Spring 2009


EECS 328: Numerical Methods for Engineers 


3:00--3:50 Monday, Wednesday, and Friday

Tech LR5
Department of Electrical Engineering and Computer Science
Northwestern University

class webpage: http://www.cs.northwestern.edu/~kao/eecs328-numerical-methods

 

(last updated 6/1/2009)

 

*** Important Announcements. Please Check Daily. ***

Synopsis:

Introduction to numerical methods, numerical differentiation, numerical integration, solution of ordinary and partial differential equations. Students write programs in languages or packages such as  C++, FORTRAN, C, or Matlab using methods presented in class.

Course Objectives:

When a student completes this course, she or he should be able to:

  1. Understand the type of numerical problem he or she is facing and relate it to one of the problem classes discussed in the course.

  2. Find a numerical routine that will solve the engineering problem, or use one of the numerical tools such as MATLAB.

  3. Design a driver that will use a number of numerical routines to perform the desired task.

  4. Interpret numerical results and devise graphical representations that facilitate their analysis.

  5. Understand the fundamental properties of computer arithmetic. Differentiate between the errors caused by computer arithmetic and those caused by the limitations of the algorithms.

  6. Predict the difficulties that may occur in solving an engineering problem due to (1) problem size, (2) conditioning, and (3) errors in the data.

  7. Understand the concepts of ill-conditioned and well-posed problems, and identify important classes of problems (such as nearly singular systems of equations) that are difficult to solve.

  8. Understand the tradeoffs between speed and memory, or between speed and robustness that often occur in practical algorithms.

 
Instructor:

Ming-Yang Kao
Office: Tech M324
Phone: 847-230-9867
Email: kao@northwestern.edu
URL: www.cs.northwestern.edu/~kao
Office Hours: 2:00--3:00 Tuesday and 11:00--12:00 Thursday, or by appointment

 
Teaching Assistants:

Gang Li
Office: Tech L460
Phone: 847-467-2299
Email: gangli2012 at u dot northwestern dot edu
URL: N/A
Office Hours: 2:00-3:00 Monday and 1:00-2:00 Thursday, or by appointment

 

Wendy Yip
Office: Tech EB59
Phone: 847-467-0363
Email: wendyyip2011 at u dot northwestern dot edu
URL: N/A
Office Hours:  11:00-12:00 Tuesday and 1:00-2:00 Wednesday, or by appointment
Pre-requisites:
  • GTK 205-1, 2, 3 and MATH 214-1, 2, 3 are required.
  • MATH 221 or GTK 205-4 are not required but may be taken concurrently.

Course Work and Grading Policy:

 

Your grade will be based on weekly reading assignments (0%), eight weekly problem sets (7.5% each, 60% in total), one midterm examination (15%), and one final examination (25%).

  • Weekly Reading Assignments: Reading assignments will be posted on the class webpage. You are responsible for the materials that are assigned but are not covered in detail or at all in class. Some of such materials are covered in the prerequisite or even earlier courses.

  • Weekly Problems Sets: Starting the first week, a problem set will be posted on the class webpage each Friday and will be due at the start of class on the following Friday. You will have one week to work on each problem set. A total of 8 problem sets will be assigned.

  • Midterm Examination: The midterm examination will be a in-class test on Friday, 5/1/2009.

  • Final Examination: The final examination will take place 12:00--2:00PM, Tuesday, 6/9/2009, as scheduled by the Registrar.

Without a Dean's excuse, no late problem set will be accepted, nor will early or make-up examinations be given. 

 
Required Textbook and Software:
  • M. T. Heath. Scientific Computing: An Introductory Survey. 2nd Edition, 2002, McGraw-Hill.
  • The programming assignments will use Matlab.

 
Tentative Schedule:

 

This schedule is subject to modification. More details will be added as they become available.

  • Topic 1 (3 meeting): Introduction, Approximations and Computer Arithmetic  (Syllabus and Chapter 1).

  • Topic 2 (3 meetings): Systems of Linear  Equations (Chapter 2).

  • Topic 3 (3 meetings): Iterative Methods for Linear Systems (Section 11.5)

  • Topic 4 (3 meetings): Eigenvalue Problems (Chapter 4)

  • Topic 5 (2 meetings): Case Study I -- Google PageRank

  • In-class Midterm Examination (1 meeting)

  • Topic 6 (3 meetings): Non-linear Equations (Chapter 5)

  • Topic 7 (3 meetings): Interpolations (Chapter 7)

  • Topic 8 (3 meetings): Numerical Integrations and Differentiation (Chapter 8)

  • Topic 9 (2 meetings): Ordinary Differential Equations (Chapter 9)

  • Topic 10 (3 meetings): Case Study II -- Divide-and-Conquer Strategies

  • Final Examination.

 
Weekly Reading Assignments and Problem Sets: