Math 5A - Differential Equations and Linear Algebra II - Winter 2009

Professor: Alex Dugas my homepage
Office: 6510 South Hall
Office Hours:  W 10:00 - 12:00, F 2:00 – 3:00, or by appointment

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 1:00 - 1:50 pm in 1006 North Hall.

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)


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

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

M 1/19
Martin Luther King day: No Class!



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

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


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

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)

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!

W 2/18
Midterm 2: Sections 5.1-5.4, 3.5-3.6



 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

 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

 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

 F 3/13
 Review



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 Perm number, and your password is also your Perm number, until you change it.   If you are not registered for this course at the start of classes, you must email your Perm number to your TA to request a WebWork account.

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)