MATH 231 – Spring 2008

Linear Algebra with Applications

Textbook: Goodaire, Edgar G., Linear Algebra: A First Course in Pure & Applied Mathematics, Pearson Prentice Hall, 2003 (ISBN: 0-13-047017-1).

 

 

 

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Lecturer

Office Hours

Location

Email

Guang (Dennis) Yang

3:00–5:00 p.m. on Monday (or by appointment)

MT 227

gy26@cornell.edu

 

 

 

 

Time

Location

Lecture

MWF 1:25–2:15 p.m.

MT 253

 

 

 

 

Points

Date

Time

Location

Additional Information

HW

150

N/A

N/A

N/A

HW rules, assignments

Prelim 1

100

2/29/2008

In-class

MT 253

Exam rules

Prelim 2

100

4/21/2008

In-class

MT 253

Exam rules

Final

150

5/8/2008

24 Hours

Take-home

Exam rules

Overall

500

N/A

N/A

N/A

 

 

Academic Integrity:

Absolute integrity is expected of every Cornell student in all academic undertakings as written in the Cornell University Code of Academic Integrity.  In this course, students may work alone or in groups (see “About Working Together” below) on the homework, but are to turn in all homework individually and acknowledge by name those persons who have provided any assistance.

 

About Working Together:

We have no objection in principle to discussion of the homework. However, one person simply telling another how to do a problem totally defeats the purpose of the problem. You get maximum benefit from a homework problem if you work hard on it alone before combining your ideas with someone else’s. The paper that you turn in should be in your own words, even if you arrived at some of those solutions via discussions with others. In particular, you may not simply copy someone else’s homework and turn it in as your own. This will be treated as a violation of Cornell’s Code of Academic Integrity. Similarly, copying solutions that you might find on the web, from students who have taken the course in previous years, or from some other source will be considered to be a violation.

 

HW Rules:

  • Friday, Monday, and Wednesday’s homework assignments are due at the beginning of the following Friday’s lecture.
  • No late homework is accepted except for cases such as:

medical emergency, course/training/sport-related field trip, etc. (Email the lecturer at the earliest possible time to explain the situation. Attach the email printout as the cover page of the homework when you turn it in.)

 

Exams Rules:

  • Calculators and books are not allowed at the exams.
  • Each student may bring a single 8-1/2×11 sheet of paper, hand written personally by the student on both sides, containing any information that the student wishes to have access to during the exam.
  • No makeup exams are anticipated. Students with special needs (such as extra exam time due to reasons approved by the university) can be accommodated by contacting the lecturer.

 

 

 

Lecture Schedules and Homework Assignments

Week

Day

Topic

Assignment

Solution

1

M

1/21

1.1 Vector addition, scalar multiplication, and linear combination

1.1: 5h, 6c, 11, 14, 15

HW1

W

1/23

1.2 Length, direction, unit vectors, and dot product

1.2: 3ad, 7, 9bf, 23a, 28, 32

F

1/25

1.2 Dot product (cont.) and the C-S inequality / 1.3 Lines

1.3: 3b, 6, 8, 9, 11b, 15, 28a

HW2

2

M

1/28

1.3 Planes and cross product

 

W

1/30

1.3 Planes and cross product (cont.)

 

F

2/1

1.4 Projections

1.4: 3d, 4b, 5bd

HW3

3

M

2/4

1.4 Projections (cont.)

1.4: 6

W

2/6

1.5 Euclidean n-space

1.5: 3c, 4b, 5b, 10b, 11bd

F

2/8

2.1 The algebra of matrices

2.1: 3c, 5cd, 8c

HW4

4

M

2/11

2.1 The algebra of matrices (cont.)

2.1: 11bc, 12c, 17, 23

W

2/13

2.2 The inverse and transpose of a matrix

2.2: 1bd, 6ab

F

2/15

2.2 The inverse and transpose of a matrix (cont.)

2.2: 2, 17, 18bc

HW5

5

M

2/18

2.3: Systems of linear equations

2.3: 2b, 4cd, 7, 8bc, 9i, 11, 13ac

W

2/20

2.3: Systems of linear equations (cont.)

 

F

2/22

2.4 Homogeneous/nonhomogeneous systems & their solutions

2.4: 1b, 6c, 7

HW6

6

M

2/25

2.3/2.4 Solutions of systems of linear equations

Read no.4 of 2.4 (pages 123 & S-23) 2.3: 16a, 26, 27, 30; 2.4: 3de

W

2/27

Elementary matrices

 

F

2/29

Prelim 1 (in class): 1.1–2.4

Fall 06 (Solution), Spring 07

 

7

M

3/3

2.7 Finding the inverse of a matrix

2.7: 3cgij, 6, 10

HW7

W

3/5

3.1 The determinant of a matrix

3.1: 3de, 14

F

3/7

3.1 cont.

3.1: 4d, 12

HW8

8

M

3/10

3.2 Properties of Determinants

3.2: 3, 4, 15f, 17

W

3/12

3.2 cont.

3.2: 9bce, 23

F

3/14

3.3 The eigenvalues and eigenvectors of a matrix

 

HW9

10

M

3/24

3.3 Solving for eigenvalues and eigenvectors

3.3: 2b, 6bh, 15, 18

W

3/26

3.3 cont. / Intro. of 3.4

 

F

3/28

3.4 Similarity and diagonalization

3.4: 5, 7, 10, 14bci

HW10

11

M

3/31

4.2 Basic concepts of vector spaces

 

W

4/2

4.2 cont.

 

F

4/4

4.2 cont.

4.2: 1c, 2cd, 4ab, 7ce

HW11

12

M

4/7

4.1 / 4.2

4.1: 4de, 5c; 4.2: 10bc

W

4/9

4.1 Column and null spaces, rank

4.1: 8c, 10abcd, 11b

F

4/11

4.1 Column spaces

4.1: 16, 17

HW12

13

M

4/14

4.3 Basis and dimension

4.3: 1bf, 9

W

4/16

4.3 cont.

 

F

4/18

4.3 cont.

4.3: 5bc, 17bc

HW13

14

M

4/21

Prelim 2 (in class): 1.1–4.3

Fall 06 (Solution), Spring 07

W

4/23

6.2 The Gram-Schmidt algorithm

6.2: 1b, 2a, 16

F

4/25

5.1 Linear transformations

5.1: 1de, 2, 7a, 8b; 6.2: 22

 

15

M

4/28

The G-S algorithm and linear trans. (Supplementary Notes)

5.1: 4, 6, 9c

 

W

4/30

Least squares approximation

 

 

F

5/2

Data fitting

8.1: 1d, 5c, 6, 7c

 

 

M

5/5

Office hours: 2:00–4:00 p.m., MT 218

 

 

 

T

5/6

Office hours: 2:00–4:00 p.m., MT 218

 

 

 

W

5/7

Office hours: 2:00–4:00 p.m., MT 218

 

 

 

Th

5/8

Final Exam

 

 

 

F

5/9

Final exam will be due at 12 noon

 

 

 

 

 

Extra Help:

  • Math Support Center (room: MT 256, phone: 5-4658)
  • Engineering advising office (room: OH 167)
  • Tau Beta Pi (phone: 5-3312)
  • SHPE and NSBE at Ujamma

 

 

 

Updates:

  • This course web is created on Jan 31, 2008.