🔬Range of Mathematical topics with practical approach related to various CS fields.
- Introduction to MatLab and GNU Octave.
- Basic code
- Floating point systems (properties, rounding, errors).
- Systems of linear equation with error in the right-hand side.
- Matrix
- Norms.
- 1'st Norm.
- 2'nd Norm.
- ♾ Norm
- condition number.
- Cholesky Decomposition
- LU decomposition
- PLU factorization
- Collect the data.
- Select the most appropriate model.
- Compute the best instance of the chosen model
- Use the model (predicting)
- Model Types:
- linear model
- polynomial model
- trigonometric model
- Gaussian normal-equation
- Lagrangian interpolation.
- Defining the Lagrange-polynomial in Newton form.
- Horner’s algorithm.
- Computing with
polyval
&polyfit
. - Hermite-interpolation.
- Piecewise interpolation.
- Piecewise Hermite-interpolation.
- Cubic spline interpolation.
- Using your own spline function.
- Approximating definite integrals.
- Interpolational quadrature formulas.
- Simple midpoint (tangent) rule.
- Simple trapesoidal rule.
- Simpson’s simple rule.
- Compound rules.
- Compound mid-point rule.
- Compound trapesoidal rule.
- Simpson’s compund rule.
- Adaptive methods.
- MatLab: Improper & Unknown Integrals calc + Anonymous Functions.
- Introduction to Complex Numbers.
- Defining Eigenvalues and eigenvectors.
- The stronger Gersgorin theorem.
- Power Iteration method.
- Defining
Rayleigh
of a matrix. - Inverse-iteration & with shifting.
- Solving Examples like ( Page ranking & Leslie-model).
- Defining Non-Learning equations.
- Method of bisection (mid-point).
- Newton-Raphson method.
- Secant method
- Fixed point iteration Algorithm.
- Intro to Optimization
- Finding local max & local min.
- fsolve for multivariate vector-function.
- fsolve for multivariate real-function.
- optimization with built-in functions.
- Intro to fibonacci sequence & golden ratio.
- Golden section search & implementing an Algorithm.
- Using built-in MatLab function for optimization and 3D ploting.
- Intro to Linear Programming.
- Graphical Method.
- LP Normal and Canonical form.
- Simplex method.
- 2 phase Simplex method.
- Duality in linear programming.
- sensitivity analysis.
- Implementing Algorithms to solve real world problems (eg. transportation probelm).