Math 3130, Linear Algebra, Fall 2012

MATH  3130   Introduction to Linear Algebra    Fall, 2012 

  

Meetings: 3:05 pm - 4:20 pm, Tu,Th, COB 325,  8/21/2012 - 12/13/2012

Instructor: Greg Morrow

Office: ENGR 272, (719) 255-3184, gmorrow@uccs.edu

Hours: Tu, Th 2:00-2:50 pm, or by appointment.

Prerequisite: Calculus III (MATH 2350)

Text: Elementary Linear Algebra, 10th ed., by Howard Anton (2010), John Wiley & Sons: Hoboken, NJ. ISBN: 0-471-45821-1

Description: Linear algebra is a fundamental tool for solving applied mathematics problems involving several variables. There are both computational and conceptual sides to this subject. At first the hand-computational side will be stressed to lay a ground-work for the concepts. Later more emphasis will be placed on the conceptual sequence of operations. On the conceptual side we will see many theorems. The theory can provide a general perspective, likened to the view from a mountaintop over a valley of applications. Some problems involving the words show or prove will be assigned in the homework and may occasionally be found on tests. The course covers systems of linear equations, determinants, Euclidean vector spaces, general vector spaces, change of basis, rank theorem, matrix transformation of Euclidean space, eigenvalues and eigenvectors, diagonalization, inner product spaces, best approximation, least squares fitting to data, orthogonal diagonalization, quadratic forms, and the principal axes theorem.

Homework and Tests: Homework will be collected according to the attached schedule. There will be two mid-semester tests, as well as a final exam. The final exam will test primarily the material covered after the second midterm exam. Calculators will not be allowed on tests. Homework will count 16% of the course grade, each mid-semester test will count 27%, and the final exam will count 30%. There will be no make-up for late homework; one homework assignment may be dropped. Arrangements for make-up exams must be made in advance except in extraordinary circumstances. Also the student is responsible in the event a make-up exam is approved (in advance only!) to make an appointment with the testing center, dservice@uccs.edu

Final exam: Thursday, Dec. 13, 1:40 pm - 4:10 pm.

Grading. 90 => grade of A, 80 => B or better, 70 => C or better. Half grades (e.g. B+) are possible
MATH 3130   Introduction to Linear Algebra   Fall, 2012

Syllabus (subject to change: revised Aug. 6, 2012)

Date     Coverage in Text    DUE DATES

8/21-8/23     1.1-1.4.

8/28-8/30    1.5-1.7;      HW I due 8/28

 Labor day, no class 9/4

9/4       2.1-2.3;           HW II due 9/6

9/11-9/13     3.1-3.5.       HW III due 9/13

9/18-9/20    4.1 - 4.2.       HW IV due 9/20

9/25-9/27  review for test;  Test 1 on Chps. 1-3 on  9/27.

See Added Instructions for HW V.

10/2-10/4     4.3-4.5;   HW V due 10/4 

10/9-10/11      4.6-4.7;       HW VI due 10/11

10/16-10/18     4.8-4.10;      HW VII due 10/18

10/23-1025     5.1;   review for test;   HW VIII due 10/25

10/30-11/1     5.2.  Test 2 on Chp. 4 on 10/30. 

11/6-11/8      6.1-6.2.  HW IX due 11/8

11/13-11/20    6.3-6.4;  HW X due 11/15

11/20    6.5;    Thanksgiving 11/22.

11/27-11/29   7.1-7.2;  HW XI due 11/27

12/4-12/6   review for final exam, 7.3.  HW XII due 12/4

12/13  Final Exam covers Chps. 5, 6, 7.  Ex. Cr. HW due.

 

MATH 3130   Introduction to Linear Algebra   Fall, 2012

Homework. (EC=extra credit)

HW I.

1.1: 6, 7a,b,c, 9a, 10a; 1.2: 2a,b,c,d, 3a,c,d, 5, 19, 38 (EC);

1.3: 5c,i, 7a,c, 10a, 12a; 1.4: 7, 8, 11, 15.

HW II.

1.5: 2, 3c,d, 5b, 7a,b, 9, 19, 30 (via Eqn (4)); 1.6: 2, 10, 15, 20; 1.7: 24, 25, 31b, 42a.

HW III. 

2.1: 1, 8 (use Eqn (2)), 15, 16, 22, 32;  2.2: 7, 11, 17, 27, 29, 30;  2.3: 4, 5, 12, 19, 24.

HW IV.

3.1: 16, 22, 26;  3.2: 14a, 25;  3.3: 3c, 5, 8, 18, 25;  3.4: 6, 15, 17, 21, 23;  3.5: 4, 17, 35 (EC).

HW V.

4.1: 1, 5, 6, 7, 10; 4.2: 1, 3, 7, 11a,d, 15a,f; 

Added Instructions for HW V.

The structures of problems 4.1 #5 and #7 are NOT vector spaces--show a specific example for each axiom that does not hold in these cases (see text answers for axioms that do not hold).

The spaces in problems 4.1 #6 and #10 are subsets of known vector spaces that happen to satisfy  the closure (1 and 6) axioms --- verify ONLY these so-called closure axioms (verify 1 and 6 only-skip verification of  the other axioms).

In problems 4.2 # 1and #3, for cases that ARE vector subspaces (see answers in book), verify the conditions of Thm. 4.2.1 --- for cases that ARE NOT vector subspaces, give an example to show that one of the conditions of Thm 4.2.1 does not hold.

 

 

 

MATH 3130   Introduction to Linear Algebra   Fall, 2012

 

HW VI.

4.3: 2, 4a,d, 5, 7, 15, 19, 22;  4.4: 3, 8, 10b, 14, 17a,b.  4.5: 2, 6, 8, 13 (verify that (0,1,0,0) and (0,0,1,0) will complete basis), 14 (EC);

HW VII.

4.6: 1, 6, 13, 18;  4.7: 2a,b, 3a,b, 4, 5b, 6c, 8c, 10e, 12c.

HW VII.

4.8: 2e, 3e, 4, 7, 8, 11. 4.9: 8a,d, 10c, 12b, 15, 18a,b, 30; 4.10: 4, 6a,b, 9a,c, 14a, 17b, 18b. 

HW IX.

5.1: 2, 6a,e, 7a,e, 8a,e, 14, 15;  5.2: 2, 6, 9, 14, 19, 22, 33;  6.1: 10, 14, 16, 28 (EC).

HW X.

 6.2: 7, 10, 11c,d, 15, 16c, 17, 18, 27 (EC); 6.3: 7, 8, 9a, 12a, 14a, 21a, 22a, 33 (EC).

HW XI.

6.4: 1, 2a, 3a, 5a, 8a, 14, 16; 6.5: 1, 2, 3, 8.  

HW XII.

7.1: 2, 3d, 4, 6; 7.2: 1d,f, 5, 6, 12, 14, 16d.

 

Extra Credit HW:

7.3: 2, 4, 5, 6, 14, 21, 25.