Math 341: Spring 2006
Computational Methods

Course information

Course Description

This course serves as an introduction to numerical analysis. Numerical analysis has a long history, going back to the 17th and 18th centuries. The invention of digital computers in the mid 20th century gave numerical analysis a predominant role in all aspects of scientific computing and gave rise to an unprecedented rush of new techniques and algorithms.

The bulk of this course deals with the issue of approximating arbitrary functions with polynomials. Estimation of errors in such approximations is the main focus of the subject. Polynomial approximations are then used to obtain algorithms for numerical differentiation, integration, and solving differential equations.

A second major topic of this course is the issue of computing solutions of system of linear equations. Several direct and iterative schemes will be discussed and approximation errors will be analyzed.

Prerequisites: Math 152 (calculus II), Math 221 (linear algebra), CMSC 201 (programming techniques).

Software

Numerical computing, commonly called "number crunching", is an integral part of this course. Matlab is the predominant software tool for numerical computing. Following the textbook, will use Matlab for illustrations and examples throughout this course.

Textbooks

Kendall Atkinson and Weimnin Han: Elementary Numerical Analysis third edition, John Wiley & Sons, 2003.

Suggested reading: MATLAB: An Introduction with Applications by Amos Gilat

Weekly homework

I will put homework assignments on this web page immediately before or after each class. Solution of problems assigned during week n are due on the Thursday of week n+1. I will have some or all of the problems graded and will return them to you on the following Tuesday.

No late homeworks will be accepted, however the two lowest homework grades will be dropped.

Exams

Exam 1 and Exam 2 will cover approximately the first third and second third of the course. They will be given in the regularly scheduled class time.

The Final Exam will be comprehensive -- it will cover the entire course -- however it will put greater emphasis on the material covered in the later parts of the course.

 The Final Exam is on May 23 10:30-12:30, in SOND 101 

Grading

Your course grade will be calculated based the weights attached to various components as shown in the adjacent table. Letter grades will be determined according to:

if { grade ≥ 85: A}
else if { grade ≥ 75: B}
else if { grade ≥ 65: C}
else if { grade ≥ 55: D}
else F

I will make and grade the exams in a fair and reasonable way, but sorry, no "curving" in this course.

Homework assignments

Homework Assignments Solutions Jan 31 Sec. 1.1, #1, 3(b), 4, 6, 7 Sec. 1.2, #5, 6, 8, 12 341-hw01.mw Feb 2 No additional problems assigned today Feb 7 Sec. 3.1: #2, 10, 12 341-hw02.mw Feb 9 Sec. 3.2: #3, 4, 5 Feb 14 No additional problems assigned today 341-hw03.mw Feb 16 Sec 3.3: #1 Feb 21 Sec. 3.4: #2, 3, 4, 7 341-hw04.mw Feb 23 Sec. 4.1: #1, 2 Feb 28 Sec. 4.1: #8, 12, 15, 18 341-hw05.mw Mar 2 Exam 1 on material corresponding to assignments on Jan 31 to Feb 21. Mar 7 Sec. 4.1: #24, 25, 28, 31, 32 341-hw06.mw Mar 9 Sec. 4.2: #1, 2, 4, 5 Mar 14 No problems assigned today 341-hw07.mw Mar 16 Sec. 4.3: #2(b), 3(c), 3(d), 10, 12, 16 Mar 21 Spring Break Mar 23 Spring Break Mar 28 Sec. 4.5: #1, 3, 7, 8, 10 341-hw08.mw Mar 30 Sec. 4.6: #3(b), 4, 5, 6 Apr 4 Sec. 4.7: #1, 2 341-hw09.mw Apr 6 Sec. 4.7: #3 Apr 11 Sec. 5.1: #1 Sec. 5.2: #1(a), 1(b), 5(a), 5(d), 6(a), 6(d) 341-hw10.mw Apr 13 Exam 2 on material corresponding to assignments on Feb 23 to April 6. Apr 18 today's hw 341-hw11.mw Apr 20 Sec. 5.4: #10 Apr 25 today's hw 341-hw12.mw Apr 27 See link above May 2 No problems assigned today 341-hw13.mw May 4 Sec. 6.4, #1, 2 (parts (a),(b)), 6, 8 Sec. 6.6, #1, 3 (you may want to write a little program to do these) May 9 No problems assigned today 341-hw14.mw May 11 Sec. 7.1, #1 (do it but I won't collect) May 16 Open question/answer session

Homework Grades   Exam #1 grade distribution   Exam #2 grade distribution   Final exam grade distribution   Cumulative grade distribution   Interpolation demos: Downloadable Maple worksheets of classroom demos curve-fitting-error1.mw curve-fitting-error2.mw curve-fitting-error3.mw curve-fitting-error4.mw curve-fitting-error5.mw   Euler and Runge-Kutta solvers: de-solvers.mw   Jacobi and Gauss-Seidel algorithms: sys-iterate.mw

Instructions for the final exam: Bring along a calculator (of any sort). The exam will be closed-book/closed-notes. However you may bring along up to 3 crib-sheets filled on both sides with whatever you think you will need. No other reference material is allowed. The exam will cover the entire course, although lesser emphasis will be placed on the early material.

 The Final Exam is on May 23 10:30-12:30, in SOND 101 

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