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MOOC Massive Open Online Courses (Academic Year 2018/2019)

Numerical Methods



Video professors: Giovanni Monegato - Politecnico di Torino (Torino - Italy)

Videolesson

Lesson n. 1: Introduction to the Course
   Introduction to the Course
   Course Objectives
   Course Outline
   MATLAB presentation 		Go to this lesson Giovanni Monegato
Lesson n. 2: Computer Arithmetic
   Contents
   Computer arithmetic
   Numerical cancellation
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 3: Introduction to MATLAB
   Contents
   Basic features and commands
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 4: The MATLAB programming language
   Contents
   More MATLAB commands
   M-files
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 5: Numerical problems and algorithms
   Contents
   Conditioning of a numerical problem
   Stability of an algorithm 		Go to this lesson Giovanni Monegato
Lesson n. 6: Linear Systems
   Contents
   Vectors and matrices
   Linear systems - Preliminaries
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 7: Gauss elimination method
   Contents
   The classical Gauss elimination method
   Partial pivoting
   Gauss method with partial pivoting
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 8: Gauss algorithm
   Contents
   Gauss algorithm
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 9: Matrix decompositions
   Contents
   Matrix decompositions
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 10: Iterative methods for linear systems
   Contents
   Classical iterative methods
   Jacobi method
   Gauss - Seidel method
   SOR method
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 11: More on MATLAB programming
   Contents
   More on MATLAB programming
   Computation of the eigenvalues of a matrix (basic ideas)
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 12: Polinomial interpolation (I)
   Inizio
   Contents
   Polinomial interpolation
   Lagrange’s formula
   Newton’s formula 		Go to this lesson Giovanni Monegato
Lesson n. 13: Polinomial interpolation (II)
   Contents
   Newton’s formula
   Choice of the interpolation nodes
   Convergence 		Go to this lesson Giovanni Monegato
Lesson n. 14: Piecewise polynomial interpolation
   Contents
   MATLAB commands and questions on polynomial interpolation
   Questions
   Interpolation with piecewise polynomial functions 		Go to this lesson Giovanni Monegato
Lesson n. 15: Cubic splines
   Contents
   Interpolation with piecewise polynomial functions
   Cubic splines 		Go to this lesson Giovanni Monegato
Lesson n. 16: Final comments on interpolation
   Contents
   Questions on cubic splines
   Interpolation of a function in a bounded interval
   MATLAB experiments 		Go to this lesson Giovanni Monegato
Lesson n. 17: Least squares fitting
   Contents
   Least squares
   MATLAB commands
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 18: Non linear equations
   Contents
   Preliminaries
   The secant method
   The tangent (or Newton’s) method
   The fixed-point method 		Go to this lesson Giovanni Monegato
Lesson n. 19: Numerical integration (I)
   Contents
   Quadrature formulas of interpolatory type
   Newton-Cotes formulas 		Go to this lesson Giovanni Monegato
Lesson n. 20: Numerical integration (II)
   Contents
   Orthogonal polynomials
   Gaussian formulas
   Composite formulas
   MATLAB commands
   Questions 		Go to this lesson Giovanni Monegato
Lesson n. 21: Some computation using MATLAB
   Contents
   Roots of equations
   Computation of integrals 		Go to this lesson Giovanni Monegato
Lesson n. 22: Initial value problems for ODEs
   Contents
   Ordinary Differential Equations
   Initial value problems (Cauchy problems)
   Canonical form of a Cauchy problem 		Go to this lesson Giovanni Monegato
Lesson n. 23: Numerical methods for initial value problems (I)
   Contents
   Numerical methods
   One-step methods
   Multistep methods
   Examples 		Go to this lesson Giovanni Monegato
Lesson n. 24: Numerical methods for initial value problems (II)
   Contents
   Numerical methods
   MATLAB commands 		Go to this lesson Giovanni Monegato
Lesson n. 25: Scientific computation using MATLAB
   Contents
   Questions
   MATLAB computation
   Overall conclusions 		Go to this lesson Giovanni Monegato