Linear Algebra - Math 221, Spring 2008


Section 1 Section 2 Section 3
Instructor Eran Nevo Yuri Berest Yuri Berest
TA Mihai Bailesteanu Mihai Bailesteanu Mihai Bailesteanu
Lectures M W F 9:05-9:55 am
111 Morrill Hall		 M W F 10:10-11:00 am
105 Space Science		 M W F 11:15 am-12:05 pm
251 Malott Hall
Section W 1:25-2:15 pm
251 Malott Hall 		W 2:30-3:20 pm
251 Malott Hall		 W 3:35-4:25 pm
224 Malott Hall
Instructor Office Hours M 1:30-2:30 pm
W 2:45-3:45 pm
MT 582 		M 5:00-6:00 pm
W 1:00-2:00 pm
MT 439 		M 5:00-6:00 pm
W 1:00-2:00 pm
MT 439
TA Office Hours T 10 - 11:30 am
R 10 - 11:30 am
MT 218 		T 10 - 11:30 am
R 10 - 11:30 am
MT 218 		T 10 - 11:30 am
R 10 - 11:30 am
MT 218
Homework due In section In section In section



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


Course Description. The course has 4 credits. This is the third semester of the upper-level calculus sequence. The prerequistites are two semesters of calculus with high performance or permission of the department. The course is recommended for students who plan to major in mathematics or a related field. (For a more applied version of this course see Math 231.)

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, third edition.
Grading. There will be 2 preliminary exams and 1 final. The grades will be calculated as follows:
Prelim I Prelim II Homework Final
15 % 15 % 30 % 40 %
The final points will be curved. Students are expected to abide by the Cornell University Code of Academic Integrity.
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 expected to be turned in your section on Wednesday every 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. Late homeworks will be permitted only under special circumstances. Missed assignments will receive no credit. The first HW is due on Wednesday, 30 January 2008.
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. Please attend the section that corresponds to your lectures. If a scheduling clash forces you to attend a different section, permission must be sought from your lecturer.
Where to get help? You are very welcome to instructor's and TA's office hours. In case you need help but you are unable to attend regular office hours, please send an email to make an appointment. Extra help is also available from Math Support Center, MT 256, tel. 255-4658, MTWRF 10 am-5 pm, Sunday 1:30-5:30 pm.
Links.


Exams

Prelim I 19 February 7:30 pm
Bache Auditorium, Malott Hall 		Chapters covered:
1,2,3
Exam The exam from last semester
Prelim II 27 March 7:30 pm
Bache Auditorium, Malott Hall		 Chapters covered:
4, 5 (without 5.5)
Exam and its solution The exam from last semester and its solution
Final 9 May, 9:00-11:30 am
Place: RF 203 		Chapters covered: 1-8 (focus on 6-8)
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 or are permitted extra time, please inform your instructor.

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

There will be a revision class before the exam.
Practice exams (links to pdf files)
Prelim , Spring 2005 and its solutions
Midterm, Fall 2006 and its solutions
Second midterm 2005 and its solutions
Second midterm spring 2007 and its solutions


Finals from previous years
They don't have solutions because they are not very similar to our final (although they have some problems that are good practice)
Final Spring 2001
Final Fall 2004
Final Spring 2004
Final Spring 2005
Final Fall 2006


IMPORTANT: Extra office hours: Prof. Yuri Berest (Monday 4-6 pm MT 439, Wednesday 2-4 pm MT 439), Eran Nevo (Monday 2-4 pm MT 582) (Eran is not able to hold office hours on Tuesday, Wednesday, Thursday), Mihai Bailesteanu (Monday, Tuesday, Wednesday 11 am - 1 pm, MT 218)
!!! Practice problems session with Mihai: Thursday 11-1 pm, Malott 206 !!!



Lecture Plan and Homework Assignments

The lecture plan and homework assignments below may be subject to change.



Week


Reading


Topics


Homework


Solutions
1
1/21-1/25 		1.1
1.2 (+App A)
Introduction, linear systems
Matrices & Gauss-Jordan elimination
1.1: 4, 20, 31, 40
1.2: 8, 20, 32, 60 		HW1
2
1/28-2/1
 1.3
2.1
2.2
Solutions of linear systems  
Linear transformations
Geometry of linear transformations
1.3: 4, 26, 44
2.1: 6, 13, 44
2.2: 2, 24, 38
HW2
3
2/4-2/8
 2.3
2.4
 Inverse transformations
Matrix Products
 2.3: 10, 20, 30
2.4: 14, 26, 40, 44
Due Wednesday, in section
HW3
4
2/11-2/15
 3.1
3.2
Image and kernel
Subspaces of Rn; basis, linear independence
3.1: 6, 22, 38
3.2: 2, 4, 16, 34
HW4
5
2/18-2/22
 3.3
3.4


Dimension and basis of a subspace
Coordinates
Review
First Midterm: Tuesday, 7:30pm,  19 February
 3.3: 10, 16, 22, 30, 38
3.4: 8, 18, 20, 44, 56

HW5
6
2/25-2/29
 4.1
4.2
4.3  
 Linear spaces
Linear transformations and isomorphisms
Matrix of a linear transformation 		4.1: 8, 12, 28, 32
4.2: 8, 12, 30, 56
4.3: 4, 10
HW6
7
3/3-3/7

 5.1  
5.2
Orthonormal bases and projections
Gram-Schmidt Process
5.1: 2, 6, 10, 16, 26, 40, 42
5.2: 4, 8, 34,
HW7

8
3/10-3/14
 5.3  
5.4
6.1
Orthogonal transformations
Least squares and data fitting
Introduction to determinants

Spring Break 3/15-3/23

9
3/24-3/28
 6.2
6.3

Properties of determinants
Geometry of determinants and Cramer's rule Review
Second Midterm: Thursday, 7:30pm, March 27 		6.1: 8, 20, 36, 44
6.2: 10, 16, 18, 28, 32
6.3: 2, 14
HW8
10
3/31-4/4
 7.1
7.2
7.3
 Dynamical systems and eigenvectors
Finding eigenvalues
Finding eigenvectors
 7.1: 6, 12, 22, 40
7.2: 8, 16, 40, 42
7.3: 4, 16, 20
 HW9
11
4/7-4/11
 7.4
7.5
 Diagonalization
Complex eigenvalues
7.4: 8, 20, 26, 32, 42, 48
7.5: 4, 12, 24, 28 		HW10
12
4/14-4/18
 7.6
8.1
 Stability
Symmetric matrices 		7.6: 4, 16, 22, 28
8.1: 6, 10, 14, 16, 22, 24, 30 		HW11
13
4/21-4/25
 8.2
8.3 		Quadratic Forms
Singular Values 		8.2: 4, 10, 14, 20, 28, 38
8.3: 4, 10, 20, 24 		HW12
14
4/28-5/2
 9.1
9.3

Continuous dynamical systems
Linear differential equations

15
5/5-5/9

Review for the Final









This page was last updated on Fri Mar 28 2008 21:43:57 GMT-0400 (EDT).