MATH 1332  (Winter 2009)




MAT 1332 C
MAT 1332 B
MAT 1332 D
Professor

Frithjof Lutscher Robert Smith?
(the question mark is part of my name)
Jing Li
Office

585 King Edward (KED), Room 203 C 585 King Edward (KED), Room 205 G
585 King Edward (KED), Room 204 B
Phone

562-5800 x3510 562-5800 x3864 562-5800 x2103
Email

flutsche (at) uottawa.ca rsmith43 (at) uottawa.ca jl3 (at) uottawa.ca
Lectures

Mondays 10:00-11:30

Wednesdays 8:30-10:00
Mondays 10:00-11:30

Wednesdays 8:30-10:00
Mondays 17:30-19:00

Wednesdays 17:30-19:00
Location

MNT 202
LMX 122
MCD 146
Office hours

Mondays 3:30-4:30
or by appointment
Tuesdays 3:30-4:30
or by appointment
Tuesdays 11-12
or by appointment

Texbook: Modeling the Dynamics of Life. Calculus for Life Scientists by Frederick R. Adler (Custom Edition). This is the same book that was already used for MAT 1330 in the Fall term 2008. Alternatively, the regular second edition of Modeling the Dynamics of Life. Calculus and Probability for Life Scientists by Frederick R. Adler is also okay.

(The textbook is available at the student-owned Agora bookstore.)

Lecture notes: Additional notes for material that is not covered in the textbook will be available through the website (below).

Calculators: Only the faculty-approved model TI 30 (and equivalent) are permitted on midterms and the final exam.

Course Content: Roughly, we will cover sections 4.4-4.7, all of chapter 5, as well as selected other topics. Lecture note for these additional topics will be available through this website in the table below.

Help Centre: Marion 021, Monday through Thursday: 10:00-7:00, Fridays 10:00-3:00. During the  Study break: 10:00-3:00.


Discussion Groups (DGDs)



MAT 1332 C

MAT 1332 B
MAT 1332 D
DGD 1   Thursday, 11:30-13    FTX 227
DGD 2   Thursday, 11:30-13    CBY  B012
(Questions about DGD 2 to:
jalsm084 (at) uottawa (dot) ca)

DGD 3   Thursday, 17:30-19    TBT 070
DGD 4   Friday, 11:30-13         MCD 121
DGD 1     Thursday, 11:30 - 13:00           CBY D103     
DGD 2     Thursday, 11:30 - 13:00           CBY D207        
DGD 3     Thursday, 17:30 - 19:00           DMS 1140
DGD 4     Friday, 11:30 - 13:00                SMD 224
DGD 1 Thursday 11:30-13:00  LPR 155

DGD 2 Thursday 17:30-19:00 DMS 1110


Assessment

There will be two midterms and a final exam, as well as regular assignments. Assignments will be posted on this website in the table below. NOTE that assignments cover the material of several classes each. You will NOT be able to do an assignment properly in a single afternoon or night. The problems in the assignments give you a good idea of the type of problems in the tests (but the ones on the tests will tend to be easier).

There will be no make-up tests. If you miss a test and you bring a doctor's note, the weight of the test will be carried to the final exam.

Assignments will be due at the beginning of class. Late assignments will not be marked.

Assignments will be returned in the DGD you are registered in. Please make sure your assignment is stapled (if more than one piece of paper) and has your name, student number and DGD written CLEARLY on the front.

The weighting of the course components will be as follows:
Assignments 10% (total)
Midterms 20% each
Final exam 50%

Any student who scores less than 40% on the final exam will receive an automatic F, regardless of their marks in assignments or midterms. Any student who scores less than 45% on the final exam cannot receive a higher course mark than E.

General comments

  1. The table below gives you information about what was covered in class together with a list of suggested exercises. It also gives you the assigments. Please check the website frequently as it will be updated regularly.
  2. There are many worked examples in the book. We will often use different ones in class; other classes might use different ones again. Please take advantage of this wide variety of exercises.
  3. Learning mathematics requires solitary work and group efforts. Get together in small groups to discuss the material but solve and write your assignments on your own! This will pay off in the end.
  4. If you have suggestions for me to improve our teaching, please tell me right away. Do not wait until the course evaluation at the end of the term, because then only the students after you will benefit from your suggestion.
  5. I am available during office hours (see above) as well as just before and right after class. Please make use of that, come talk to me about the material, about any questions related to this course. Please do not expect me to answer emails or phone calls on a weekend.

Timetable for lectures, assignments and tests


Week
Date
Material covered
(numbers refer to sections in the textbook)
Additional Material (Notes) will be posted here
Suggested Exercises
 (numbers refer to exercises in the textbook)
Assignments
Solutions


Download Notes part 1 here



1
Jan 7
4.4
plus: arctan function (Notes pages 2-3)
4.4: 1, 3, 5, 7, 9, 11, 13, 15, 25, 27, 33 Assignment #1
due Jan 21
Integration I

Section B
Section C
Section D

2
Jan 12
4.5
4.5: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39
Jan 14
4.6
plus: integrals and volumes (Notes pages 3-6)
4.6: 1, 3, 5 (no graphing necessary), 7, 9, 11, 13, 15, 29, 31, 33
see also the worked examples in the Notes
Solutions
3
Jan 19
Partial fractions (Notes pages 7-14)
Notes page 10 Assignment #2
due Jan 28
Integration II


Section B
Section C
Section D

Jan 21
4.7 (excluding "leading behavior")
4.7: 5, 7, 9, 11, 13, 19, 21, 27, 29

See these corrections to some textbook exercises

4
Jan 26
5.1 (excluding "Euler's method")
5.1: 1, 3, 7, 15, 17, 23, 25, 27, 29, 33, 35, 39

Jan 28
5.4
5.4: 3, 5, 11, 13, 15, 19, 25, 27
Solutions
5
Feb 2
5.2, 5.3
5.2: 1, 3, 5, 7, 9, 15, 17, 25, 29, 33, 35, 39
5.3: 1, 13, as many as possible out of 21-39 (these are related to the ones from 5.2)

Click here for a java-applet to draw slope fields, or here for a more elaborate applet tool (DFIELD).

You can explore Euler's method for the exponential growth and the logistic model.
Assignment #3
due Feb 9
ODEs


Section B
Section C
Section D

Feb 4
5.2, 5.3 and Euler's method
Solutions
6
Feb 9
5.5
5.5: 1-4, 21, 23, 25, 33
The Romeo and Juliet example

Feb 11
Midterm #1
Material:
everything up to Feb 4, excluding Euler's method. More detailed:
4.4, 4.5, 4.6, 4.7 (not "leading behavior")
5.1, 5.4, 5.2, 5.3 (not "Euler's method")
partial fractions, integrals and volumes

There is a total of 7 questions on the midterm.


Solutions for sections B,C

Solutions for section D
7

Reading week
Feb 16-20

Lecture notes for Complex Numbers and Linear Algebra


8
Feb 23
Complex numbers








Practice Problems for all of these topics are in the lecture notes. In addition, any first-year textbook on linear algebra will provide you with lots of extra exercises.




The forest succession example to play with.
Assigment #4
due Mar 11
Linear Algebra I

Section B
Section C
Section D


Solutions
Feb 25
Linear Algebra I:
Linear systems, Gauss algorithm
9
Mar 2
Linear Algebra II:
Matrices and operations
Mar 4
Linear Algebra III:
Inverse matrices and determinant
Assignment #5
due Mar 23
Linear Algebra II

Section B
Section C
Section D





Solutions
10
Mar 9
Linear Algebra IV:
Eigenvalues and eigenvectors
Mar 11
Linear Algebra V:
Markov Chains
Lecture notes for Functions of several variables
11
Mar 16
Functions of several variables I:
Definitions, level sets




A few practice problems are posted here.
Mar 18
Functions of several variables II:
partial derivatives
12
Mar 23
Functions of several variables III:
Jacobi matrix








There will be
no more
assignments
to hand in.




Mar 25
Midterm #2

Midterm Solutions for B,C

Solutions for D
Lecture notes for systems of differential equations
Additional notes from previous years
See also TEXTBOOK sections 5.5-5.7

13
Mar 30
Linear systems of differential equations
See lecture notes and this old assignment

Also most of the exercises in sections 5.5-5.7 are helpful, except for the ones using Euler's method

This link gives you a web-based applet tool (PPlane) to draw phase-planes and solutions.

Excel spreadsheet for competition

Excel spreadsheet for Predator-prey systems

April 1
Systems of differential equations I:
Phase plane and linearization

14
April 6
Systems of differential equations II:
Competition

April 8
Systems of differential equations III:
Predator and Prey

From April 14-27, the Math Help Centre will be open 10am - 5pm daily. On April 28 and 29, the hours are 10am - 3pm.




Office hours prior to the Final exam
MAT 1332 B: Monday April 27, 3-5pm
MAT 1332 C: Thursday April 23, 11-12:30, Friday, April 24 2:30-4
MAT 1332 D:

April 28
Final exam
All the material covered in class will be on the final exam, except for
- comparison principle
- Euler's method

In preparation for the final exam, we recommend to go over all the assignment and midterm questions as well as these  additional practice problems with solutions.









Timetable for DGDs


Week
Topics and materials
1
Review techniques of integration (integration by parts, substitution)
Riemann sums
2
Fundamental theorem
Integrals, Areas and Volumes
3
Partial fractions
Improper Integrals
4
Improper Integrals
Solving Separable Differential Equations
5
Steady states and stability
Phase line diagrams
Solution curves
6
Euler's method
5.5
7
Reading week
8
Complex numbers
Gauss algorithm
9
Matrix operations, inverses and determinants
10
Eigenvalues, -vectors and Markov chains
11
Partial derivatives
12
Jacobi matrix, zero sets of functions
13
Linear systems of equations, Phase plane
14
End of classes