MATH 413, Partial Differential Equations

Spring, 2009

BULLETIN DESCRIPTION: Study of partial differential equations, boundary-value problems, and Fourier series. Prerequisite: MATH 289, MATH 312.

INSTRUCTOR: Dr. Ken Wiggins, 338 KRH, 527-2088

Office Hours: 3 M, 2 Tu-Th, 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:

Fourier series solutions of partial differential equations
Partial differential equations in various coordinate systems
Sturm-Liouville Theory

TEXT: Partial Differential Equations and Boundary Value Problems, 2^nd edition, by Nakhle Asmar, 2005, Prentice Hall

SOFTWARE: Maple software will be used in this course.

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

Assessment Category	Weight	Grade	Percent	Grade	Percent	Grade	Percent	Grade	Percent
Homework	25%	A	91-100%	B	83-85%	C	70-74%	D	58-62%
Midterm test	35%
		A-	89-90%	B-	80-82%	C-	65-69%	D-	55-57%
Final examination	40%
		B+	86-88%	C+	75-79%	D+	62-64%	F	0-54%

HOMEWORK: The surest way to succeed in this course is to study each day. To aid you in your study, homework problems will be assigned each week, and nine of these assignments will be required. All assignments will be due at the beginning of class on Fridays, but they may be turned in as late as noon without penalty. Papers submitted later than noon on Friday will may be accepted.

MIDTERM TEST: This in-class test will cover the first half of the course.

FINAL EXAMINATION: This test is scheduled for 8-9:50 AM, Wednesday, June 10. 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.

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 taken 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	A Preview of Applications and Techniques Maple Example, Partial Derivative Maple Example, Moving Wave The Vibrating String	H1	Section 1.1 #1,2,8,10,13; Section 1.2 #3,5,7,9
2	Periodic Functions Fourier Series Maple Example Another Maple Example Arbitrary Periods Half-range Expansions Maple Example	H2	Section 2.1 #1d,4,6,9a,15; Section 2.2 #3,6,9,17 (You need not calculate all 20 partial sums as requested in #6 and #9. Experiment and plot enough to make your point.) Section 2.3 #4 (See #9 in section 2.2),11 (Look at #20-33)
3	Mean Square Approximation Complex Series Uniform Convergence Maple Example	H3	Section 2.4 #4a (cosine series only),17ab; Section 2.5 #4,6; Section 2.6 #9
4	The Direchlet Test for Convergence Partial Differential Equations in Rectangular Coordinates Vibrating Strings The Wave Equation	H4	Section 2.9 #14,24 (Look at #4,19,26,29); Section 2.10 #5; Section 3.1 #6,9; Section 3.2 #7
5	Midterm test formulas D'Ambert's Method One Dimensional Heat Equation Maple plots for 3.5 #11	H5	Section 3.3 #8a, (Look at #4); Section 3.4 #15abc (Look at #3, 14b)

6	Heat Conduction in Bars Midterm Test	H6	Section 3.5 #13; Section 3.6 #13 Give numerical values of the first five coefficients. (Look at #4)
7	Various Heat Equations Review of variation of parameters	H7	Section 3.7 #11; Section 3.8 # 2
8	Two Dimensional Wave And Heat Equations Silver plate application The Maximum Principle Differential Equations in Polar and Cylindrical Coordinates Bessel Functions	H8	Section 3.9 #8; Section 3.11 #6; Section 4.1 #5
9	Partial Differential Equations in Spherical Coordinates	H9	Section 4.7 #3; Section 4.2 #10 (Look at #1);
10	Sturm-Liouville Theory Engineering Application	H10	Additional required exercises; Section 6.1 #9,10; A fourth part was added to Theorem 4. Show how the proof of this theorem given in class also covers this condition. Finally, use this theorem to prove that the Legendre polynomials are orthogonal on [-1,1] with weight function 1.; Look at More Supplemental Exercises
11	Final Examination, 8-9:50 AM, Wednesday, June 10