Math 4242/4457 : Applied Linear Algebra/Methods of Applied Math I (Section 30)
Fall Semester 2007, 2:30 - 3:20 pm, MWF, Mechanical Engineering 108, Offered on the UNITE Distributed Learning system

Prereq-2243 or 2373 or 2573; fall, spring, summer, every year)
Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications

4 credits (Credit will not be granted if credit has been received for: MATH 4457; prereq 2243 or 2373 or 2573)

Instructor: Willard Miller
Office: Vincent Hall 513
Office Hours: 10:10-11:05 M, 13:25-14:15 W, 9:05-9:55 F, or by appointment
Phone: 612-624-7379
miller@ima.umn.edu, miller@math.umn.edu

Prerequisites: Previous exposure to linear algebra: determinants and Cramer's rule.

Textbook: Applied Linear Algebra, by Peter J. Olver and Chehrzad Shakiban, Prentice-Hall, Upper Saddle River, NJ, 2006.

Class Description: A foundation course in linear algebra, with applications. Topics include: linear transformations, vector spaces, matrix calculus, solutions of systems of linear equations, determinants, orthogonality, LDU decompositions, SVD decompositions, canonical forms. Applications include: Gram-Schmidt process, least-squares approximations, graph theory, linear systems, etc. This material is basic, both for the understanding of the theory of linear algebra and for numerical computation.

Software: MATLAB (by The Mathworks, Inc.) will be used in the lectures and for some of the homework, No previous exposure is expected.

Policies:

1. Eleven homework assignments [NO late homework will be accepted without good excuses]. It is fine to do homework in collaboration with your classmates, but your writeup should be your own work.
2. Two Midterms plus the Final Exam [NO laptops. Standard calculator is OK. NO makeup tests without rigorous emergency reasons. Athletes please present "Proofs of Activities" in advance].
3. Grading Policy: Homework (25%), Two Midterms (40%), Final Exam (35%)

Content and Style: Will cover most of Chapters 1-8. Homework assignments from the textbook, which has many well designed exercise problems. The theory will predominate, but there will be considerable attention to applications in other fields.

Student Conduct: Statement on Scholastic Conduct: Each student should read the college bulletin for the definitions and possible penalties for scholastic dishonesty. Students suspected of cheating will be reported to the Scholastic Conduct Committee.

Paper Grader: Xingjie Li lixxx835@math.umn.edu
Office: 320 VinH
Office Hours: 15:30-17:00 T, 10:00-11:30 Th
Phone: (612) 625-0072

Introduction to MATLAB (courtesy of Professor Peter Olver) Postscript file PDF file

Math 4242/4457, Section 30 Fall 2007 Tentative Syllabus

		Week	Topic	Section	HW due
W	SEP 05	1	Matrices and Vectors	1.1-1.2
F	SEP 07	1	Gaussian Elimination	1.3
M	SEP 10	2	Pivoting and Permutations	1.4
W	SEP 12	2	Matrix Inverses	1.5
F	SEP 14	2	Introduction to MATLAB
M	SEP 17	3	Practical Linear Algebra	1.6/1.7	1
W	SEP 19	3	General Linear Systems	1.8
F	SEP 21	3	Determinants	1.9
M	SEP 24	4	Real Vector Spaces	2.1	2
W	SEP 26	4	Subspaces	2.2
F	SEP 28	4	Spans and Linear Independence	2.3
M	OCT 01	5	Bases and Dimension	2.4	3
W	OCT 03	5	The Fundamental Matrix Subspaces	2.5
F	OCT 05	5	Graphs and Incidence Matrices	2.6
M	OCT 08	6	Inner Products	3.1	4
W	OCT 10	6	Inequalities	3.2
F	OCT 12	6	Positive Definite Matrices	3.4
M	OCT 15	7	Completing the Square	3.5
W	OCT 17	7	Minimization of Quadratic Functions	4.1/4.2	5
F	OCT 19	7	Least Squares and the Closest Point	4.3
M	OCT 22	8	Data Fitting and Interpolation	4.4
W	OCT 24	8	Review
F	OCT 26	8	Midterm I: Chapters 1-3, Chapter 4 (sections 4.1-4.3)
M	OCT 29	9	Orthogonal Bases	5.1	6
W	OCT 31	9	The Gram-Schmidt Process	5.2
F	NOV 02	9	Orthogonal Matrices	5.3
M	NOV 05	10	Orthogonal Polynomials	5.4
W	NOV 07	10	Orthogonal Projections and Least Squares	5.5	7
F	NOV 09	10	Orthogonal Subspaces	5.6
M	NOV 12	11	Springs and Masses	6.1
W	NOV 14	11	Springs and Masses	6.1
F	NOV 16	11	Linear Functions	7.1
M	NOV 19	12	Linear Transformations	7.2	8
W	NOV 21	12	Simple Dynamical Systems	8.1
F	NOV 23	12	Thanksgiving Vacation
M	NOV 26	13	Eigenvalues and Eigenvectors	8.2
W	NOV 28	13	Review		9
F	NOV 30	13	Midterm II: Chapters 4-7
M	DEC 03	14	Eigenvector Bases and Diagonalization	8.3
W	DEC 05	14	Eigenvalues of Symmetric Matrices	8.4	10
F	DEC 07	14	Singular Values	8.5
M	DEC 10	15	Incomplete Matrices	8.6
W	DEC 12	15	Review		11
M	DEC 17		Final Exam, 10:30-12:30 in ME 108

HW1 : Due in class: Monday, September 17
1.2.8 (a,b), 1.2.22, 1.2.23, 1.2.29, 1.3.1 (c), 1.3.1 (d), 1.3.3 (e), 1.3.17, 1.3.22 (a,h), 1.3.24, 1.3.26, 1.3.32 (c), 1.4.2 (a,b,c), 1.4.6, 1.4.9, 1.4.19 (c), 1.4.24.

HW2: Due in class: Monday, September 24
1.5.12, 1.5.18, 1.5.24 (e), 1.5.31 (e), 1.7.1 (b), 1.7.16, 1.7.21 (b), 1.7.22 (b), 1.7.24, 1.8.1 (b,c), 1.8.2 (f ), 1.8.5, 1.8.7 (c,i), 1.8.10.

HW3 Due in class: Monday, October 1
2.1.4, 2.1.6 (a), 2.1.7, 2.2.2 (a,b,f,g,h), 2.2.6 (a), 2.2.16 (a,b,d,f,h), 2.3.3 (a,b), 2.3.8 (a), 2.3.14, 2.3.21 (a,b,f,g), 2.3.22, 2.3.26, 2.3.29, 2.3.33 (a,c,f ).

HW4 Due in class: Monday, October 8
2.4.1 (b,c), 2.4.2 (a,b,d), 2.4.10, 2.4.14 (a), 2.4.19 (ac), 2.5.5 (a,d), 2.5.9, 2.5.13, 2.5.21 (b,c), 2.5.25 (d), 2.5.27 (c), 2.5.31, 2.6.1 (d), 2.6.3 (c), 2.6.4 (c), 2.6.7 (a).

HW5 Due in class: Wednesday, October 17
3.1.2 (b,e,f ), 3.1.9, 3.1.25, 3.2.3, 3.2.5, 3.2.12, 3.2.19, 3.2.21, 3.2.33, 3.4.2, 3.4.7, 3.4.15, 3.4.22 (ii,iii), 3.4.23 (iii), 3.4.25, 3.5.1 (a,d,e), 3.5.2 (c), 3.5.6 (b).

HW6 Due in class: Monday, October 29
4.2.3 (b,d,e), 4.2.5 (b,e), 4.2.7 (a), 4.2.9, 4.3.1, 4.3.2 (a), 4.3.8, 4.3.14 (b), 4.3.15 (d), 4.4.1 (b), 4.4.4, 4.4.5.

HW7 Due in class: Wednesday, November 7
4.4.15, 4.4.19, 4.4.33, 4.4.40 (a), 4.4.43, 4.4.51, 5.1.2, 5.1.5, 5.1.13 (a,b,c), 5.1.18, 5.1.22, 5.1.27, 5.2.1 (a), 5.2.6 (a,b,f ), 5.2.8 (for 5.2.1 (a)).

HW8 Due in class: Monday, November 19
5.3.1 (a,b,c), 5.3.8, 5.3.17 (a,b-ii,iii,c), 5.3.27 (a), 5.3.28 (ii), 5.4.1 (b), 5.4.2 (a), 5.4.11 (c), 5.5.1 (b,c), 5.5.2 (c), 5.5.4, 5.5.11 (b), 5.5.13, 5.6.1 (c), 5.6.2 (c,d), 5.6.17 (d), 5.6.20 (b).

HW9 Due in class: Wednesday, November 28
6.1.1, 6.1.3 (for 6.1.1 only), 6.1.7, 6.1.8 (a), 6.1.14, 6.1.16 (b).

HW10 Due in class: Wednesday, December 5
7.1.1 (a,b), 7.1.2 (a,c), 7.1.27 (a,e), 7.1.28, 7.1.38, 7.1.53, 7.2.1 (i,a,b), 7.2.24 (a), 7.2.25 (a).

HW11 Due in class: Wednesday, December 12
8.2.1 (d,i), 8.2.8 (b), 8.2.15 (d,i), 8.2.22, 8.2.24, 8.2.29 (a,b), 8.2.35 (a,b,c[i]), 8.3.1 (b,d,e), 8.3.16, 8.3.21 (b) , 8.4.1 (d), 8.4.15 (d), 8.4.18, 8.5.1 (d), 8.5.2 (d), 8.5.11.

Class notes on proof of Cauchy-Schwarz inequality

December 12 rough review notes for final exam

Practice midterm exam 1, with (very brief) solutions

Midterm exam 1, with solutions

Mean 69, Median 70, Standard Deviation 19
Advisory grades
85-100 A
80-84 A-
75-79 B+
70-74 B
65-69 B-
60-64 C+
55-59 C
50-54 C-
40-49 D+
30-39 D

Mean 80, Median 84, Standard Deviation 16
Advisory grades
90-100 A
85-89 A-
80-84 B+
70-79 B
65-69 B-
60-64 C+
55-59 C
50-54 C-
40-49 D+
30-39 D