Topics in Applied Mathematics I

Math 311-101 — Summer I, 2013

Instructor: Dr. Francis J. Narcowich
Office: 302 Milner Hall
E-mail: fnarc@math.tamu.edu
Phone: (979) 845-7554 (Messages only.)
URL: /~francis.narcowich/
Office Hours: MTWR 11:45 a.m.-12:45 p.m., and by appointment.

Catalogue Description: MATH 311 - Topics in Applied Mathematics I

Systems of linear equations, matrices, determinants,vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization, inner product spaces,orthogonal functions; vector analysis, including gradient, divergence, curl, line and surface integrals, Gauss', Green's and Stokes' theorems. Prerequisites: MATH 221, 251 or 253; MATH 308 or concurrent enrollment, or junior or senior classification or approval of instructor. Credit will not be given for more than one of MATH 304, MATH 309, MATH 311 and MATH 323.

Time & Place: MTWRF 10:00 a.m.-11:35 a.m., BLOC 161.

Required Text: Stephen J. Leon and Susan Jane Colley, Math 311: Custom Edition for Texas A&M University at College Station, Pearson Learning Solutions, Boston, MA, 2012. ISBN 13: 978-1-256-98369-9.

Tests

Syllabus: The course covers most of chapters 1-6 in part I (Leon), and sections 8.4, 10.1,10.2, 11.1-11.3 in part II (Colley). For a schedule, which may change due to contingencies and unforseen circumstances, see the table below.

Grading System: Your grade will be based on two in-class tests and homework. Each in-class test will count for 40% of your grade, and the homework for 20%. Your letter grade will be assigned this way: 90-100%, A; 80-89%, B; 70-79%, C; 60-69%, D; 59% or less, F.

Make-up Policy: I will give make-ups (or satisfactory equivalents) only in cases authorized under TAMU Regulations. In borderline cases, I will decide whether or not the excuse is authorized. Also, if you miss a test, quiz, or cannot turn in a homework, contact me at fnarc@math.tamu.edu soon as possible. Normally, this is the next business day, unless there are extenuating circumstances.

Homework Assignments: I will assign and pick up homework two or three times per week. Each assignment will have several problems, but not of them will be graded. Late homework will be accepted (or excused completely) only for legitimate reasons, and may be penalized if circumstances warrant.

Copying Course Materials: ``All printed hand-outs and web-materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor.''

Aggie Honor Code:   "An Aggie does not lie, cheat, or steal or tolerate those who do."

Americans with Disabilities Act Policy Statement: "The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe that you have a disability requiring an accommodation, please contact the Department of Student Life, Services for Students with Disabilities, in Room 126 of the Koldus Building or call 845-1637."

Schedule

Date Section Topic
6/3/13 Part I (Leon): 1.1-1.2 Linear equations and row reduction
6/4/13 1.3, 1.4 Matrix algebra, "basic matrix trick'
6/5/13 1.4, 1.5 Matric inversion via row reduction
6/6/13 1.5, 2.1 Elementary matrices, determinants
6/7/13 2.1, 2.2, 3.1 Properties of determinants, vector spaces
6/10/13 3.1, 3.2 Vector spaces, subspaces, span
6/11/13 3.2,3.3 Span, linear independence
6/12/13 3.3, Coordinate Vectors Linear independence, "coordinate theorem" (Theorem 3.2, p. 139), coordinate vectors
6/13/13 3.4, Coordinate Vectors Basis and dimension, coordinate vectors
6/14/13 3.4, 3.6, Methods for Finding Bases Null space, row space and column space, and bases for them
6/17/13 Methods for Finding Bases, 4.1 Bases, linear transformations
6/18/13 4.1 Linear transformations, review
6/19/13 N/A Test 1
6/20/13 4.1, 4.2 Lineaer transformations and their representations
6/21/13 4.2, Change of Basis Representations of lineaar transformations, applications, changing coordinates
6/24/13 Change of Basis, 6.1, 6.3 Change of basis, eigenvalue problems, diagonalization
6/25/13 5.4, 6.4 Inner product spaces, Hermitian matrices
6/26/13 Part II (Colley): 8.4, 10.1 Gradient, divergence, curl, and line integrals
6/27/13 10.1, 10.2, 11.1 Line integrals and Green's Theorem, parametrized surfaces
6/28/13 11.2, 11.3 Surface integrals, Stokes's Theorem
7/1/13 11.3 Stokes's Theorem and Gauss's Theorem
7/2/13 N/A Catch-up, review
7/3/13 N/A Test 2
7/4/13 N/A Independence Day
7/5/13 N/A Finish up

Updated: June 21, 2013 (fjn)