MATH 341 Numerical Analysis, Winter, 2004

BULLETIN DESCRIPTION: Study of numerical methods with computer applications; topics include numerical solutions of nonlinear equations, systems of equations, ordinary differential equations, interpolation, and numerical integration. Prerequisites: CPTR 141; MATH 289.  Corequisite: MATH 312.

INSTRUCTOR: Dr. Kenneth L. Wiggins, 338 KRH, 527-2088

OFFICE HOURS: : Monday-Wednesday 2-3, Thursday 3-4, Friday 11-12, Other Office hours by appointment

OBJECTIVES: After finishing this course, students should be able solve problems and to organize and effectively communicate ideas involving each of the following:

TEXT: Numerical Analysis, 7th  edition, by Burden and Faires, 2001, Brooks/Cole

ASSESSMENT: All assessment will be based on both the correctness and quality, including the quality of your presentation.

Assessment Category

Weight

Homework

20%

Projects

20%

Midterm test

30%

Final examination

30%

Grade

Percent

Grade

Percent

Grade

Percent

Grade

Percent

A

91-100%

B

83-85%

C

70-74%

D

55-59%

A-

89-90%

B-

80-82%

C-

65-69%

D-

50-54%

B+

86-88%

C+

75-79%

D+

60-64%

F

0-49%

HOMEWORK: Homework assignments will be given each week, and these will be due each Friday at the beginning of class.  However, you may turn in your assignment at noon on Friday without penalty.  All solutions should be presented clearly and should include documentation of the solution process.  Assignments should be folded lengthwise, and you should place your name, “MATH 341”, the date, and the problem section number(s) on the outside of your paper.  This information should also be included on the inside of the first page of your homework. 

The homework assignments will be scored at 10 points each even though there will be variation in the length and difficulty of these assignments. Because of the amount of work required to grade numerical analysis homework, late papers ordinarily will not be accepted. If you are ill, contact your instructor concerning late work.   If h represents the number of homework assignments that you turn in, and if p represents the number of projects that you turn in, then you need  p ³ 3 and p + h ³ 10.

COMPUTER PROJECTS: Six projects will be assigned, and three of these will be required. The projects will require a computer program of some type using a standard computer language, such as Pascal or C.  If you wish to use a high level environment such as Maple or Matlab, first obtain permission from the instructor.

MIDTERM TEST: This test will cover both theory and computational methods.

FINAL EXAMINATION: This test is scheduled for 2-3:50 p.m., Wednesday, March 17. Attendance is required, so make your travel plans early with this appointment in mind.

CLASS ATTENDANCE: Students are expected to attend all classes. In addition, students are expected to give their full attention to the class discussions. Modifications in the homework assignments or test schedule may be announced in class.

DISABILITIES: If you have a physical and/or learning disability and require accommodations, please contact your instructor or the Special Services office at 527-2090. This syllabus is available in alternative print formats upon request. Please ask your instructor.

Week

Date

Topic

Assmt #

Exercises to Work

1

Jan 6-10

Errors and computer arithmetic

H1

§1.1 #1a,3c,5,14 ; §1.2 #1a,3c,12 (12d should reference parts b and c),15a,16a

 

 

Algorithms, Big-Oh errors Big-Oh errors #2

 

 

2

Jan 13-17

Solving equations,  Project #1 assigned

H2

§1.3 #1a,6a,7d,8,14; Supplementary exercises ;§2.1 #3b,6,10

 

 

Using Maple, examples

 

 

 

 

Using Excel, example

 

 

3

Jan 20-24

Newton's method

H3

§2.2 #6,11a; §2.3 #6a,8ai ; §2.4 #1a,2a,9;

 

 

Error analysis

 

 

 

 

Muller's method

 

 

4

Jan 27-31

Interpolation, Project #1 due 1/27.

H4

§2.6 #2a,3a; §3.1 #1a,2a,16a,26(replace "feasible" with "more accurate"); §3.2 #1a,2a,9,13

 

 

Divided differences

 

 

 

 

Project #2  assigned

 

 

 

 

 

 

 

5

Feb 3-7

Numerical differentiation, Project #2 due 2/3.

H5

 §4.1 #3a,4a,18,21(use  12 or fewer significant digits);§4.2 #1b,2b,9

 

 

Richardson's extrapolation

 

 

 

 

Review

 

 

 

 

Midterm Test

 

 

 

 

Numerical integration

 

 

6

Feb 10-14

Romberg integration

H6

§4.3 #1a,2a,3a,4a,5a,9,16; §4.4 #1a,2a,7b; §4.5 #1a,2a,3a; Supplementary exercises

 

 

Project #3 assigned

 

 

 

 

Adaptive quadrature, Example

 

 

 

 

ODE's

 

 

7

Feb 17-21

Holiday-no classes

H7

§5.1 #1a,2a ; §5.2 #1c,7 (Use h=0.2, 0.1, .05, .001, .0001, .00001 with 6 significant digits.)

 

 

Euler's method

 

 

 

 

Project #4 assigned

 

 

 

 

Runge-Kutta methods

 

 

 

 

Error control

 

 

8

Feb 24-28

Multistep methods

H8

§5.4 #1a,10a; §5.5 #2a (one step if done without automated program, use hmax=0.25); §5.9 #1a (one step if done without automated program)

 

 

Project #3 due 2/24.

 

 

 

 

Systems of ODE's

 

 

 

 

Project #5 assigned

 

 

 

 

Gaussian elimination

 

 

9

Mar 3-7

Project #4 due 3/3.

H9

 §6.1 #2a,4a (single precision indicates accuracy consistent with type float),6; §6.2 #5d,7c,9d (Rounding arithmetic may be used rather than chopping arithemtic. If you use rounding arithmetic, say so.); §3.4 #3c,5c,7,25

 

 

Pivoting

 

 

 

 

Cubic spline interpolation

 

 

 

 

Bezier curves

 

 

10

Mar 10-14

Project #5 due 3/10.         Curve fitting

Orthogonal functions

H10

§3.5 #2ad; §8.1 #7a,(look at #4);§8.2 #1c,14,(look at #4c); Supplementary problems

 

 

Discrete approximaton          Trigonometric polynomials

 

 

 

 

Review

Project #6 due 3/14

 

 

11

March 19

Final Exam, 8 a.m.