Math 2243 - Linear Algebra and Differential Equations Fall 2004

Announcements:

12/8 Final exam is 1:30-4:30 pm Thursday Dec 16. Section 21 will take the exam in Vincent Hall 113. Section 23 will take the exam in Murphy Hall 130.
Remeber to bring a number 2 pencil and your University ID. "All students must have their official University I.D. Card with them at the time of the final exam and must show it to one of the proctors when handing in their exam. The proctor will NOT accept a final exam from a student without an I.D. Card."

11/26 There are some errors in the text for this week's homework set, depending on which printing you have. I have first printing, and in it there are incorrect answers in the book for problems 6.2.43 and 6.3.23.
For 6.2.28, the vector v in part a) should be [1, -2, 1]. For 6.2.43, they label the tank as having an initial concentration of .5 lb/gal and it should be .25 lb/gal.
In general, the best way to check a solution is to plug it back into the differential equation and to ensure it satisfies any initial conditions.
In the resources section, there is a link to the book's official errata.

11/19 For homework 9, I have postponed problems from section 6.1 so that they will be due with assignment 10. I have posted quiz 3.

I updated assignment 9.

10/22 I will hold extra office hours on Monday October 25, 1:25-2:15.

9/24 I will hold extra office hours on Monday September 27, 1:25-2:15. I added a couple links about partial derivatives.

Section 23, has moved from Folwell Hall to EE-Csci building room 3-230

Course Information:

Lecture: MWF 11:15am-12:05pm Classroom Building 175
Discussion Section 21: TTh 10:10am-11:00am VinH 311
Section 23 11:15am-12:05pm EE-Csci 3-230

Professor Miller's page. This has the main syllabus along with course information.

As mentioned on the course site, of the 700 total points there are 100 points assigned for homework and quizzes. Quizzes will comprise 30 pts, homework 70pts.

Contact Information:

TA: Matthew Dobson
Office: 420 Vincent Hall
Telephone: (612) 625-5099
Office Hours: Tues 9:05-9:55 and 1:25-2:15(or by Appointment)
Lind Hall Hours: Wed 9:05-9:55 and Fri 1:25-2:15. Held in Lind Hall 150
e-mail: dobson@math.umn.edu
Note: the best way to contact me is through e-mail.

Homework:

Assignment 1: due Sept 9/16
Section 1: 26
Section 2: 3, 16, 17, 18, 26, 30
Section 3: 16, 20, 21, 22, 26, 40
Show work on all exercises. On 2: 16, 17, 18 and 3: 20, 21, 22 write a two or three sentence description about why the direction field matches the differential equation. Just putting a letter won't get any credit.

Assignment 2: Due Sept 23
Section 1.3: 32, 53
Section 1.4: 1, (8, 10)*
Section 1.5: 3, 4, 9
Section 2.1: 8, 10, 12
(*)For section 1.4 numbers 8 and 10, do the following to estimate the value of y(1):

  1. Use Euler's Method with step size h=0.5 by hand.
  2. Using a claculator or computer use Euler's method with step sizes h=.1, h=.01 and h=.001. Just report the estimated value of y(1). Do not print out a list of the 1000+ intermediate values that will be calculated. Mention what program you use.
  3. Solve the equation exactly to get the exact value of y(1)
  4. Does your approximation get better as h decreases?

Assignment 3: Due Oct 7
Section 2.2: 3, 19, 34
Section 2.3: 4, 24
Section 2.4: 2, 8, 17
Section 2.5: 17, 21, 24

Assignment 4: Due Oct 14
Section 2.6: 5, 6, 15, 16
Section 3.1: 4, 5, 32, 40, 44
Section 3.2: 7, 8, 31, 32

Assignment 5: Due Oct 21
Section 3.3: 7, 8, 14, 18
Section 3.4: 5, 6, 7, 16, 18, 36
Section 3.5: 5, 6, 8, 9, 13, 14, 16, 20, 36

Assignment 6: Due Oct 28
Section 3.6: 1, 2, 7, 8, 21, 22
For 7,8,21,22 if the set is linearly dependent, find a linearly independent subset.

Assignment 7: Due Nov 4
Section 4.1: 4,8,22,28,36,52
Section 4.2: 16,20,22,23,24
Section 4.3: 15, 16, 18, 22, 26
Make sure to justify answers to the matching problems.

Assignment 8: Due Nov 11
Section 4.2: 29, 37, 38
Section 4.4: 6, 24, 26, 27, 33, 40
Section 4.5: 8-11, 13, 16, 17
Section 4.6: 2, 8, 9, 10, 19, 32, 33
For section 4.4: 24, 26, 27, and 33 don't just guess a solution: always use the method of undetermined coefficients.

Assignment 9: Due Nov 23
Section 5.1: 5, 6, 14, 17, 34, 40
Section 5.2: 6, 23, 30, 34, 45
Section 5.3: 6, 9, 18, 26, 46
Section 5.4: 7, 8, 9, 27, 28

Assignment 10: Due Dec 2
Section 6.1: 10, 18, 34
Section 6.2: 18, 22, 28, 43
Section 6.3: 10, 23
Section 6.4: 10, 12

Assignment 11: Due Dec 14
Section 6.5: 1,2,5
Section 7.1: 29, 31
Section 7.2: 1, 6, 11, 18
Section 8.1: 13, 17, 18
Section 8.2: 3, 5

Additional Material:

In 1.1, we discuss Malthus's model for population growth. Here is a copy of Malthus's An Essay on the Principle of Population. I got this copy from Project Gutenberg which is an excellent resource for public domain texts.

I have written a short tutorial on using a spreadsheet for Euler's Method. For the tutorial, I used Microsoft Excel, but hopefully other spreadsheets are similar. If you don't have a spreadsheet program and have a fast internet connection you could try OpenOffice.org. It's free software.

Here are two sites discussing partial derivatives: a very brief Math Tutorial and a longer page Brief Calculus.

This is an errata list for our text.


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