Introduction to partial differential equations for scientists and engineers using mathematica / Kuzman Adzievski and Abul Hasan Siddiqi.

By:

Adzievski, Kuzman

Contributor(s):

Siddiqi, Abul Hasan

Material type: Text

TextPublication details: Boca Raton : CRC Press, c2014.Description: xiii, 634 p. : ill. ; 25 cmISBN:

9781466510562 (cloth : acidfree paper)

Subject(s):

Partial Differential equations

DDC classification:

515.353 23 Ad245

Contents:

1. Fourier Series 1.1. Fourier Series of Periodic Functions -- 1.2. Convergence of Fourier Series -- 1.3. Integration and Differentiation of Fourier Series -- 1.4. Fourier Sine and Cosine Series -- 1.5. Projects Using Mathematica -- 2. Integral Transforms 2.1. The Laplace Transform -- 2.1.1. Definition and Properties of the Laplace Transform -- 2.1.2. Step and Impulse Functions -- 2.1.3. Initial-Value Problems and the Laplace Transform -- 2.1.4. The Convolution Theorem -- 2.2. Fourier Transforms -- 2.2.1. Definition of Fourier Transforms -- 2.2.2. Properties of Fourier Transforms -- 2.3. Projects Using Mathematica -- 3. Sturm-Liouville Problems 3.1. Regular Sturm-Liouville Problems -- 3.2. Eigenfunction Expansions -- 3.3. Singular Sturm-Liouville Problems -- 3.3.1. Definition of Singular Sturm-Liouville Problems -- 3.3.2. Legendre's Differential Equation -- 3.3.3. Bessel's Differential Equation -- 3.4. Projects Using Mathematica -- 4. Partial Differential Equations 4.1. Basic Concepts and Terminology -- 4.2. Partial Differential Equations of the First Order -- 4.3. Linear Partial Differential Equations of the Second Order -- 4.3.1. Important Equations of Mathematical Physics -- 4.3.2. Classification of Linear PDEs of the Second Order -- 4.4. Boundary and Initial Conditions -- 4.5. Projects Using Mathematica -- 5. The Wave Equation 5.1.d'Alembert's Method -- 5.2. Separation of Variables Method for the Wave Equation -- 5.3. The Wave Equation on Rectangular Domains -- 5.3.1. Homogeneous Wave Equation on a Rectangle -- 5.3.2. Nonhomogeneous Wave Equation on a Rectangle -- 5.3.3. The Wave Equation on a Rectangular Solid -- 5.4. The Wave Equation on Circular Domains -- 5.4.1. The Wave Equation in Polar Coordinates -- 5.4.2. The Wave Equation in Spherical Coordinates -- 5.5. Integral Transform Methods for the Wave Equation -- 5.5.1. The Laplace Transform Method for the Wave Equation -- 5.5.2. The Fourier Transform Method for the Wave Equation -- 5.6. Projects Using Mathematica -- 6. The Heat Equation 6.1. The Fundamental Solution of the Heat Equation -- 6.2. Separation of Variables Method for the Heat Equation -- 6.3. The Heat Equation in Higher Dimensions -- 6.3.1. Green Function of the Higher Dimensional Heat Equation -- 6.3.2. The Heat Equation on a Rectangle -- 6.3.3. The Heat Equation in Polar Coordinates -- 6.3.4. The Heat Equation in Cylindrical Coordinates -- 6.3.5. The Heat Equation in Spherical Coordinates -- 6.4. Integral Transform Methods for the Heat Equation -- 6.4.1. The Laplace Transform Method for the Heat Equation -- 6.4.2. The Fourier Transform Method for the Heat Equation -- 6.5. Projects Using Mathematica -- 7. Laplace and Poisson Equations 7.1. The Fundamental Solution of the Laplace Equation -- 7.2. Laplace and Poisson Equations on Rectangular Domains -- 7.3. Laplace and Poisson Equations on Circular Domains -- 7.3.1. Laplace Equation in Polar Coordinates -- 7.3.2. Poisson Equation in Polar Coordinates -- 7.3.3. Laplace Equation in Cylindrical Coordinates -- 7.3.4. Laplace Equation in Spherical Coordinates -- 7.4. Integral Transform Methods for the Laplace Equation -- 7.4.1. The Fourier Transform Method for the Laplace Equation -- 7.4.2. The Hankel Transform Method -- 7.5. Projects Using Mathematica -- 8. Finite Difference Numerical Methods 8.1. Basics of Linear Algebra and Iterative Methods -- 8.2. Finite Differences -- 8.3. Finite Difference Methods for Laplace & Poisson Equations -- 8.4. Finite Difference Methods for the Heat Equation -- 8.5. Finite Difference Methods for the Wave Equation -- Appendices A. Table of Laplace Transforms -- B. Table of Fourier Transforms -- C. Series and Uniform Convergence Facts -- D. Basic Facts of Ordinary Differential Equations -- E. Vector Calculus Facts -- F.A Summary of Analytic Function Theory -- G. Euler Gamma and Beta Functions -- H. Basics of Mathematica-- Bibliography-- Answers to the Exercises-- Index of Symbols-- Index.

Summary: With a special emphasis on engineering and science applications, this textbook provides a mathematical introduction to PDEs at the undergraduate level. It takes a new approach to PDEs by presenting computation as an integral part of the study of differential equations.

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Item type	Current library	Call number	Status	Date due	Barcode	Item holds
Books	ISI Library, Kolkata	515.353 Ad245 (Browse shelf(Opens below))	Available		135406

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Previous	515.353 Partial differential equations for probabilists	515.353 Cauchy problem	515.353 Ad244 Proceedings	515.353 Ad245 Introduction to partial differential equations for scientists and engineers using mathematica /	515.353 Ag269 Lectures on exponential decay of solutions of second order elliptic equations : bounds on eigenfunctions of N-Body schrodinger operators	515.353 Ag277 Partial differential equations IX	515.353 Am484 Progrss in partial differential equations	Next

"A Chapman & Hall book."

Includes bibliographical references (p. 574) and indexes.

1. Fourier Series
1.1. Fourier Series of Periodic Functions --
1.2. Convergence of Fourier Series --
1.3. Integration and Differentiation of Fourier Series --
1.4. Fourier Sine and Cosine Series --
1.5. Projects Using Mathematica --

2. Integral Transforms
2.1. The Laplace Transform --
2.1.1. Definition and Properties of the Laplace Transform --
2.1.2. Step and Impulse Functions --
2.1.3. Initial-Value Problems and the Laplace Transform --
2.1.4. The Convolution Theorem --
2.2. Fourier Transforms --
2.2.1. Definition of Fourier Transforms --
2.2.2. Properties of Fourier Transforms --
2.3. Projects Using Mathematica --

3. Sturm-Liouville Problems
3.1. Regular Sturm-Liouville Problems --
3.2. Eigenfunction Expansions --
3.3. Singular Sturm-Liouville Problems --
3.3.1. Definition of Singular Sturm-Liouville Problems --
3.3.2. Legendre's Differential Equation --
3.3.3. Bessel's Differential Equation --
3.4. Projects Using Mathematica --

4. Partial Differential Equations
4.1. Basic Concepts and Terminology --
4.2. Partial Differential Equations of the First Order --
4.3. Linear Partial Differential Equations of the Second Order --
4.3.1. Important Equations of Mathematical Physics --
4.3.2. Classification of Linear PDEs of the Second Order --
4.4. Boundary and Initial Conditions --
4.5. Projects Using Mathematica --

5. The Wave Equation
5.1.d'Alembert's Method --
5.2. Separation of Variables Method for the Wave Equation --
5.3. The Wave Equation on Rectangular Domains --
5.3.1. Homogeneous Wave Equation on a Rectangle --
5.3.2. Nonhomogeneous Wave Equation on a Rectangle --
5.3.3. The Wave Equation on a Rectangular Solid --
5.4. The Wave Equation on Circular Domains --
5.4.1. The Wave Equation in Polar Coordinates --
5.4.2. The Wave Equation in Spherical Coordinates --
5.5. Integral Transform Methods for the Wave Equation --
5.5.1. The Laplace Transform Method for the Wave Equation --
5.5.2. The Fourier Transform Method for the Wave Equation --
5.6. Projects Using Mathematica --

6. The Heat Equation
6.1. The Fundamental Solution of the Heat Equation --
6.2. Separation of Variables Method for the Heat Equation --
6.3. The Heat Equation in Higher Dimensions --
6.3.1. Green Function of the Higher Dimensional Heat Equation --
6.3.2. The Heat Equation on a Rectangle --
6.3.3. The Heat Equation in Polar Coordinates --
6.3.4. The Heat Equation in Cylindrical Coordinates --
6.3.5. The Heat Equation in Spherical Coordinates --
6.4. Integral Transform Methods for the Heat Equation --
6.4.1. The Laplace Transform Method for the Heat Equation --
6.4.2. The Fourier Transform Method for the Heat Equation --
6.5. Projects Using Mathematica --

7. Laplace and Poisson Equations
7.1. The Fundamental Solution of the Laplace Equation --
7.2. Laplace and Poisson Equations on Rectangular Domains --
7.3. Laplace and Poisson Equations on Circular Domains --
7.3.1. Laplace Equation in Polar Coordinates --
7.3.2. Poisson Equation in Polar Coordinates --
7.3.3. Laplace Equation in Cylindrical Coordinates --
7.3.4. Laplace Equation in Spherical Coordinates --
7.4. Integral Transform Methods for the Laplace Equation --
7.4.1. The Fourier Transform Method for the Laplace Equation --
7.4.2. The Hankel Transform Method --
7.5. Projects Using Mathematica --

8. Finite Difference Numerical Methods
8.1. Basics of Linear Algebra and Iterative Methods --
8.2. Finite Differences --
8.3. Finite Difference Methods for Laplace & Poisson Equations --
8.4. Finite Difference Methods for the Heat Equation --
8.5. Finite Difference Methods for the Wave Equation --

Appendices
A. Table of Laplace Transforms --
B. Table of Fourier Transforms --
C. Series and Uniform Convergence Facts --
D. Basic Facts of Ordinary Differential Equations --
E. Vector Calculus Facts --
F.A Summary of Analytic Function Theory --
G. Euler Gamma and Beta Functions --
H. Basics of Mathematica--

Bibliography--
Answers to the Exercises--
Index of Symbols--
Index.

With a special emphasis on engineering and science applications, this textbook provides a mathematical introduction to PDEs at the undergraduate level. It takes a new approach to PDEs by presenting computation as an integral part of the study of differential equations.

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