MATH, Contents

MATH01 : Linear algebra

Basic concepts
Linear equation systems
Eigenvalue problems
Nonlinear equations
Singular value decomposition
Sparse matrices
Polynomials
Polynomial interpolation
Spline interpolation
Multivariate interpolation

MATH02 : Calulus

Permutation and combination
Limits and series
Sums and products
Derivative calculus
Integral calculus
Vector calculus
Special functions and numbers
Variations
Numerical integration Methods
Numerical integration with SciPy
Multiple integration
Symbolic and arbitrary-precision integration
Integral transforms

MATH03 : Complex analysis

Complex functions
Cauchy–Riemann equations
Line integral
Cauchy integral theorem and formula
Laurent series
Liouville theorem
Residue theorem

MATH04 : Differential equation

ODE analytical solutions
ODE numerical methods
ODE numerical integration
PDE analytical solutions
PDE finite element method
PDE finite difference method
PDE finite volume method
Sturm–Liouville theory
Green function

MATH05 : Statistics

Probability
Descriptive statistics
Distribution
Parameters estimation
Hypothesis tests
Covariance and correlation
Regression analysis
Analysis of variance
Non-parametric tests
Time series

MATH06 : Optimization

Convex analysis
Univariate optimization
Unconstrained multivariate optimization
Nonlinear least square problems
Constrained optimization
Linear programming
Combinatorial
Metaheuristics