Contents [hide]
- Preface
- Introduction
- Part I: Basic Concepts
- How to define vectors
- How to define matrices
- Basic Operations with matrices
- Linear Systems of equations
- Determinants and Inverses
- Special matrices
- Eigenvalues and Eigenvectors
- Diagonalization procedure
- Sylvester formula
- The Resolvent method
- Polynomial interpolation
- Positive matrices
- Roots
- Miscellany
- Part II: Fourier Series
- Hilbert spaces
- Sturm--Liouville problems
- Singular Sturm--Liouville problems
- Inhomogeneous problems
- Eigenfunction Expansions
- Fourier series
- Periodic extension
- Complex Fourier series
- Even and odd functions
- Examples
- Gibbs phenomena
- Convergence of Fourier series
- Cesàro summation
- Square wave functions
- Orthogonal expansions
- Chebyshev expansions
- Legendre expansion
- Bessel expansion
- Hermite expansion
- Laguerre expansion
- Motivated examples
- Part III: Integral Transformations
- Part IV: Parabolic Differential Equations
- 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
Return to computing page for the first course APMA0330
Return to computing page for the second course APMA0340
Return to computing page for the fourth course APMA0360
Return to Mathematica tutorial for the first course APMA0330
Return to Mathematica tutorial for the second course APMA0340
Return to Mathematica tutorial for the fourth course APMA0360
Return to the main page for the course APMA0330
Return to the main page for the course APMA0340
Return to the main page for the course APMA0360
Introduction to Linear Algebra with Mathematica