MATH 314 Linear Algebra with Applications

Spring 2016

 

 

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  TWR 11 am -12 pm and by appointment.
Telephone: 505 277-2214
email: jvassil@math.unm.edu

webpage: http://www.math.unm.edu/~jvassil

Texts :  Linear Algebra, 7th or 8th Edition by Leon.

Course Meetings:  The course lectures will be held in Dane Smith Hall 326 on Tuesdays and Thursdays from 2-3:15 pm. 

Topics:  Linear equations, matrix arithmetic and algebra, determinants, vector spaces, linear independence, spanning set, change of basis, linear transformations, scalar products, inner product spaces, least squares, Gram-Schmidt, eigenvalues and eigenvectors, diagonalization.

Quizes (100 points): There will be  quizzes approximately every other week which are based on the homework problems assigned in the course.  Quiz dates and sections to be covered on the quiz are indicated on the calendar below.  The lowest  quiz will be dropped and your quiz score will be determined by the average on the remaining quizzes.

Homework (200 points):  Homework will be assigned and posted weekly on Tuesdays and will be collected the following Tuesday at the beginning of class.  Homework will not be graded unless it is written in order and labeled appropriately.  Each week around 4 of the assigned problems will be graded. The weekly assignments will each be worth 20 points. I will drop your lowest two homework scores and the remaining homework will be averaged to get a score out of 200. 

Exams (400 points):  I will give two midterms (100 points) and a final (200 points). There are no make up exams. If a test is missed, notify me as soon as possible on the day of the exam. For the midterms only, if you have a legitimate and documented excuse, your grade will be recalculated without that test.  The midterms are scheduled on February 25, April 7 and May 10 (10 am-12 pm).

Grades:  General guidelines for letter grades (subject to change; but they won't get any more strict): 90-100% - A; 80-89% - B; 70-79% - C; 60-69% - D; below 60% - F.  In assigning Final Grades for the course, I will compare your grade on all course work (including the Final) and your grade on the Final Exam.  You will receive the better of the two grades.

Tentative Schedule (for Dr. Vassilev’s Linear Algebra):

Date

Section

Topic

Homework

1/19

1.1

Linear Equations

 1.1:  1(a, b, d), 2(a, c), 3(a, b, d), 4(a, b, c), 5(a, b, c), 6(a, c, f), 7, 8 (Editions 7 and 8)

1/21

1.2

Row Echelon Form


1/26

1.3

Matrix Arithmetic

 1.2:  1, 2, 3, 5(a, c, e, f,h), 6(a, d), 8, 11, 12
1.3:  1, 2, 3, 4, 5(a, c), 6(a), 8, 9, 10
All of the above problems are in both the 7th and 8th Editions and
1.3 15 from 8th Edition or 1.3 28 from 7th Edition

1/28

1.4

Matrix Algebra (Quiz 1 Sections 1.1-1.3)


2/2

1.5

Elementary Matrices

7th Edition: 1.3: 20(a), 9, 10, 15, 26(b), 29(a)
1.4: 1, 2, 8(a,d), 10(a,f), 12(a,d), 15

8th Edition: 1.4 1(a), 6, 7, 12, 28, 30(a)
1.5: 1, 2, 8(a,d), 10(a,f), 12(a,d), 15

2/4

2.1

Determinants


2/9

2.2

Properties of Determinants (Quiz 2 1.4-1.5)

 7th and 8th Editions:
2.1: 1, 2, 3(a,d,f,g,h), 4, 5, 6
2.2: 1, 2, 3(a,c,e f), 4, 5, 7(c, d), 9, 12(a)

2/11

2.3

Applications of the Determinant


2/16

3.1

Vector Spaces

 7th and 8th Editions:
2.3: 1(a,c), 2(a,c,d), 3, 5(a,b), 8
3.1: 3, 6, 7, 9, 10, 14

2/18

3.2

Subspaces (Quiz 3 2.1-2.3)

2/23


Review (Scanned Quiz Solutions)

 7th Edition: 3.2: 1(a,c,e), 3(a,d), 4(a,d), 8(b,c), 10(a,c), 14(a,d), 16
8th Edition 3.2: 1(a,c,e), 3(a,d), 4(a,d), 10(a,b), 12(a,c), 16(a,d), 18

2/25

Midterm 1 (Sections 1.1-2.3)

 Solutions

3/1

3.3

Linear Independence

 7th Edition: 3.3: 1(a,c), 2(a,c), 4(a), 6(a,c), 7(a) 10(a,b)
8th Edition 3.3: 1(a,c), 2(a,c), 4(a), 8(a,c), 9(a) 12(a,b)

3/3

3.4

Basis and Dimension (Quiz 4 3.1-3.3)

3/8

3.5

Change of Basis

 Both editions:
3.4: 3, 4, 5(a,b,c), 7, 10, 14(c)
3.5: 1(a), 2(a), 3, 4, 5, 6, 7, 8, 10

3/10

3.6

Row Space and Column Space

3/22

4.1

Linear Transformations (Quiz 5 3.4-3.5)

 7th Edition: 3.6 1, 2(b), 3, 4(b,d), 6, 7, 8, 10, 11
8th Edition: 3.6 1, 2(b), 3, 4(b,d), 6, 8, 9, 15, 16
Both Editions 4.1 1(a,b,d), 3, 4, 5(a,c,d), 6(a,d), 8(a,c), 10

3/24

4.2, 4.3

Matrix Representation of Linear Transformations

3/29

5.1

Inner Products

 4.2 1, 2(a,b,c), 3(a,b), 4(a), 5(a,b,c)
4.3 1(a,b,e)
5.1 1(a,b), 2(a,b), 3(a,c), 4, 7

3/31

5.2

Orthogonal Subspaces (Quiz 6 3.6, 4.1-4.3)

4/5


Review (Scanned Quiz Solutions)

4/7


Midterm 2 (Sections 3.1-4.3)

 Solutions

4/12

5.3

Least Squares

 5.2 1(a,b,c,d), 2
5.3 1(a,c), 3(a), 5, 6

4/14

5.4, 5.5

Inner Product Spaces, Orthonormal Sets (Quiz 7 5.1-5.3)

4/19

5.6

Gram-Schmidt

 5.4 1, 2, 3, 5, 9
5.5 1, 2, 3, 6, 8
5.6 1(a), 3, 4, 5, 8

4/21

6.1

Eigenvalues and Eigenvectors

4/26

6.2

Systems of ODEs (Quiz 8 5.4-6.1)

  6.1 8th Edition 1(a,c,d,e,f,g,k), 2, 3, 8, 9
       7th Edition 1(a,c,d,e,f,g,k), 2, 3, 6, 7
6.2 1(a,b,d,e), 2(a,b), 3, 4, 5
 

4/28

6.3

Diagonalization

5/3

Review

 6.3 1(a,c), 2(a,c), 6, 7 (These don't need to be turned in.)

5/5

Review (Scanned Quiz Solutions)

5/10

Final Exam 10 am