MATH 341 Numerical Analysis, Winter, 2006
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 MTu, 2 WTh, 11 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, and the student edition is available to you at a cost of $75.
Of course, Maple is available in the computer labs.
ASSESSMENT: All assessment will be based on both the correctness
and quality, including the quality of your presentation.
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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 1 p.m. 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. Some of these homework
assignments will require the use of Maple software.
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 > 2 and p + h > 9.
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 10-11:50 AM., Monday,
March 13. 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 |
Topic |
Assmt |
Exercises to Work |
1 |
Errors and computer arithmetic, see k:/class/math/341/LectureNotes/IntroLecture.mws |
H1 |
§1.1 #1a,3c,5,14 ; §1.2 #1a,3c,12,15a,16a |
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See the following files: Algorithms, Big-Oh errors Big-Oh errors #2 |
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Using Maple, examples. See the Maple files in k:/class/math/341/demo. |
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Using Excel, example |
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2 |
Bisection method, Project #1 assigned |
H2 |
§1.3 #1a,6a,7d,8,14; For additional required problems, click here. ;§2.1 #3b,6b,12 |
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Newton's method See k:/class/math/341/maple/newtons.mws, k:/class/math/341/maple/newton&secant.mws |
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3 |
H3 |
§2.2 #6,11a,15; §2.3 #6b,8b ; §2.4 #1a,3a,11; |
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4 |
Interpolation, Project #1 due 1/23. |
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 |
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Project #2 assigned |
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5 |
Numerical differentiation,
Project #2 due 2/6. |
H5 |
§4.1 #5a,7a,24,27(use 12 or
fewer significant digits);§4.2 #1b,2b,9 |
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Midterm Test Midterm Key |
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6 |
H6 |
§4.3 #1a,3a,5a,7a,15,20; §4.4 #1a,3a,11b; §4.5 #1a,3a,5a |
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Project #3 assigned |
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7 |
H7 |
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.) |
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Project #4 assigned |
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8 |
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.mws for starting values.) |
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Project #3 due 2/27 |
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Project #5 assigned |
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9 |
Project #4 due 3/3 |
H9 |
§5.9 #1a (one step if done without automated program) §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.) |
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Pivoting |
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Project #5 due 3/10. |
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10 |
H10 |
§3.4 #3c,5c,11,29; §3.5 #2ad; §8.1 #7a,(look at #4);§8.2 #1c,14,(look at #4c); For additional required problems, click here. |
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Project #6 due 3/13 |
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11 |
Final Exam, March 13, 10-11:50 AM |
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