Ingénierie Informatique (Academic Year 2018/2019) - Programmazione e sicurezza

Numerical methods

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

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Ingénierie Informatique (Academic Year 2018/2019) - Programmazione e sicurezza

Numerical methods

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