# Topics in Applied Mathematics I

## Math 311-101 — Summer I, 2016

Instructor: Dr. Francis J. Narcowich
Office: Blocker 611D
E-mail: fnarc@math.tamu.edu
Phone: (979) 845-7554 (Messages only.)
URL: http://www.math.tamu.edu/~francis.narcowich/
Office Hours: TWR 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 117.

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
• Midterm, Wednesday, June 15, 2016.
• Final Exam, Tuesday, July 5, 2016.

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 a midterm, a final and homework. The midterm and the final will each count for 40% 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 you have a disability requiring an accommodation, please contact Disability Services, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call 979-845-1637. For additional information, visit the Department of Disability Services.

Schedule

Date Section Topic
5/31/16 Part I: 1.1-1.2 Linear equations and row reduction
6/1/16 1.3, 1.4 Matrix algebra
6/2/16 1.4, 1.5 Matrix inversion and elementary matrices
6/3/16 2.1, 2.2 Determinants and their properties
6/6/16 2.2, 3.1 Evaluating determinants, vector spaces
6/7/16 3.1, 3.2 Vector spaces, subspaces, span
6/8/16 3.2, 3.3 Subspaces, linear independence, "basic matrix trick"
6/9/16 3.3, 3.4, 3.5 basis and dimension, coordinates
6/10/16 3.5, 3.6 Change of basis, row and column spaces, finding bases
6/13/16 4.1, 4.2 Linear transformations and their representation
6/14/16 4.3 Similarity, catch up, review
Wednesday, 6/15/16 N/A Midterm
6/16/16 5.1, 5.2 Scalar products and orthogonal subspaces
6/17/16 5.3, 5.4 Least-squares approximation and inner product spaces
6/20/16 5.5 Orthonormal sets
6/21/16 5.6, 6.1 Gram-Schmidt and eigenvalue problems
6/22/16 6.2, 6.3 Simple harmonic motion and diagonalization
6/23/16 Part II: 7.4, 10.1 Gradient, divergence, curl, and line integrals
6/24/16 10.1, 10.2 Line integrals and Green's Theorem
6/27/16 11.1 Parametrized surfaces
6/28/16 11.2 Surface integrals
6/29/16 11.3 Stokes's Theorem
6/30/16 11.3 Gauss's Theorem (Divergence Theorem)
7/1/16 11.3 Stokes's Theorem and Gauss's Theorem, review
Tuesday, 7/5/16 N/A Final exam (10:30 a.m.-12:30 p.m.) held in BLOC 113

Updated: May 26, 2016 (fjn)