MATH 341 Numerical Analysis, Winter, 2009

Walla Walla University


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: 3 M, 2 Tue-Thu, 1 F, 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, 8th  edition, by Burden and Faires, 2005, Thomson, Brooks/Cole

SOFTWARE: The primary software package used in this course will be Maple.


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

Category

Weight

Homework & quizzes

15%

Three tests

50%

Final exam

35%

 

Grade

Percent

Grade

Percent

Grade

Percent

Grade

Percent

A

91-100%

B

83-85%

C

70-74%

D

58-61%

A-

89-90%

B-

80-82%

C-

65-69%

D-

55-57%

B+

86-88%

C+

75-79%

D+

62-64%

F

0-54%

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 as late as 3 PM on Friday without penalty.  Papers submitted later than 3 PM on Friday will not be accepted.  All solutions should be presented clearly and should include documentation of the solution process.  Assignments should be folded lengthwise, and you should label you paper as shown at left.  This information should also be included on the inside of the first page of your homework.   Some of these homework assignments will require the use of Maple computer software.

TESTS:  Three tests will be given, and they will cover both theory and computational methods.

FINAL EXAMINATION: This test is scheduled for Monday, March 16 from 10 to 11:50 AM. 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, and to be courteous, respectful, and supportive of the learning environment.  Cell phones, computers, personal organizers, and all other electronic devices are not to be used by students during class.   Modifications in the homework assignments or test schedule may be announced in class.

SPECIAL CONSIDERATION FOR EXTRA EFFORT:  Your lowest test grade will be dropped and replaced with your final examination grade if you meet the following conditions:  You must

·         Be present, on time, and attentive for at least 37 of the 39 scheduled class sessions

·         Turn in all 10 homework assignments (on time).

·         Make a higher grade on the final examination than you did on your lowest test.

ACADEMIC INTEGRITY: Some collaboration on homework is allowed, but the work you submit for grading must be your own.  Any type of cheating on a test or examination, including but not limited to copying another student’s work or using unauthorized notes or electronic equipment, will result in a zero grade for the test or a failing grade for the quarter, and possibly further disciplinary action take by the Associate Vice President for Academic Administration.

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

Topic

Assmt

Exercises to Work

1

Introduction

Numerical errors and computer arithmetic

IEEE Example

Using Maple, examples.

Algorithms pdf

Algorithm- Maple

Example

Example

Bisection method 

H1

§1.1 #1a,3c,5,14

§1.2 #1a,3c,12,15a,16a

2

Fixed-point iteration Example

Maple Example

Newton's method

Maple example

Newton and secant Maple example

Order of convergence

H2

§1.3 #1a,6a,7d,8,14; For additional required problems, click here.

§2.1 #3b,6b,12

3

Multiple zeros and Newton

Polynomial evaluation

Synthetic division

Example of Newton's method with Horner's Rule

H3

§2.2 #6,11a,15

 §2.3 #6b,8b 

§2.4 #1a,3a,11;

4

Muller's method Example 1 Example 2

Interpolation

Maple Example

Maple Example

Divided differences

Divided differences -- details

H4

§2.6 #2a,3a; §3.1 #1a,3a,5a,9a,30(replace "feasible" with "more accurate"); §3.2 #1a,11,13 (replace "third order forward differences" with "third divided differences."),17

Test #1 key, Wednesday

5

Numerical Differentiation, Example

Richardson's Extrapolation

Example

Numerical integration

Example

H5

 §4.1 #5a,7a,24,27(use  12 or fewer significant digits);§4.2 #1b,2b,9

6

Romberg integration ,

Example

Adaptive quadrature, Example

Example

H6

§4.3 #1a,3a,5a,7a,15,20; §4.4 #1a,3a,11b; §4.5 #1a,3a,5a


7

Differential Equations

Euler's method

Maple example

Runge-Kutta methods

Second-order RK Maple example

Fourth-order RK Maple example

H7

Test #2 key, Wednesday

For additional required problems, click here.; §5.1 #1a,2a (If the theorem doesn't apply, say so and justify your claim.),3a ; §5.2 #1c,11 (Use h=0.2, 0.1, .05, .001, .0001, .00001 with 6 significant digits.)

8

Error control

Rungke-Kutta-Fehlberg Maple example

Multistep methods

Maple derivation

Systems of differential equations

Maple example

H8

§5.4 #1a,13a; §5.5 #2a (one step if done without automated program, use hmax=0.2); §5.6 #3b (Change instructions -- Use 4th order Adams-Bashforth and Adams-Moulton combination to advance the solution to 2. See RK4-Problem3bSection5-6 for starting values.)

9



Cubic spline interpolation

Drawing example

Parametric spline example

Hermite spline example

Bezier spine example

H9

§5.9 #1a (one step if done without automated program); §3.4 #3c,5c,11,29; §3.5 #2ad

10

Gaussian elimination

Pivoting

Maple example

H10

;§6.1 #2a,5a,7c (carry 7 significant digits),10; §6.2 #10b,14b,18b (Rounding arithmetic may be used rather than chopping arithmetic. If you use rounding arithmetic, say so.)

Test #3 sample problems, Test #3. Friday

11

Final Exam, March  16, 10-11:50 AM