MATH 341 Numerical Analysis, Winter, 2007
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:
- numerical algorithms for each of the topics
listed in the course description
- discuss convergence and error analysis on these
algorithms
- the advantages and disadvantages of the methods
studied
- using computers and mathematical software to
solve problems
TEXT: An Introduction to Numerical Methods and Analysis, by James F.
Epperson, 2002, Wiley
SOFTWARE: The primary software package used in this course will
be Maple.
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 PM on Friday without penalty. Papers submitted
later than 1 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 computer software.
TESTS: Three tests
will be given, and they will cover both theory and computational methods.
FINAL
EXAMINATION: This test is scheduled
for Wednesday, March 14 from 8 to 9:50 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 35 of the 37 scheduled
class sessions
·
Turn in all 9 homework assignments (on time).
·
Make a higher grade on the final examination than you did on your
lowest test.
ACADEMIC
INTEGRITY:
See page 12 of http://www.wwc.edu/academics/bulletins/undergrad/2004-2006/03_academic_info.pdf
. 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.
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Week |
Topic |
Assignment |
Exercises to Work |
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1 |
Introduction to numerical analysis and review of important theorems of calculus |
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H1 |
§1.1 #1, 11b, 15; §1.2 #2; §1.3 #3ab, 6, 7 (calculator only), §1.5 #2; §1.6 #1d, 4d |
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Approximating the natural logarithm |
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3 |
Horner’s rule |
H2 |
§2.1 #1d (Then efficiently evaluate both
the polynomial and its derivative at |
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Approximating derivatives |
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Approximating solutions of differential
equations |
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Interpolation, The trapezoidal rule |
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Tridiagonal systems of equations |
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4 |
H3 |
§2.5 #11a, 16a; §2.6 #8 |
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Boundary-value problems |
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The bisection method |
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5 |
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H4 |
§2.7 #5; §3.1 #2a, 3a; §3.2 #1, 5h; §3.3 #3i; §3.5 #7 |
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Secant method |
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Fixed-point iteration |
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6 |
Lagrange interpolation |
H5 |
§3.7 #1a; §3.8 #1;
§4.1 #1, 2b, 8, 10; §4.2 #2ab; §4.3 #1, 10 (linear and quadratic only) |
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Divided differences, interpolation errors |
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7 |
Muller’s method |
H6 |
§4.4 #1 (one step only by hand), §4.5
#1, 6, Use Table 4.8 and Richardson’s extrapolation, as presented in class,
to approximate the derivative of the gamma function at 1.5 as accurately as
you can. |
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Numerical Differentiation and extrapolation |
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8 |
Numerical integration |
H7 |
§4.8 #5, 10 (approximate at 1.1 and 1.7 only) , #11 (1.1 and 1.7 only); §5.3 #3 (10 -6 only), 6a (Maple statements okay), Supplementary problem. |
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Simpson’s Rule |
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Romberg integration |
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9 |
Adaptive
integration |
H8 |
§5.8 #2a (Theorem 5.8 not necessary), 3a (Maple OK), Additional problems; §6.5 #1a, 2a, 6b |
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Runge-Kutta methods |
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Multistep methods |
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10 |
Systems of differential equations |
H9 |
§6.6 #1a, 5b (Use h=1/5 only); §6.8 #1acd (As part e, use the Adams-Bashforth-Adams-Moutlon predictor corrector with RK4 for starting values. |
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Application |
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11 |
Final Exam, March 14, 8-9:50 AM |
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