Jeremy Schiff: Tools for Numerical Analysis (83-214)

Tools for Numerical Analysis (83-214)

This is a one-semester course to introduce electrical engineering and computer engineering students to numerical methods. Each week there is a 90-minute lecture (Wed 10-12, building 507, room 17) and a 90-minute recitation. (Recitations are given by Ruthi Leabovich and Shai Refaeli on Sundays 10-12 and Tuesdays 8-10. The first 2 recitation sessions will be held in computer labs.) My office hours are Thursday 14:00-16:00 in the math building (building 216), room 301 (top floor, north west corner of building).

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.

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!

Resources

I will be happy to post here any internet resources for this course that have been recommended to me by students.
As far as books are concerned, there are Open University books in Hebrew on "hishuv numeri" that are a bit old, but cover most of the necessary material (though without Matlab). For texts in English you might try Chapra and Canale or Mathews and Fink.

Exercise Sets

You will need a postscript viewer (GSview or gv) to view the links below
Submission: It is compulsory to submit at least 4 out of the exercise sets. They will be looked at, but not graded in detail. There is no formal grade for the exercise sets, but regular submission is a requirement for a passing grade in the course.

Exercise Set 1, Error analysis: ps, pdf
Exercise Set 2, Numerical linear algebra: ps, pdf
Exercise Set 2a, A couple of extra exercises about conditioning ps, pdf
Exercise Set 3, Finding roots and minima ps, pdf
Exercise Set 4, Interpolation ps, pdf (sorry, there was an error in the original version)
Exercise Set 5, Approximation ps, pdf
Exercise Set 6, Integration ps, pdf

See Ruthi's and Shai's sites for help and solutions.

Exams

The exam at the end of the course will be a 2.5 hours exam, and will account for 100% of the course grade. The exam will be divided into two parts, the first (without choice) consisting of short, easy questions intended to check knowledge of the basic facts/methods taught in the course, the second (with choice) consisting of longer, slightly deeper questions intended to check understanding (as opposed to simple "knowledge").
Below you can find some past exams:
You will need a postscript viewer (GSview or gv) to view the links below
Warning: Usually there are minor changes in the course from year to year (for example if lectures are cancelled because of strikes). Do not be surprised if there are questions in a previous year's exam that you cannot do!

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