MATH 312 Syllabus

MATH 312 Ordinary Differential Equations, Autumn, 2004

BULLETIN DESCRIPTION: Study of solutions of first order differential equations, solutions of linear differential equations of order n, linear systems, and series solutions. Prerequisite: MATH 283

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

OFFICE HOURS: 2 TuWTh, 3 M, 11 F, Other Office hours by appointment

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

First-order equations. Picard's existence and uniqueness theorem; separable equations, exact equations, linear equations (integrating factors), solutions by substitution, applications of first order equations.
Higher-order Equations. Existence and uniqueness results, reduction of order, homogeneous equations, differential operators, undetermined coefficients, variation of parameters, harmonic motion, series solutions.
The Laplace Transform. The inverse Laplace transform, translation theorems, transforms of derivatives, solving initial-value problems with Laplace transforms.
Systems of Differential Equations. The Laplace transform method, differential operators, matrix methods using eigenvalues and eigenvectors.

TEXT: A First Course in Differential Equations with Modeling Applications, 7th edition, by Dennis G. Zill, Brooks-Cole, 2001

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

Assessment Category	Weights
Homework & quizzes	15%
Three tests	50%
Final examination	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: The surest way to succeed in MATH 312 is to study each day. To aid you in your study, homework problems will be assigned each day. Most of these will be collected and graded. Be sure to show your work neatly on these papers and to complete your work on time. Homework papers are due the day after they are assigned but they may be turned in the next day at the beginning of class without penalty. Papers later than that will not be accepted.

QUIZZES: Occasionally quizzes may be given over the lectures and homework.

TESTS: Three 50-minute examinations will be given during the quarter. These will cover the lectures and the homework.

FINAL EXAMINATION: This test is scheduled for 2-3:50 p.m., Monday, December 13. If, on any single day, you have either four final examinations or three consecutive final examinations, see Dr. Clinton Valley about rescheduling one of the exams. Otherwise, except for emergencies, plan to take the exam at the scheduled time.

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 #	Pages to Read	Exercises to Work
1	Sept 27	Terminology	H1	1-14	§1.1 #1,3,4,13,16,19,27,33
		Initial-Value Problems	H2	14-22	§1.2 #3,9,15,16,18,21,24,34
		Mathematical Models	H3	22-38	§1.3 #3,5,9,15
		Solution Curves	H4	39-51	§2.1 #1abc,20
2	Oct 4	Separable Variables	H5	51-60	§2.2 #7,11,19,25,35,36
		Linear Equations	H6	60-71	§2.3 #3,6,14,30
		Exact Equations	H7	72-80	§2.4 #7,9,21,27,32
		Substitutions	H8	80-85	§2.5 #5,8,11,17,22
3	Oct 11	Linear Models	H9	95-109	§3.1 #3,12,15,25,32
		Catch-up/review
		Test #1, through §3.1
4	Oct 18	Nonlinear Models Example 1 , Example 2	H10	109-120	§3.2 #3,7,22
		Higher-order equations-theory Interesting Property of Wronskians	H11	138-154	§4.1 #1,2,6,9,11
		Continuation	H12		§4.1 #17,21,23,31,33,38
		Reduction of Order	H13	154-157	§4.2 #3,6,11,23
5	Oct 25	Homogeneous equations	H14	158-167	§4.3 #7,13,25,28,38,54
		Undetermined coefficients	H15	178-187	§4.5 #5,8,13,17,22,23,24
		Continuation	H16		§4.5 #35,42,43,53,59,68
		Variation of parameters	H17	188-193	§4.6 #3,6,10,25
6	Nov 1	Catch-up / review
		Test #2 – through §4.7
		Linear IVP's	H19	216-237	§5.1 #2,3,6,17,18,20
		Continuation Example	H20		§5.1 #22,29,33,46 (Maple ok)
7	Nov 8	Linear BVP's	H21	237-247	§5.2 #1,11,12
		Series solutions	H22	268-280	§6.1 #3,5,9,11,17,25
		Singular points	H23	280-291	§6.2 #1,8,21
		Laplace transform	H24	306-314	§7.1 #1,3,11,24,32,37,39,40
8	Nov 15	Inverse transform	H25	314-324	§7.2 #3,6,9,12,17,21,26,35
		Translation theorems	H26	324-338	§7.3 #3,10,13,18,21,27,41,43,57,63
		Transforms of derivatives	H27	338-350	§7.4 #3,7,12,17,24,27,31,43
		Applications	H28	351-360	§7.5 #3,13; 7.6 # 15
9	Nov 29	Catch-up/review
		Test #3, through §7.5
		First-order systems	H30	364-375	§8.1 #1,3,6,8,11,17,25
10	Dec 6	Homogeneous linear systems	H31	375-393	§8.2 #3,9,13,21,24,39
		Nonhomogeneous linear systems	H32	393-399	§8.3 #3,23,24
		Continuation
		Review
11	Dec 13	Final Examination Formula sheet for the final exam 2-3:50 p.m.