Syllabus (Hebrew and English)
Since there are only 11 lectures this year, we will not get close to finishing the syllabus, so here is a list of topics actually covered:
Class | Topics |
---|---|
1 | Introduction to Maple and Matlab My Matlab demonstration Made in Matlab 5, but still good for 6. (7 is out, I haven't seen it yet.) See also the Matlab tutorial provided by Mathworks My Maple demonstration |
2 | Error Analysis and Numerical Differentiation Formulas |
3 | Numerical Linear Algebra 1 |
4 | Numerical Linear Algebra 2: How to use LU, Choleski and QR factorizations to solve linear systems (Ax=b), Householder algorithm for computing QR factorization, simple algorithm for computing LU factorization (without pivoting) |
5 | Numerical Linear Algebra 3: Conditioning of the
Ax=b problem. Root finding and optimization: interval bisection and Newton's method for solving equations in a single variable. |
6 | Root finding and optimization: Quadratic convergence of Newton's method. Stopping conditions for root finding. Newton's method for solving systems of equations. Golden ratio search. |
7 | Root finding and optimization: Stopping conditions for minimum search. General discussion of multidimensional minimum searches. Linesearch methods. Steepest Descent. Newton's method. Matlab commands for root finding and optimization. |
8 | (15 Dec) Interpolation: polynomial interpolation (Lagrange's and Newton's methods), linear splines, cubic splines (natural spline and not-a-knot conditions) |
9 | (29 Dec) Approximation. The least squares method for fitting a curve to a set of points. The least squares/Legendre polynomial method for approximating a function by a polynomial. You can download the handout about Legendre polynomials in either ps or pdf formats. |
10 | (5 Jan) Numerical Integration. You can download the handout about nodes for Gaussian quadrature in either ps, pdf or html formats. |
11 | Brief introduction to solving ODEs (Jan 12). Euler's method, improved Euler method, Runge Kutta method. Higher order equations and systems. Stability and stiffness. Matlab commands. |
Important note: the different units in the course are almost independent, if you get lost in one, you will find yourself again in the next one! So don't give up!
Postscript format | Pdf format Note: these files do not look good on the screen, but should print out OK. The margins are also messed up. I recommend using the postscript files! |
Grades in the Moed aleph 5765 exam
Grades in the Moed bet 5765 exam.
See also
Response to complaint of some students (pdf file).
Back to my main teaching page
Back to my main page