Author(s): Adzievski, Kuzman; Siddiqi, A. H
Publisher: CRC Press
Year: 2014
Language: English
Pages: 634
Tags: Математика;Дифференциальные уравнения;Дифференциальные уравнения в частных производных;
Content: 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.
