014006 – Introduction to Numerical Analysis

Course Objectives

The course aims to provide tools and methods of linear algebra. Emphasis is given to topics that will be useful in other disciplines. The course includes theoretical discussions (i.e. theorems) and practical implementations of the methods. Many of the theorems will be stated without proofs.

Lecture Topics

1. Introduction. Taylor series, partial derivatives.

2. Description of various errors: rounding errors truncating errors

3. Systems of linear equations

4. Finding roots of algebraic equations

5. Nonlinear systems of equations

6. Optimization of functions without constraints

7. Interpolation

8. Curve fitting: least squares approximation, regression

9. Numerical integration

10. Numerical derivation

11. Solution of ordinary differential equations

Prerequisites

104002 – Calculus 2

234112 – Programming C

104131 – Ordinary Differential Equations (may be taken in parallel)

Teaching Staff

Lecturer: Tomer Toledo
Email: toledo@ technion.ac.il
Telephone: 04-829-3080
Office hours: Tuesday, 9:30-10:30
Office: Rabin building, Room 727

Student Evaluation

Assignments – 20%:

Homework assignments include writing computer programs in MATLAB. Submitting assignments is mandatory. Failure to submit the exercises will result in an “incomplete” grade for the course. Late submission will result in automatic grade 0 for the exercise. The exercises may be submitted in pairs. Submission in larger groups will not be approved in any case. All assignments must be submitted in hard copy (including computer programs). In addition, each member of the group is required to submit the computer programs through moodle.

Assignments must be solved using MATLAB only. You may not use other software.

Students may collaborate in groups to get ideas how to access the home assignments and to study the course material and software. Computer programs, the results of the runs and the text that accompanies them must be done independently.

Recitation:

Students must attend the recitation group that they are registered in.

Most recitations will take place in regular classes. A number of recitations will be dedicated to learning MATLAB. These exercises will take place in the computer classes in the Borowitz building.

Final Exam – 80%:

A grade of 55% at least is required on the exam in order to pass the course.

Reading Requirements

  • S.C. Chapra and R.P. Canale, “Numerical Methods for Engineers”, McGraw-Hill, 2002.
  • R.L. Burden and J.D. Faires, “Numerical Analysis”, Brooks Cole, 2004.
  • Auxiliary pages for lectures by Carol Braester, “Introduction to Numerical Methods”, 1998.

Contact Hours per Week

Lecture: 2 hours

Recitation: 2 hours

Credit: 3.0