Linear Algebra - Math 2210, Fall 2009


Note: (Monday, November 2, 2009): The solutions for Prelim 2 are now posted. See the link below in
chart on Exams.

Lectures Time & Place Instructor
1

MWF 9:05-9:55
MLT224

R. Sjamaar
2 MWF 10:10-11
MLT207
P.Kahn
3 MWF 11:15-12:05
MLT207
P.Kahn
4 MWF 12:20-1:10
MLT224
L.Wahlbin
5 MWF 1:25-2:15
MLT406
A.Schatz
Discussion Sections Time & Place TA
1 W 2:30-3:20, MRL106 Delgado
2 W 3:35-4:25, MRL106 Delgado
3 R 12:20-1:10,OLH216* Pabiniak
4 R 1:25-2:15, RCK112* Pabiniak
5 R 2:30-3:20, MLT251* Pabiniak
* No sections on Thursday, August 27.


Course Description Textbook Grading Exams Links
About Homework Reading Sections Where to get help Lectures and Assignments


Location of Final Exam:TBA

Course Description. The course has 4 credits. It is the third semester of the calculus sequence recommended for students who plan to major in mathematics or a related field. The prerequisites are two semesters of calculus with high performance or permission of the department.

The course covers linear algebra with applications to differential equations. The approach is more theoretical than in our other calculus courses: we teach theorems as well as computational techniques. One goal is to introduce theorem-proving. By the end of the semester, you should be able to understand most of the proofs in the subject, and you should be able to give some proofs on your own. Topics will include: vectors, matrices and linear equations, vector spaces and linear transformations, determinants, eigenvectors and diagonalization, orthogonality, and differential equations.

Textbook. Otto Bretscher, Linear Algebra with Applications, fourth edition. Addall.com
Grading. There will be 2 preliminary exams and 1 final. The grades will be (tentatively) calculated as follows:
Prelim I Prelim II Homework Final
20 % 20 % 20 % 40 %
The expected median course grade will be a B. Students are expected to abide by the Cornell University Code of Academic Integrity. In the case of a grading error (exams or homework), you have one week from the time the assignment was first returned to request a regrade.

Homework. This is the most essential part of the course. No matter how well you think you understand the material in class, you won't really learn it until you do problems on your own. New homework assignments will be posted weekly on the course webpage. Solutions to these assignments are to be turned in in your discussion section on the following week. You may collaborate on homework but you must write up your work individually and are expected to be fully in command of all the answers you give. Please write neatly and use clear, well-structured prose. Homeworks will be graded on a 12 point scale, with 10 of the points obtained through correctness of the write-up, and 2 points for completeness of the homework. Late homeworks will not be accepted.

The first homework assignment is due in your discussion section during the week: Aug 31 - Sept 4.

Reading. A full lecture of mathematics is hard to follow if you do not have at least some familiarity with the material. So read ahead in the text as per the schedule below.
Sections. Sections will be used to answer questions arising from the homework or the lectures. Extra examples may be described. You should attend the section that you are registered for.

Office hours, help, etc. You are very welcome to attend instructor's and TA's office hours, which are as follows:  Kahn, M 1:45-3:45, MLT 571; Schatz, W 11:00-1:00, MLT 557; Sjamaar, Tu 11:30-1:30, MLT 551; Wahlbin, M 3:45-4:45 and R 3-4, MLT 573; Delgado, R 12:45-2:45, MLT 218; Pabiniak, Tu 2:00-4:00, MLT 218.  

In case you need help but you are unable to attend regular office hours, please send an email to make an appointment.

Email addresses: Kahn: kahn@math.cornell.edu; Schatz: schatz@math.cornell.edu; Sjamaar: sjamaar@math.cornell.edu; Wahlbin: wahlbin@math.cornell.edu; Delgado: hl378@cornell.edu; Pabiniak: mdp72@cornell.edu.

Extra help is also available from Math Support Center, Malott Hall 256, tel. 255-4658, tentatively MTWRF 10 am-5 pm, Sunday 1:30-5:30 pm.

Links.


Exams

Prelim I Tuesday, Sept 29, 7:30 pm-9:00 pm
WRNB45
Chapters covered:
1,2,3 (3.1, 3.2)
Solutions
Prelim II Thursday, Oct 29, 7:30 pm-9:00 pm
WRNB45
Chapters covered:
1---5.2, with focus on 3.3 through 5.2..
Solutions
Final Thursday, Dec 10, 7:00 pm- 9:30 pm.
Room TBA
Chapters covered: 1.1 - 8.3 (focus on 6-8, no data fitting, no Fourier coefficients)

All the exams will be closed book tests. Calculators, notes and books will not be allowed in exams. Please do not bring cell phones, personal audio players, or other electronics. For full credit, answers should be fully explained and neatly presented. Please write all answers on the exam booklet; scratch paper may not be handed in.

If you have a clash with the Final, please inform your instructor as soon as possible in the term. It may not be possible to fulfill last minute requests.

If you require special accommodations on exams, such as extended time or quiet time, and you have a letter to this effect from SDS, please contact your instructor as early as possible in the term to make the necessary arrangements.

The final will cover material from all parts of the course, but with an emphasis on topics studied since Prelim 2.

Practice exams (links to pdf files)
Fall 2008 Prelim 1
Fall 2007 Prelim 1 Solutions
First Prelim Spring 2005 and its solutions
First Midterm Fall 2005 and its solutions
Fall 2008 Prelim 2 and itssolutions.
Spring 2008 Prelim 2 and its solutions.
Second midterm Spring 2005 and its solutions
Second midterm spring 2007 and its solutions

Finals from previous years
Note that some problems refer to material not covered in our course.
Final Spring 2001
Final Fall 2004
Final Spring 2004
Final Spring 2005
Final Fall 2006




Lecture Plan and Homework Assignments

The lecture plan and homework assignments below are in a more solid-state, but still could change. The numbers in parens in red are the homework problem numbers in the third edition of the text. Other numbers in black are the same in both editions, unless otherwise noted (see sections 2.3 and 2.4).


14


Week


Reading


Topics


Homework


Solutions

1
8/28
1.1
Introduction to linear systems
1.1: 8, 16, 18, 30, 44(42)

2
8/31-9/4
1.2,
1.3,
2.1

Matrices, vectors, Gaussian elimination
Solutions of linear systems, Linear transformations

1.2: 6, 8, 12, 30, 46
1.3: 14, 24, 30, 48, 58
2.1 : 6, 14, 24, 34, 44


3
9/7-9/11
2.2,
2.3
2.4

Geometry of Linear Transformations,
Matrix products
Inverse transformations

2.2: 6, 14, 20, 38, 40
2.3: 14, 16, 20, 52, 60
2.4: 6, 16, 30, 34, 40
Serious changes (from Ed. 3 to 4) in sections 2.3 and 2.4.
Exercises are in Ed 4 only

4
9/14-9/18
3.1
3.2
Image and kernel of a transformation
Subspaces of Rn; bases and linear independence
3.1: 10, 16, 22, 36, 38
3.2: 4, 16, 28, 44, 50

5
9/21-9/25
3.3,
3.4
Dimension of a space and subspace
Coordinates
3.3: 16, 24, 38, 68(48), 76(56)
3.4: 10, 24, 30, 58, 72

6
9/28-10/2

 

4.1
4.2

Review
Prelim I Tuesday Sep 29
Linear spaces
Linear transformations and isomorphisms

4.1: 4, 10, 14, 32, 48
4.2: 10, 24, 42, 60, 70

7
10/5-10/9

4.3

Note: Do only the exercises in 4.3 and hand these in as scheduled.
Read 5.1,5.2, but the submission of exercises for these sections will be postponed. There will be a further announcement about this.

 

4.3: 8, 24, 36, 46, 64

Fall Break (Oct 10 - Oct 13)
8
10/14-10/16

5.1
5.2

 

Matrix of linear transformation
Orthogonal Bases
Gram-Schmidt Process and QR Factorization

5.1: 6, 16, 26, 34, 38
(for 34 and 38 no geometric interpretation)
5.2: 6, 18, 32, 34, 40

 


9
10/19-10/23



5.3
5.5

 

Orthogonal Transformations
Inner product spaces
5.3: 4, 8, 34, 40
5.5: 8, 10, 14, 20

10
10/26-10/30

6.1
6.2

Introduction to determinants
Review
Properties of determinants

Prelim II Thursday Oct 29

6.1: 18, 28, 50
6.2: 8, 16, 28, 46, 50

11
11/2-11/6

6.3
7.1

Geometry of determinants
Dynamical systems and eigenvectors
6.3: 10, 30
7.1: 28, 34

12
11/9-11/13
7.2
7.3
Finding eigenvalues
Finding eigenvectors
7.2: 8, 12, 18, 38
7.3: 14, 20, 24, 32

13
11/16-11/23
7.4
7.5
8.1
Diagonalization
Complex Eigenvalues
Symmetric Matrices
7.4: 26, 42, 50, 56
7.5: 6, 24, 28, 50
8.1: 4, 10, 14, 22, 24
 
Thanksgiving (Nov 25 - Nov 29)


14
11/30-12/4

Final Exam 12/10, 7pm-9:30pm, Room TBA


8.1
misc

Symmetric matrices (cont'd)
Review

No Homework  
   




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