🔬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).