MATH 312 Ordinary Differential Equations, Autumn, 2006
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, wiggke@wwc.edu
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,
8th edition, by Dennis G. Zill, Brooks-Cole, 2005
ASSESSMENT: All assessment will be based on both correctness and
quality including the quality of your presentation.
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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, and 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.
Please fold your homework lengthwise and label it as illustrated in the
diagram on the left.
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 10-11:50 a.m., Monday, December 11.
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 during all class sessions. 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: 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.
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 36 of the 39 scheduled class
sessions
·
Turn
in at least 95% of the homework.
·
Make
a higher grade on the final examination than you did on your lowest test.
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Week |
Date |
Topic |
Assmt # |
Exercises to Work |
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1 |
Sept 25 |
H1 |
§1.1 #1, 3, 4, 13, 16, 19, 27, 33 |
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H2 |
§1.2 #3, 9, 15, 16, 18, 21, 24, 34 |
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H3 |
§1.3 #3, 5, 9, 15 |
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H4 |
§2.1 #1abc, 6, 24 |
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2 |
Oct 2 |
H5 |
§2.2 #7, 11, 19, 25, 35, 36 |
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H6 |
§2.3 #3, 6, 14, 30 |
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H7 |
§2.4 #7, 9, 21, 27, 32 |
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H8 |
§2.5 #5, 8, 11, 17, 22 |
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3 |
Oct 9 |
H9 |
§3.1 #3, 12, 15, 25, 32 |
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Catch-up/review |
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Test #1, through §3.1 Answer key |
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4 |
Oct 16 |
H10 |
§3.2 #3, 9, 16 |
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Higher-order equations-theory Interesting Property of Wronskians |
H11 |
§4.1 #1, 2, 6, 9, 11 |
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Continuation |
H12 |
§4.1 #17, 21, 23, 31, 33, 38 |
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H13 |
§4.2 #3, 6, 11, 23 |
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5 |
Oct 23 |
H14 |
§4.3 #7, 13, 25, 28, 38, 50 |
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H15 |
§4.5 #5, 8, 13, 17, 22, 23, 24 |
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Continuation |
H16 |
§4.5 #35, 42, 43, 53, 59, 68 |
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H17 |
§4.6 #3, 6, 10, 25 |
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6 |
Oct 30 |
Catch-up / review |
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Test #2 – through §4.7 Answer key |
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H18 |
§5.1 #2, 3, 6, 17, 18, 20 |
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Continuation Example |
H19 |
§5.1 #22, 29, 33, 46 (Maple ok) |
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7 |
Nov 6 |
H20 |
§5.2 #1, 11, 12 |
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H21 |
§6.1 #3, 5, 9, 11, 17, 25 |
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H22 |
§6.2 #1, 8, 21 |
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H23 |
§7.1 #1, 3, 11, 24, 32, 37, 41, 42 |
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8 |
Nov 13 |
H24 |
§7.2 #3, 6, 9, 12, 17, 21, 26, 35 |
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H25 |
§7.3 #3, 10, 13, 18, 21, 27, 41, 43, 57, 63 |
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H26 |
§7.4 #3, 7, 12, 17, 21, 24, 27, 31, 43 |
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Nov 19-25 |
Thanksgiving vacation |
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9 |
Nov 27 |
Applications |
H27 |
§7.5 #3, 13; 7.6 # 15 |
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Catch-up/review |
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Test #3, through §7.5 Answer key |
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H28 |
§8.1 #1, 3, 6, 8, 11, 17, 25 |
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10 |
Dec 4 |
H29 |
§8.2 #3, 9, 13, 21, 24, 39 |
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H30 |
§8.3 #11, 23, 24 |
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Continuation |
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Review |
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11 |
Dec 11 |
Final Examination 10-11:50 AM Formulas not provided; you may bring a formula sheet. Formulas you might want to include on your sheet. |
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