MATH401 / Fall 2015

This is the course website for MATH401 “Applications of Linear Algebra” Section 0401. Information about the course will be posted here.

Syllabus: Various applications of linear algebra: theory of finite games, systems of ordinary differential equations, linear programming, matrix methods as applied to finite Markov chains, random walk, incidence matrices, graphs and directed graphs, networks and transportation problems.

Textbook: the main reference is P.J. Olver-C. Shakiban: Applied Linear Algebra 1st ed, and we will follow this book closely. Homeworks will be assigned from the textbook.

Classes: TuTh 2:00-3:15pm in MTH0303.

Office hours: Th 11AM-12PM in my office (MATH4416), and by appointment.

Homework: Due every week.

Midterms: October 15, November 24

Final: Thursday, December 17, 10:30am-12:30pm.

Grade calculation: Homework 20%, Final 30%, Midterm 1 25%, Midterm 2 25%

Grader: Xiao Lin (linxiao365ATgmailDOTcom)

First day handout with detailed course information and grade policy.

Schedule:

·         Sept 1, Sections 1.1, 1.2, 1.3.

·         Sept 3, Sections 1.4(Skip permuted factorization) 1.5 (Skip LDV factorization), 1.6 (Skip factorization of symmetric matrices), 1.8

·         Sept 8, Sections 1.9, 2,1, 2.2
HW1: 1.2.8, 1.2.23, 1.3.14(a,b,c,d),1.3.22(c,d), 1.4.9(a,b,c,d), 1.5.24(d,e), 1.8.2(e,f),1.8.4, 1.9.1(c,d),1.9.5, 2.1.2

·         Sept 10, Section 2.3, 2.4

·         Sept 15, Section 2.4, 2.5
HW2: 2.2.1(a,b), 2.2.9, 2.3.3(a,b), 2.3.8(a), 2.3.21(e,f), 2.3.33(a,c), 2.4.9(a,b), 2.4.12(a,b),2.5.1(b,c), 2.5.21(a,b).

·         Sept 17, Section 2.6

·         Sept 22, Section 6.1(skip positive definiteness and minimization)
HW3: 2.6.1(abcd),2.6.3(abcd), 2.6.6(ab), 2.6.12 (use formula 2.47), 6.1.1(abcd), 6.1.2, 6.1.3(only redo 6.1.1), 6.1.4(a) ßYou may use Matlab on the last problem

·         Sep 24, Section 6.2 (skip after equation (6.38))

·         Sept 29, Section 6.3

·         Oct 1, Section 6.3 (Skip second sentence of Theorem 6.8 and Example 6.9)
HW4: see email!

·         Oct 6: Section 8.2

·         Oct 8: Section 8.3 (know how to diagonalize matrices, Theorem 8.18 and related examples only), 8.4(know how to ortho-diagonalize symmetric matrices, Theorem 8.26 and corresponding examples only)

·         Oct 13, Section 8.6 (only Jordan decomposition)
HW5: 8.3.15(bcde), 8.4.1(abcd), 8.6.6(abcd), 8.6.7, 8.6.9(abcd) No Matlab! With diagonalization of any sort, I also want to see the basis of eigenvectors as well.

·         Oct 15, MIDTERM 1(solutions)

·         Oct 20, Section 8.1, 9.1

·         Oct 22, Section 9.1, 9.2 (Skip Proposition 9.17 and examples 9.18,9.21)
HW6: 9.1.12(bcde), 9.1.13 (bcd)(if you are confused about how to use the initial value, example 9.8 should be helpful), 9.1.20(adf), 9.1.24

·         Oct 27, Section 9.2, 9.3

·         Oct 29, Section 9.3,9.4
HW7: 9.2.1(b,c,d,e), 9.3.2(i,ii,iii), 9.3.3(b,c,d), 9.4.2(a), 9.4.4(b), 9.4.32(b,c)

·         Nov 3, Section 10.1

·         Nov 5, Section 10.2
HW 8: 10.1.13(a,b,c), 10.1.14(b), 10.1.18(b,c), 10.1.19(b), 10.2.1(a,c), 10.2.3(b,c), 10.2.5(a,b)

·         Nov 10, Section 10.4|

·         Nov 12, Google PageRank™ algorithm (here), (Skip the Power Method Convergence Theorem)
HW 9: 10.4.1(bef), 10.4.3, 10.4.4, 10.4.5, 10.4.12. Solve Problem 3 and Problem 4 in the notes above on the PageRank algorithm.

·         Nov 17, Section 4.2, 4.3

·         Nov 19, Section 4.3,4.4
HW 10: 4.3.1, 4.3.3 (first find a basis for the plane in question, then proceed as in the previous problem), 4.3.4(c you may use Matlab to solve linear equations),  4.3.14(b), 4.3.15(b,c), 4.4.1(a,b), 4.4.2 ( you may use Matlab to solve linear equations), 4.4.14(you may use Matlab to solve linear equations) 4.4.15(a,b,c).

·         Nov 24, MIDTERM 2

·         Dec 1, Section 5.1, 5.2(skip modification of Gram-Schmidt)
HW 11 5.1.22, 5.1.26, 5.1.27, 5.2.1(ab), 5.3.27(abc) [Last problem: Use the  Gram-Schmidt process to construct orthogonal functions starting with the following continuous functions on the [0,1] interval: (a) f_1(x) = x+1, f_2(x)=x-1, f_3(x) = x^2 – x. (b) g_1(x) = 2, g_2(x) = x-1, g_3(x) = x^2 + 1]

·         Dec 3, Section 5.3(skip Householder’s method), 5.4.

·         Dec 8, Section 5.7(Skip the Fast Fourier Transform)

·         Dec 10, Section 5.7 + Review
Suggested problems (do not turn in): 5.4.1(abc), 5.7.1(a), Redo the previous problem with f(x)=cos(x), f(x)=x+ x^2 and f(x)=x.