- Linear Algebra
- Vector and its calculus
- Matrices, determinants, and eigen-value problems
- Linear transformations, projection, affine transformation
- Tensor analysis
- Group theories
- Lie algebra
- Differential Equations
- Ordinary differential equations
- Nonlinear ordinary differential equations
- Partial differential equations
- Nonlinear partial differential equations
- Function Theories
- Infinite series
- Polynomials
- Transformations
- Special functions
- Approximations
- Complex Variables
- Cauchy-Riemann conditions
- Contour integral
- Mapping and branch points
- Residue theorem
- Definite integrals
- Integral Equations
- Integral transform
- Calculus of variations
- Geometry, topology, and Other Mathematical Tools
- Euclidean and non-Euclidean geometry
- Differential forms
- Lie derivative
- Topology
- Graph theory
- Knot theory
- Braid group
- Renormalization theory

- Solutions for the equations of n-th degree
- Derivation of a wave equation
- Gamma function and the related formulas
- Quaternion, split-quaternion, and octonion
- Zeta functions

- Calculation of (
**A**×**B**)×(**C**×**D**) - Application of δ(ax)=(1/a)δ(x)
- Stokes theorem and contour integral
- Cosine transformation of cos(x)

- coming soon...