Math 313.002   Linear Algebra    Morrow, Fall 2009

 

Meetings:  TR 3:05 pm – 4:20 pm, SENG B134

Instructor:  Greg Morrow

Office:  EN 272, (719) 255 –3184, gmorrow@uccs.edu

Hours:  TR:  1:45 – 2:55, or by appointment

 

Prerequisite:  Calculus I (Math 135)

Text:  Introduction to Linear Algebra, 4th ed., by Gilbert Strang (2009),Wellesley Cambridge Press: Wellesley, MA. ISBN: 978-0-9802327-1-4

SIAM website for this test: http://www.ec-securehost.com/SIAM/WC09.html

 

MIT Open Course Ware website based on the 3rd edition of this text: http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/CourseHome/

 

Description:  Linear algebra is a fundamental computational tool for solving applied mathematics problems involving several variables. At first the hand-computational side will be stressed to lay a ground-work for the concepts.  After this, more emphasis will be placed on the conceptual framework; for example the four fundamental subspaces theme will recur in problems of later chapters. For reading of the first 2 chapters of the text, some review of vectors and equations of lines and planes in 2 and 3 dimensional space may be useful (say from the first chapter of a calculus 3 book). This material and ongoing supplementary material throughout the course will also be covered by notes in pdf (see Notes 1, Notes 2, etc. below). The Matlab computer algebra software will be introduced somewhat later in the course as a way to illustrate the concepts being covered but this software is not required for students to have—those who wish to become more familiar with it may find it available on EAS servers with instructions for connecting to it via remote desktop client, say, at:  http://www.eas.uccs.edu/it/using_rdp.shtml. The course covers chapters 1- 6 of the text. A key focus will be on problems appearing in the text.

 

Homework and Tests:  Homework will be assigned and collected weekly.  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 20% of the course grade, each mid-semester test will count 26%, and the final exam will count 28%. 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 that a make-up exam is approved to make an appointment to take the exam with disability services (X 3354 ) and then report this appointment to Morrow via email.

 

Final exam:  Thursday, December 17, 1:40 pm – 4:10 pm.

 

Grading.  90’s => grade of A, 80’s => B or better, 70’s => C or better.  Half grades (e.g.  B+) are possible.

Math 313.002   Linear Algebra     Morrow, Fall 2009

Syllabus and Homework (revised Nov. 3, 2009)

Notes 1

Aug 25.   1.1-1.2: Vectors, linear combinations, angle between vectors

Aug 27.   2.1-2.2: Elimination of variables

 

HW 1 

1.1: #2, 8, 16; 1.2: #7a,b, 12, 13, 27;
2.1: #5, 7, 21, 29; 2.2: #2, 12, 21, 26.

Due: Tues, Sep 1.

 

Notes 2

Sept 1.   2.3-2.4: Elimination and permutation matrices, and block multiplication

Sept 3.   2.5: Inverse Matrices

 

HW 2

2.3: #3, 17, 23, 26; 2.4: #6, 9, 10, 26, 29.

Due: Thurs, Sept 10.

 

Notes 3

Sept 10.   2.6-2.7: LU Factorization; Symmetric Matrices and the Transpose


HW 3

2.5: #4, 10b, 23, 30, 34; 2.6: #8, 9a, 15, 20;

2.7: #1, 2, 5, 15 (Extra Credit).

Make 2.5 #34 extra credit. Simply verify the answers in back of the text assuming 2by2 sub-matrices and using block multiplication!

Due: Thurs, Sept 17. (NOTE CHANGE of due date)                                                                                                         

 

Notes 4

Sept 15.  3.1: Vector Spaces and Subspaces

Sept 17.  3.2: Nullspace

 

HW 4

3.1: #3, 10, 20a, 23, 24;
3.2: #1, 2, 5, 17, 18, 23. 

Due: Thurs, Sept 24.

 

Review for Exam 1

Sept 22.   Review

 

EXAM 1, Tues, Sept. 29. Covers 1.1-3.2 (excluding 1.3).

 

 

 

Notes 5

Sept 24.   3.3: Rank and row reduced form

Oct. 1.   3.4: Complete solution of a linear system

 

HW 5

3.3: #2b, 7 (omit), 10, 19;
3.4: #1, 3, 5, 8b, 19, 31(extra cr.).

Due: Tues, Oct. 6.

 

 

 

Notes 6

Oct. 6.   3.5: Independence, basis, dimension

Oct .8:  3.6: Four subspaces

HW 6

3.5: # 1, 2, 7, 8, 13, 16;

3.6: # 3, 18, 23, 24.
Due: Thurs, Oct 15.

 

Notes 7

Oct. 13.  4.1: Orthogonal Complement

Oct. 15.  4.2: Projections


HW 7
4.1: # 6, 11, 21, 28
4.2: # 1, 5, 6, 11, 12 13, 17.
Due: Thurs, Oct 22.

 

Notes 8

Oct 20. 4.3: Least squares approximation

Oct 22.  4.4: Gram-Schmidt and QR factorization

 

HW 8

4.3: # 1, 9, 20, 21;
4.4: # 10, 13, 14, 21, 23.

Due: Tues., Nov. 3 (DUE DATE POSTPONED as of Oct. 29)

 

Review for Exam 2

Sample Solution Review for Exam 2  (typo: #2(b): particular solution x2=t-s, x1=2s-t, x3=0.)

Oct 27. Review

 

EXAM 2, Tues, Nov. 3. Covers 3.3-4.4

 

 

 

Notes 9

Oct. 29. 5.1: Determinants

Nov 5. 5.2-5.3: Permutation and co-factor expansions: volume.

 

HW 9

5.1: # 1, 14, 15, 21, 22;
5.2: # 4, 17, 19;
5.3: # 1, 4, 8, 16, 24.
Due:  Thurs, Nov 12.

 

Notes 10

Nov 10.  6.1: Introduction to Eigenvalues
Nov 12. 6.2: Diagonalizing a Matrix

 

HW 10

6.1: # 1, 12, 24, 26, 32;
6.2: # 1, 2, 16, 17, 33 (extra cr.).

Due: Thurs, Nov 19.

 

 

 

 

Notes 11

Nov 17.  6.4: Symmetric matrices are (orthogonally) diagonalizable
Nov 19. 6.5: Positive Definite Matrices

 

HW 11

6.4: # 4, 5, 12, 18, 25, 26;
6.5: # 1, 2, 5, 9, 17, 22, 24.

Due: Thurs, Dec. 3.

 

Notes 12

Dec 1.  6.6: Similar matrices
Dec 3. 6.7: Singular value decomposition


HW 12

6.6: # 1, 4, 5, 9, 20;
6.7: #  1, 2, 3, 6, 7. 

Due: Thurs, Dec 10.

 

Review for Final Exam

Dec 8. Review

Dec 10.  Review

 

FINAL EXAM, Thurs, Dec 17, 1:40- 4:10 pm. Covers 5.1-6.7 (excluding 6.3)