Forskjeller
Her vises forskjeller mellom den valgte versjonen og den nåværende versjonen av dokumentet.
Begge sider forrige revisjon Forrige revisjon Neste revisjon | Forrige revisjon Siste revisjon Begge sider neste revisjon | ||
ma2501:2019v:lecture_plan [2019-01-14] elenac |
ma2501:2019v:lecture_plan [2020-01-06] elenac [Activity] |
||
---|---|---|---|
Linje 1: | Linje 1: | ||
+ | ===== Curriculum ===== | ||
+ | |||
+ | The Chapters of the book by Süli and Mayers specified in the third column of the " | ||
+ | |||
+ | The supplementary materials specified on the fourth column of the " | ||
+ | |||
+ | All problems sets considered in the lectures. | ||
+ | |||
+ | All [[https:// | ||
+ | |||
+ | All [[https:// | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | === Formulae, concepts and definitions you need to remember === | ||
+ | |||
+ | This is a non exhaustive list of formulae and definitions you are encourage to remember for the exam. | ||
+ | |||
+ | * Definition of contraction | ||
+ | * Lipscitz condition for functions | ||
+ | * Definition of convergence of order p and quadratic convergence | ||
+ | * Newton method for scalar equations and for systems | ||
+ | * Fixed point equation and fixed point iteration | ||
+ | * Contractions and convergence of fixed point iteration. | ||
+ | * Definition of spectral radius of a matrix | ||
+ | * Definition of eigenvalues and eigenvectors | ||
+ | * Definition of condition number | ||
+ | * Definition of 1- 2- and infinity-norm for vectors, matrices, and functions of one variable | ||
+ | * Cauchy-Schwartz inequality. | ||
+ | * Symmetric matrices | ||
+ | * Symmetric and positive definite matrix | ||
+ | * LU factorisation, | ||
+ | * QR factorisation and how to use Householder transformations to obtain the QR factorisation (see problems lecture 4 ). | ||
+ | * Gauss-Seidel Jacobi and SOR iterative methods and conditions for their convergence | ||
+ | * Lagrange interpolation polynomial | ||
+ | * Error formula for the interpolation polynomial | ||
+ | * Newton form of the interpolation polynomial and divided differences | ||
+ | * Newton-Cotes quadrature formulae. | ||
+ | * Chebishev polynomials (definition and basic properties) | ||
+ | * Forward Euler method, Backward Euler method for ODEs | ||
+ | * Need to know how to apply a Runge-Kutta method to an ODE, when you are given the parameters of the Runge-Kutta method (Butcher tableau). | ||
+ | * Consistency of one-step methods. | ||
+ | * Need to know how to apply a linear multistep method to an ODE when you are given the parameters of the linear multi-step method. | ||
+ | * Zero-stability and consistency for linear multistep methods. | ||
+ | * Familiarity with finite difference formulae, forward differences, | ||
+ | * Stability and consistency for finite differences approximations of boundary value problems. | ||
+ | * How to prove convergence of a consistent and stable finite difference discretisation of a boundary value problem. | ||
+ | ===== Notes ===== | ||
+ | |||
+ | Note on {{ : | ||
+ | |||
+ | Note on {{ : | ||
===== Activity ===== | ===== Activity ===== | ||
- | ^ Week ^ Dates ^ Theme ^ Süli and Mayers | + | ^ Week ^ Dates ^ Theme ^ Süli and Mayers |
- | | 2 | 07.01 10.01 | Introduction to the course, principles of computational mathematics, | + | | 2 | 07.01 10.01 | Introduction to the course, principles of computational mathematics, |
- | | 3 | 14.01 17.01 | Convergence of Newton method. Newton for systems. Introduction to Python. Supervision of the first assignment. | + | | 3 | 14.01 17.01 | Convergence of Newton method. Newton for systems. Introduction to Python. Supervision of the first assignment. |
- | | 4 | 21.01 24.01 | Solution of systems of linear equations | + | | 4 | 21.01 24.01 | Solution of systems of linear equations |
- | | 5 | 28.01 31.01 | Least squares, condition numbers stability of linear systems, SVD | 2.7, 2.9 | + | | 5 | 28.01 31.01 | Least squares, condition numbers stability of linear systems, SVD | 2.7, 2.9 (2.8 is not part of the curriculum). |
- | | 6 | 04.02 07.02 | + | | 6 | 04.02 | Gaussian Elimination |
- | | 7 | 11.02 14.02 | Polynomial interpolation | + | | 7 | 11.02 14.02 | Polynomial interpolation |
- | | 8 | 18.02 21.02 | Polynomial interpolation | + | | 8 | 18.02 21.02 | Polynomial interpolation. Divided differences (See problems Lecture 7). | 8.1,8.2 (lemma 8.1, Theorem 8.1 only idea of the proof),8.3 (Theorems 8.2 and 8.5 included but without proof, theorems 8.3 and 8.4 excluded), 8.4, 8.5 |
- | | 9 | 25.02 28.02 | Numerical integration and differentiation | + | | 9 | 25.02 28.02 | Project second part |
- | | 10 | 04.03 07.03 | Project second part | + | | 10 | 04.03 07.03 | Numerical integration and differentiation. |
- | | 11 | 11.03 14.03 | Numerical Integration | + | | 11 | 11.03 14.03 | Numerical Integration |
- | | 12 | 18.03 21.03 | Initial value problems for ODEs | 12 | | | + | | 12 | 18.03 21.03 | Initial value problems for ODEs | Note on ODEs. Chapters 1-6 except 4.2 and 5, and 6.5. | | |
- | | 13 | 25.03 28.03 | Initial value problems for ODEs | 12 | | | + | | 13 | 25.03 28.03 | Initial value problems for ODEs | Note on ODEs. Chapters 1-6 except 4.2 and 5, and 6.5. | | | |
- | | 15 | 01.04 04.04 | Boundary value problems | + | | 15 | 01.04 04.04 | [[https:// |
- | | 16 | 08.04 11.04 | Boundary value problems | + | | 16 | 08.04 11.04 | Boundary value problems |
- | | 18 | 29.04 | + | | 18 | 29.04 | Questions and answers |