7.3.3 Laplace Equation in Cylindrical Coordinates
422(2)
7.3.4 Laplace Equation in Spherical Coordinates
424(8)
7.4 Integral Transform Methods for the Laplace Equation
432(13)
7.4.1 The Fourier Transform Method for the Laplace Equation
432(6)
7.4.2 The Hankel Transform Method
438(7)
7.5 Projects Using Mathematica
445(6)
8 Finite Difference Numerical Methods 451(71)
8.1 Basics of Linear Algebra and Iterative Methods
451(21)
8.2 Finite Differences
472(9)
8.3 Finite Difference Methods for Laplace & Poisson Equations
481(14)
8.4 Finite Difference Methods for the Heat Equation
495(11)
8.5 Finite Difference Methods for the Wave Equation
506(16)
Appendices
A Table of Laplace Transforms
522(2)
B Table of Fourier Transforms
524(2)
C Series and Uniform Convergence Facts
526(3)
D Basic Facts of Ordinary Differential Equations
529(13)
E Vector Calculus Facts
542(7)
F A Summary of Analytic Function Theory
549(7)
G Euler Gamma and Beta Functions
556(3)
H Basics of Mathematica
559(15)
Bibliography 574(1)
Answers to the Exercises 575(55)
Index of Symbols 630(1)
Index 631
Adzievski, Kuzman; Siddiqi, Abul Hasan
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