Contents [hide]
- Preface
- Introduction
- Part I: Basic Concepts
- Part II: Fourier Series
- Hilbert spaces
- Sturm--Liouville problems
- Singular Sturm--Liouville problems
- Inhomogeneous problems
- Eigenfunction Expansions
- Fourier series
- Global Convergence of Fourier series
- Convergence of Fourier series
- Periodic extension
- Complex Fourier series
- Even and odd functions
- Discrete Fourier transform
- Fast Fourier tranform
- Applications
- Gibbs phenomena
- Cesàro summation
- Square wave functions
- Orthogonal expansions
- Chebyshev expansions
- Legendre expansion
- Bessel expansion
- Hermite expansion
- Laguerre expansion
- Motivated examples
- Part III: Integral Transformations Part III U: Unified Transform
- Part IV: Parabolic Differential Equations
- Heat conduction equations
- Boundary Value Problems for heat equation
- Neumann IBVPs for heat equation
- Mixed IBVPs for heat equation
- Third kind IBVPs for heat equation
- Other heat transfer problems
- 2D heat transfer problems
- Fourier transform
- Fokas method
- Resolvent method
- Fokker--Planck equation
- Numerical solutions of heat equation
- Black Scholes model
- Monte Carlo for Parabolic
- Part V: Hyperbolic Differential Equations
- Part VI: Elliptic Equations
- Laplace equation
- Dirichlet problem
- Neumann problems for Laplace equation
- Mixed problems for Laplace equation
- Laplace equation in infinite stripe
- Laplace equation in infinite semi-stripe
- Numerical solutions of Laplace equation
- Laplace equation in polar coordinates
- Laplace equation in a corner
- Laplace equation in spherical coordinates
- Poisson's equation
- Helmholtz equation
- Liouville's equation
- Monte Carlo for Elliptic
Part VI P:
Potential Theory
- Laplace equation
- Dirichlet problem
- Neumann problems for Laplace equation
- Mixed problems for Laplace equation
- Laplace equation in infinite stripe
- Laplace equation in infinite semi-stripe
- Numerical solutions of Laplace equation
- Laplace equation in polar coordinates
- Laplace equation in a corner
- Laplace equation in spherical coordinates
- Poisson's equation
- Helmholtz equation
- Liouville's equation
- Monte Carlo for Elliptic
- Part VII: Numerical Methods Part VII F: Finite Difference Schems
- FD for heat equation
- FD for wave equation
- FD for Laplace equation
- Laplace equation
- Dirichlet problem
- Neumann problems for Laplace equation
- Mixed problems for Laplace equation
- Laplace equation in infinite stripe
- Laplace equation in infinite semi-stripe
- Numerical solutions of Laplace equation
- Laplace equation in polar coordinates
- Laplace equation in a corner
- Laplace equation in spherical coordinates
- Poisson's equation
- Helmholtz equation equation
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Introduction to Linear Algebra with Mathematica
