Mathematics 54, Fall 2011

TuTh 8:00am-9:30pm, Room 105 Stanley


Syllabus:  Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; second-order differential equations with constant coefficients. Fourier series and partial differential equations.


Professor  Alberto Grunbaum
Telephone: (510) 642-5348
email: grunbaum@math.berkeley.edu
Office: 903 Evans Hall
Office hours: Wed 11:30-13:00, Thursday 11:00-12.30

Textbooks: Lay, Nagle, Saff and Snider Linear Algebra and Differential Equations , Costume edition
                                              Class meetings and sections: The class meets in Stanley 105 8:00-9:30 am on Tuesdays and Thursdays. If you take this course you are expected to attend lectures, enroll in and attend one of the discussion sections listed below, do the homework each week, and take the two midterms and the final. All discussion sections meet MWF.

Section Time Place Instructor
201
 8am
 106   WHEELER
J. Ferguson
202
 9am
 61   EVANS
J. Ferguson
203
 9am
 179   STANLEY
B. Haberman
204
 10am
 179 STANLEY
 B. Harrop-Griffiths
205
 11am
 179   STANLEY
P. Tabrizian
206
 12pm
 179  STANLEY
 P. Tabrizian
207
 12am
 87   EVANS
R. Vianna
208
 1pm
 4   EVANS
 B. Haberman
 209
 2pm
 6   EVANS
B. Harrop-Griffiths
   210
  2pm
 3111    ETCHEVERRY
D. McCarty
   211
  4pm
 104   BARROWS
D. McCarty
   212
  5pm
 2   EVANS
D. McCarty


Exams:

All the exams are "closed book". In particular you may not bring textbooks, notebooks or calculators.
No one should be too surprised if the problems in the midterms and/or the final are VERY SIMILAR to those in the homework. It follows that a good way to prepare for these exams is to attempt every problem in the homework assignment every single week. You will be motivated to do this in a way that is explained below.               

Exam Date Material covered
Midterm # 1    Set 15
 Lay, Ch. 1-2
Midterm # 2    Oct 25
 Lay, Ch. 3-6
Final Exam    Dec 14, 3.00-6.00pm
  Lay+NS&S


Grading:

 You will receive four grades, one for each of the following: homework and quizzes, the two midterms and the final exam. Homework and quizzes count 20%, the same for each midterm and the final counts for 40%. The overall grade is roughly based on a curve. As a guideline, a 90% score is at least A-, 75% is  at least B- and 60% is at least  C-. Grades for exams or quizzes can only be changed if there is a clear error on the part of the grader, such as adding up marks incorrectly or forgetting to grade a question. The grade distribution for Math 54 in recent years was roughly as follows:  25% A,  35%B, 25%C and 15% D/F.
HOWEVER, I would be perfectly happy to give an A+ to everyone if they do deserve it. At the beginning of the class each one of you is starting at this mark. Just make sure that you work very hard and you will earn an A+.

VERY IMPORTANT

The final homework and quiz grade will be computed from the grades for the 20 best homeworks and 10 best quizzes. If you miss the first midterm the grade for the second midterm will count double. If you miss the second then the grade for the final will count for 60%. If you miss both midterms or the final, then you will fail the class. There will be no makeup exams or quizzes.

Homework and quizzes:

There will be a quiz given each Wednesday in the discussion sections.  Homework for the Tuesday class is due on the following Monday, and for the Thursday class it is due on the following Friday.   There will be no make-up quizzes and late homework will not be accepted.  Collaboration on homework is encouraged, but you need to write up your own.
The GSI for your section will pick 3-4 problems every week and assign a "Pass/Fail" grade to these randomly chosen problems. But you have to attempt all problems and points will be taken out for problems that you do not try. This is my way of motivating you to really do all the problems. This will be useful when the midterms and the final exam come along. You should not surprised is some of the problems in these tests are identical or very similar to some homework problems.

Following is the list of daily topics and homework assignments. The lectures do not cover all the course material, so you also need to read and understand the sections from the book. Reading ahead of the lectures should help a lot.
I cannot promise that I am going to cover all topics with the same level of detail. Reading the book CAREFULLY (there is no other way to read mathematics or science) is the only way to master this material. Another good way is to try to explain the material to your friends: only then you will realize that this is good for you too. I encourage people to form groups where you can try this sort of Socratic method.



Date
Content
  Homework Assignment
1
 8/25
 Lay, Ch. 1: Linear Equations,  1.1-2  1.1: Odds 1-15, 20, 28;  1.2:Odds 1-15, 23-26,30
2
8/30
 Lay, Ch. 1: Linear Equations,  1.3-5 1.3: Odds 1-15, 22,25; 1.4:1,5,7,9,11,17,18,29,34;  1.5:         1,5,9,14,24,29-32
3
9/1
 Lay, Ch. 1: Linear Equations,  1.6-9 1.6: 1,3,9,11,14;  1.7: Odds 1-17,21,22,33-36;  1.8: 1,3,9,11,17;  1.9: Odds 1-17,23,24; 
4
9/6
 Lay, Ch. 1,2: Matrix Algebra, 1.10 2.1-3 1.10: 1,3,9;  2.1: Odds 1-17,23,24,27;  2.2: 1,3,9,11,19,21,38;  2.3: Odds 1-17,21,24,30; 
5
9/8
 Lay, Ch. 2: Matrix Algebra,  2.5, 2.8-9 2.5: 1,3,9,11,17;  2.8: Odds 1-17,21,23;  2.9: 1,3,9,11,17,21,23,24
6
9/13
 Review: Lay, Ch. 1-2
7
 9/15
 Midterm 1
8
 9/20
 Lay, Ch. 3: Determinants, 3.1-3 3.1: 1,5,9,13,19-22, 41; 3.2:1,3,5,7,11,19,21,27,31,33-35; 3.3:Odds 1-11,21,25,32
9
 9/22
 Lay, Ch. 4: Vector Spaces, 4.1-3 4.1: 1,3,9,11,17,24,27,32;  4.2: Odds 1-17,23,25,30;  4.3: 1,3,9,11,17,21,32,33; 
10 9/27
 Lay, Ch. 4: Vector Spaces, 4.4-5 4.4: 1,3,9,11,17,27;  4.5: Odds 1-17,26,27
11
9/29
 Lay, Ch. 4: Vector Spaces, 4.6-7 4.6: Odds 1-17,23,33;  4.7: 1,3,9,11,17
12
 10/4
 Lay, Ch. 5: Eigenvalues and Eigenvectors, 5.1-3 5.1: 1,3,9,11,17,21;  5.2: Odds 1-17,21;  5.3: 1,3,9,11,17,21
13 10/3
 Lay, Ch. 5:Eigenvalues and eigenvectors, 5.4-5
5.4: 1,3,9,11,17;  5.5: Odds 1-17
14 10/11
 Lay, Ch. 6: Orthogonality, 6.1-2 6.1:1,5,7,9,13,17,21,22,24;  6.2:3,9,11,15,19,21
15
 10/13
 Lay, Ch. 6: Orthogonality, 6.3-5 6.3: 1,3,5,7,11,17,21;  6.4: Odds 1-13
;  6.5: 1,3,7,13,15,17
16
10/18
 Lay, Ch. 6: Orthogonality, 6.6-8 6.6: 1,3,7,13,15;  6.7: Odds 1-15,19,22,24;  6.8: 1,2,3,4
17 10/20
 Review: Lay, Ch. 3-6
18
 10/25
 Midterm 2
19 10/27
 Lay, Ch. 7: Symmetric matrices, 7.1-2 7.1: 7,11,13,17,22,24,32,33,34;  7.2: 5,9,19
20 11/1
 NS&S, Ch.4 :Second order linear ODE, 4,1-3 4.1: 1,3,5,8,9,10;  4.2: Odds 1-17,26,30;  4.3: 1,3,9,11,17,33
21 11/3
 NS&S, Ch.4 :Second order linear ODE, 4,4-6 4.4: Odds 1-17;  4.5: Odds 1-17,26,30;  4.6: 1,3,9,11,15,20
22 11/8
 NS&S, Ch.4:Second order linear ODE, 4.7-8 4.7: 3,7,12,13;  4.8: 1,3,9,11; 
23 11/10
 NS&S, Ch.4,6:Second order linear ODE, 4.9, Higher order linear differential equations, 6.1-2 4.9: Odds 1-7;  6.1: 1,3,9,11,13,23,27;  6.2: Odds 1-17,19,25; 
24 11/15
 NS&S, Ch.9:Systems of Linear ODE, 9.4-6 9.4: 1,3,9,11,17,21,25,27;  9.5: Odds 13-21,31,33,35;  9.6: 1,3,9,11,17,19; 
25
 11/17
 NS&S, Ch. 9: Systems of linear ODE, 9.7-8 9.7: 3,5,10,13,15,27; 9.8:1,3,5,7
26
 11/22
 NS&S, Ch. 10: Fourier series PDE, 10.1-3 10.2:1,3,5,9,11,13,21,27,31, 10.3: Odds 1-11,17,19,26,27,31
27 11/24
 Thanksgiving
28 11/29
 NS&S, Ch. 10:Fourier series PDE, 10. 4-5 10.4: Odds 1-13,18; 10.5:Odds 1-9,13
29 12/1
 NS&S, Ch. 10:Fourier series PDE, 10.6-7 10.6: Odds 1-5,13,15; 10.7:Odds 1-7
30
 12/6
 Review: Ch. 7,8,9,10 NS&S
31
 12/8
 Review: Ch. 7,8,9,10 NS&S
-- 12/14
  Final Exam, 3.00pm-6.00pm
 TBA

Some words of advice:

The material is this class is, for most students taking 54, the bread and butter for many other classes to come later. The real physical/biological world is mostly governed by non-linear phenomena, and in this class we will ONLY cover an approximation to the real thing, namely linear equations and linear differential equations. We will cover many topics in a few weeks and the rhythm will be VERY DEMANDING. Some of you may find the first few weeks rather easy and may be tempted to drop the ball. BAD IDEA. A few lectures later you will find yourselves lost. Stay focused from day one, and make sure that you get a high mark in this class.