Math 5A -
Differential Equations and Linear Algebra II - Winter 2009
Professor: Alex Dugas my homepage
Office: 6510 South Hall
Office Hours: W
Finals' Week
(3/16-3/19): M 3-4, W 10-11, Th 11-12.
Prerequisites: Math 3C, with a grade of C or better.
Text: Farlow, Hall, McDill, West.
Differential Equations & Linear
Algebra. Second Custom Edition for UCSB. Pearson
Prentice Hall, 2007.
Lecture: MWF
Section: You must sign up for and attend a discussion section for this
course.
The section times and locations are as follows:
The GSI for this course is Garrett Johnson. His office hours are:
Announcements:
Course Timetable (subject to change) |
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Date |
Topics |
Reading |
Homework Due |
|
M 1/5 |
Simple Harmonic Motion. Solution to
the Undamped Unforced Oscillator |
4.1 p. 195-9 |
HW # 1 Wed 1/14 11:59 pm |
|
W 1/7 |
Simple
Harmonic Motion (cont.). Polar form of Solutions, Damping. Phase Planes |
4.1
p. 199-202 |
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F 1/9 |
Solving 2nd order DE's:
Real root case |
4.2 p. 210-15 |
HW # 2 Wed 1/14 11:59 pm |
|
M 1/12 |
Solving 2nd order DE's:
Complex roots |
4.3 p. 229-36 |
HW # 3 Sun 1/18 11:59 pm |
|
W 1/14 |
Nonhomogeneous equations. Undetermined Coefficients. |
4.4 p. 244-8 |
HW # 4 Wed 1/21 11:59 pm |
|
F 1/16 |
Undetermined
Coefficients (cont.) |
4.4 p. 248-52 |
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M 1/19 |
Martin
Luther King day: No Class! |
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W 1/21 |
Variation of Parameters. |
4.5 p. 255-9 |
HW # 5 Sun 1/25 11:59 pm |
|
F 1/23 |
Forced Oscillations. |
4.6 p. 261-7 |
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M 1/26 |
Converting higher order
DEs to systems of 1st order DEs. Phase Plane Portraits. (This
material will not be on the Midterm) |
4.7 p. 278-80 4.1 p. 200-02 |
No HW due Wed 1/28 |
|
W 1/28 |
Midterm
1: Chapter 4 |
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F 1/30 |
Linear Algebra: Vector
spaces, span, basis, dimension. |
Review 3.5:
p.167-74 3.6: p. 177-82, 186-90. |
HW #6 (due 2/1) 3.2: 27, 31, 40; 3.3: 1, 5, 7, 16 3.5: 5, 8, 14, 20, 21, 38-41 |
|
M 2/2 |
Linear Independence.
Basis. Linear Transformations. Matrices. |
5.1: p.
285-290 |
Hw #6 Wed 2/4 11:59 pm |
|
W 2/4 |
Properties of Linear
Transformations. Image and Kernel. (The book contains many
examples of Images and Kernels in 5.2 that you should read.) |
5.1: p. 291-2 5.2: p. 300-306 |
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F 2/6 |
Examples of Linear
Transformations on vector spaces of functions.
Calculus and ODE examples. |
5.3 p. 322-3 |
HW #7 Sun 2/8 11:59 pm |
|
M 2/9 |
Definitions of
Eigenvalues and
Eigenvectors, Eigenspaces. Examples. |
5.3: p.
311-17 |
HW #8 Thur 2/12 11:59 pm |
|
W 2/11 |
More Examples of
Eigenvalues/vectors. Complex Eigenvalues. Decoupling an ODE System. |
5.3 p. 318-23 5.4 p. 333 (Ex. 7) |
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F 2/13 |
Coordinates and
diagonalization. |
5.4 p. 327-32 p. 334-6. |
HW #9 Mon 2/16 11:59 pm |
|
M 2/16 |
Presidents'
day: No Class! |
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W 2/18 |
Midterm
2: Sections 5.1-5.4, 3.5-3.6 |
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F 2/20 |
Change of Coordinate Matrices.
Change of Coordinate formula for Linear Transformations. Systems of
first order ODE's |
6.1: p. 343-50 |
HW
#10 Wed 2/25 11:59 pm |
|
M 2/23 |
Linear Systems with Real
Eigenvalues |
6.2: p. 357-60, p. 362-5 |
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W 2/25 |
Linear Systems with Complex
Eigenvalues. (Decoupling Systems by diagonalization) |
6.3: p. 372-7 |
HW
# 11 Sun 3/1 11:59 pm |
|
F 2/27 |
Phase-Plane Portraits.
Systems with Real eigenvalues. Equilibrium points.
Stability. Pictures |
6.1: p. 350-4 6.2: p. 360-2 |
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M 3/2 |
More Phase-plane portraits for
systems with real and complex eigenvalues. |
6.3: p. 375-9 |
HW
#12 Th 3/5 11:59 pm |
|
W 3/4 |
Phase Plane Portraits for
degenerate cases: 0 - eigenvalues, repeated eigenvalues. Equilibrium points for Nonhomogeneous systems. |
6.4: p. 386-94 |
||
F 3/6 |
Nonhomogeneous Linear
Systems. Undetermined Coefficients. Variation of Parameters. |
6.7: p. 411-18 |
HW #13 Wed 3/11 11:59 pm |
|
M 3/9 |
Qualitative Analysis of
Nonlinear Systems. Equilibria and Nullclines. |
7.1: p. 421-6 |
No HW due. Practice: 7.1: 10 - 13, 7.2: 2 - 5 |
|
W 3/11 |
Linearization of Nonlinear
Systems. |
7.2: p. 431-7 |
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F 3/13 |
Review |
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Th
3/19 |
Final Exam
4:00 - 7:00 pm |
Homework: Homework exercises will be
assigned
every week to be completed online using WebWork.
Your
username is your
Typically, there will be TWO assigments per week, due on Wednesday and Sunday by 11:59 pm.
The due dates are always subject to change, so pay attention to what it
says on the assignment or in WebWork. Homeworks completed after
the due date will be scored but not counted.
Please
direct any questions you may have regarding the use of WebWork to your
TA. Each assignment also includes some reading in the text (see
the table
above). It is vital that you do this reading in addition to the
problems: it will not only help you solve the homework problems
correctly, but it may contain helpful information that was
not covered in lecture.
Exams: There will be two in-class midterm
exams on Wednesday, January 28
and Wednesday, February 18.
The final exam will be Thursday March
19, 4:00 - 7:00 pm. The problems on the exams will closely
resemble those on the homeworks. No books or calculators, etc.
are allowed, but you may bring one 3" x 5" note card, containing
hand-written notes. No make-up exams will be given, except in
extaordinary circumstances. You have the option of dropping one
midterm (see below). If you have a serious conflict with any of
these exams or miss one for any reason, it is your responsibility to
notify me immediately so that other arrangements may be made.
Grades: Grades will be computed from your scores on
homeworks, quizzes
and exams as follows: Homework/Quizes/Section = 20%, Each Midterm =
20%, Final
= 40%. The lowest 20% component of your grade will be
automatically dropped (For example, you may drop 1 midterm or have the
final count as 20% instead of 40%). No letter grades will be
assigned until the end of the semester, and the exact grading scale
will depend on the difficulty of the exams.
However, a 90% or above will guarantee you at least an A, an 80% will
be at
least a B, and 70% will be at least a C.
Course Content:
We will cover most of chapters 4-7 from the
text. Here is a rough outline of the course. A more
detailed timeline will be posted in the table above as the quarter
progresses.
- Weeks 1-3: Second Order Differential
Equations. (Ch. 4)
- Weeks 4-6: Linear Transformations,
Eigenvalues and Eigenvectors. (Ch. 5)
- Weeks 7-9: Linear systems of Differential
Equations. (Ch. 6)
- Week 10: Nonlinear systems of Differential
Equations. (Ch. 7)