TY - BOOK AU - Adzievski,Kuzman AU - Siddiqi,Abul Hasan TI - Introduction to partial differential equations for scientists and engineers using mathematica SN - 9781466510562 (cloth : acidfree paper) U1 - 515.353 23 PY - 2014/// CY - Boca Raton PB - CRC Press KW - Partial Differential equations N1 - "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 N2 - 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 ER -