Partial Differential Equations and Mathematica /
"Early training in the elementary techniques of partial differential equations is invaluable to students in engineering and the sciences as well as mathematics. However, to be effective, an undergraduate introduction must be carefully designed to be challenging, yet still reasonable in its dema...
| Main Authors: | , , |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton, FL :
CRC Press,
2002.
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| Edition: | Second edition. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; 0: Introduction to Mathematica; 0.1 Introduction; 0.2 Conventions; 0.3 Getting Started; 0.4 File Manipulation; 0.5 Ordinary Differential Equations; 0.6 To the Instructor; 0.7 To the Student; 0.8 MathSource; 1: Introduction; 1.1 Notation and Definitions; 1.2 Initial and Boundary Conditions; 1.3 Classification of Second-Order Equations; 1.4 Some Known Equations; 1.5 Superposition Principle; 1.6 Mathematica Projects; 1.7 Exercises; 2: Method of Characteristics First-Order Equations; First-Order Equations
- 2.1 Linear Equations with Constant Coefficients2.2 Linear Equations with Variable Coefficients; 2.3 First-Order Quasilinear Equations; 2.4 First-Order Nonlinear Equations; 2.4.1 Cauchy's Method of Characteristics; 2.5 Geometrical Considerations; 2.6 Some Theorems on Characteristics; Second-Order Equations; 2.7 Linear and Quasilinear Equations; 2.8 Mathematica Projects; 2.9 Exercises; 3: Linear Equations with Constant Coefficients; 3.1 Inverse Operators; 3.2 Homogeneous Equations; 3.3 Nonhomogeneous Equations; 3.4 Mathematica Projects; 3.5 Exercises; 4: Orthogonal Expansions; 4.1 Orthogonality
- 4.2 Orthogonal Polynomials4.3 Series of Orthogonal Functions; 4.4 Trigonometric Fourier Series; 4.5 Eigenfunction Expansions; 4.6 Bessel Functions; 4.7 Mathematica Projects; 4.8 Exercises; Table 4.1. Eigenvalue Problem in Cartesian Coordinates; Table 4.2. Eigenvalue Problem in Polar Coordinates; 5: Separation of Variables; 5.1 Introduction; 5.2 Hyperbolic Equations; 5.3 Parabolic Equations; 5.4 Elliptic Equations; 5.5 Cylindrical Polar Coordinates; 5.6 Spherical Coordinates; 5.7 Nonhomogeneous Problems; 5.8 Mathematica Projects; 5.9 Exercises; 6: Integral Transforms
- 6.1 Integral Transform PairsI. Laplace Transforms; 6.2 Notation; 6.3 Basic Laplace Transforms; 6.4 Inversion Theorem; 6.5 Mathematica Projects; 6.6 Exercises; II. Fourier Transforms; 6.7 Fourier Integral Theorems; 6.8 Properties of Fourier Transforms; 6.8.1 Fourier Transforms of the Derivatives of a Function; 6.8.2 Convolution Theorems for Fourier Transform; 6.8.3 Some Fourier Transform Formulas; 6.9 Fourier Sine and Cosine Transforms; 6.9.1 Properties of Fourier Sine and Cosine Transforms; 6.9.2 Convolution Theorems for Fourier Sine and Cosine Transforms; 6.10 Finite Fourier Transforms
- 6.11 Mathematica Projects6.12 Exercises; 7: Green's Functions; 7.1 Generalized Functions; 7.1.1 Dirac Delta Function in Curvilinear Coordinates; 7.2 Green's Functions and Adjoint Operators; 7.2.1 The Concept of a Green's Function; 7.2.2 Adjoint Operator; 7.3 Elliptic Equations; 7.3.1 Green's Function for the Laplacian; 7.3.2 Harmonic Functions; 7.3.3 Symmetry of Green's Functions; 7.3.4 Green's Function for the Helmholtz Operator; 7.4 Parabolic Equations; 7.5 Hyperbolic Equations; 7.6 Applications of Green's Functions; 7.6.1 Dirichlet Problem; 7.6.2 Neumann Problem; 7.6.3 Robin Problem