A Collection of Problems on Mathematical Physics
International Series of Monographs in Pure and Applied Mathematics
Published on 22. October 2013
782 pages
978-1-4831-8486-9 (ISBN)
Description
A Collection of Problems on Mathematical Physics is a translation from the Russian and deals with problems and equations of mathematical physics. The book contains problems and solutions. The book discusses problems on the derivation of equations and boundary condition. These Problems are arranged on the type and reduction to canonical form of equations in two or more independent variables. The equations of hyperbolic type concerns derive from problems on vibrations of continuous media and on electromagnetic oscillations. The book considers the statement and solutions of boundary value problems pertaining to equations of parabolic types when the physical processes are described by functions of two, three or four independent variables such as spatial coordinates or time. The book then discusses dynamic problems pertaining to the mechanics of continuous media and problems on electrodynamics. The text also discusses hyperbolic and elliptic types of equations. The book is intended for students in advanced mathematics and physics, as well as, for engineers and workers in research institutions.
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B. M. Budak | etc. | D.M. Brink
Collection of Problems on Mathematical Physics
Book
12/1963
Pergamon
€13.62
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Content
Translation Editor's NotePrefaceChapter I. Classification and Reduction to Canonical Form of Second Order Partial Differential Equations 1. The Equation for a Function of Two Independent Variables a11+uxx+2a12uxy+a22uyy+b1ux+b2uy+cu = f(x, y) 1. The Equation with Variable Coefficients 2. The Equation with Constant Coefficients 2. The Equation with Constant Coefficients for a Function of n Independent VariablesChapter II. Equations of Hyperbolic Type 1. Physical Problems Reducible to Equations of Hyperbolic Type; Statement of Boundary-Value Problems 1. Free Vibrations in a Non-Resistant Medium; Equations with Constant Coefficients 2. Forced Vibrations and Vibrations in a Resistant Medium; Equations with Constant Coefficients 3. Vibration Problems Leading to Equations with Continuous Variable Coefficients 4. Problems Leading to Equations with Discontinuous Coefficients And Similar Problems (Piecewise Homogeneous Media, etc.) 5. Similarity of Boundary-Value Problems 2. Method of Traveling Waves (D'Alembert's Method) 1. Problems for an Infinite String 2. Problems for a Semi-Infinite Region 3. Problems for an Infinite Line, Consisting of Two Homogeneous Semi-Infinite Lines 4. Problems for a Finite Segment 3. Method of Separation of Variables 1. Free Vibrations in a Non-Resistant Medium 2. Free Vibrations in a Resistant Medium 3. Forced Vibrations Under the Action of Distributed and Concentrated Forces in a Non-Resistant Medium and in a Resistant Medium 4. Vibrations with Inhomogeneous Media and Other Conditions Leading to Equations with Variable Coefficients; Calculations with Concentrated Forces and Masses 4. Method of Integral Representations 1. The Method of the Fourier Integral 2. Riemann's MethodChapter III. Equations of Parabolic Type 1. Physical Problems Leading to Equations of Parabolic Type; Statement Of Boundary-Value Problems 1. Homogeneous Media; Equations with Constant Coefficients 2. Inhomogeneous Media; Equations with Variable Coefficients and Matching Conditions 3. Similarity of Boundary-Value Problems 2. Method of Separation of Variables 1. Homogeneous Isotropic Media. Equations with Constant Coefficients 2. Inhomogeneous Media. Equations with Variable Coefficients and Matching Conditions 3. Method of Integral Representations and Source Functions 1. Homogeneous Isotropic Media. Application of the Fourier Integral Transform to Problems on the Infinite Line and the Semi-Infinite Line 2. Homogeneous Isotropic Media. Calculation of Green's Functions 3. Inhomogeneous Media; Equations with Piecewise Continuous Coefficients and Matching ConditionsChapter IV. Equations of Elliptic Type 1. Physical Problems Leading to Equations of Elliptic Type, and the Statement of Boundary-Value Problems 1. Boundary-Value Problems for Laplace's and Poisson's Equation in a Homogeneous Medium 2. Boundary-Value Problems for Laplace's Equation in Inhomogeneous Media 2. Simplest Problems for Laplace's and Poisson's Equations 1. Boundary-Value Problems for Laplace's Equation 2. Boundary-Value Problems for Poisson's Equation 3. The Source Function 1. The Source Function for Regions with Plane Boundaries 2. The Source Function for Regions with Spherical (Circular) and Plane Boundaries 3. The Source Function in Inhomogeneous Media 4. The Method of Separation of Variables 1. Boundary-Value Problems for a Circle, Ring and Sector 2. Boundary-Value Problems for Strips, Rectangles, Plane Layers and Parallelepipeds 3. Problems Requiring the Application of Cylindrical Functions 4. Problems Requiring the Application of Spherical and Cylindrical Functions 5.
