Contents [hide]
- Preface
- Introduction
- Part I: Matrix Algebra
- 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: Linear Systems of Ordinary Differential Equations
- Motivation
- Variable coefficient systems of ODEs
- Floquet theory
- Constant coefficient systems of ODEs
- Planar Phase Portrait
- Euler systems of equations
- Fundamental matrices
- Reduction to a single equation
- Method of undetermined coefficients
- Variation of parameters
- Laplace transform
- Second order ODEs
- Spring-mass systems
- Electric circuits
- Applications
- Part III: Non-linear Systems of Ordinary Differential Equations
- Planar autonomous systems
- Numerical solutions
- Stability
- Linearization
- Spring-mass system
- Conservative systems
- Gradient systems
- Competing species
- Predator-Prey equations
- Harvesting species
- Lyapunov second method
- HIV models
- Periodic solutions
- Asynchronous solutions
- Limited Cycles
- van der Pol equations
- Neuroscience
- Biochemistry
- Miscellany
Part III C: Chaos
- Part IV: Numerical Methods
- Part V: Fourier Series
- Sturm--Liouville problems
- Singular Sturm--Liouville problems
- Fourier transform
- Fourier series
- Periodic extension
- Complex Fourier series
- Even and odd functions
- Examples
- Gibbs phenomenon
- Convergence of Fourier series
- Modes of convergence
- Cesàro summation
- Square wave functions
- Orthogonal expansions
- Bessel expansion
- Chebyshev expansions
- Legendre expansion
- Hermite expansion
- Laguerre expansion
- Motivated examples
- Part VI: Partial Differential Equations Part VI P: Parabolic Equations
- Heat conduction equations
- Boundary Value Problems for heat equation
- Other heat transfer problems
- Fourier transform
- Fokas method
- Resolvent method
- Fokker--Planck equation
- Numerical solutions of heat equation
- Black Scholes model
- Monte Carlo for Parabolic
- Wave equations
- IBVPs
- 2D wave equations
- Forced wave equations
- Transverse vibrations of beams
- Numerical solutions of wave equation
- Klein–Gordon equation
- 3D wave equations
- Cagniard method
- 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: Special Functions
- Chebyshev functions
- Legendre functions
- Hermite polynomials
- Laguerre polynomials
- Lambert function
- Mathieu function
- Elliptic functions
- Hypergeometric functions
- Kummer's equation
- Miscellany
Part VI H: Hyperbolic equations
Part VI E: Elliptic equations
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Introduction to Linear Algebra with Mathematica
Glossary
Preface
Scaling
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