Introduction to partial differential equations for scientists and engineers using Mathematica. ([2016?])

• Record Type: Book
• Further Information: Note: Kuzman Adzievski, Abul Hasan Siddiqi.
• Authors: Adzievski, Kuzman; Siddiqi, A. H
• Contents: Machine generated contents note: 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 -- 2.1. 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 -- 3.1. 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 -- 4.1. 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 -- 5.1.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 -- 6.1. 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 -- 7.1. 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 -- 8.1. 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 -- 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.
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2016
• Copyright Date: 2014
• Extent: 1 online resource, illustrations
• Subjects: 515.353; Differential equations, Partial; Differential equations, Partial; Electronic books
• Languages: English
• ISBNs: 9781466510579; 1466510579
• Notes: Note: Includes bibliographical references.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.