# Course Syllabus for MATH 311

COURSE TITLE: Topics in Applied Mathematics

TEXTBOOK: Linear Algebra and Vector Calculus at A&M by Leon and Colley

CATALOG DESCRIPTION: Matrices, determinants, systems of linear equations, eigenvalues, eigenvectors, diagonalization of symmetric matrices. Vector analysis, including normal derivative, gradient, divergence, curl, line and surface integrals, Gauss', Green's and Stokes' theorems. Prerequisite: MATH 221, 251 or 253; MATH 308 or current enrollment therein.

Math 311 is one of two courses designed primarily for engineering aand physics majors. It is also taken by meteorology majors and, as an elective, by many computer science majors. Most of the students will be juniors or seniors.

The first 60% of the course is devoted to linear algebra, with a strong bias toward applications to analysis. The remaining 40% is devoted to the material traditionally called vector calculus (or vector analysis), along with some other topics in advanced calculus which provide nice applications of the linear algebra covered in the first part.

In our discussions with Engineering, the most important topics in this course are 1) change of basis and 2) an intuitive feel for the theorems in vector/several variable calculus, most notably the change of variables formula for integrals and the divergence theorem. Engineering students need to have a good facility for how a change of basis affects the matrix of a linear map. As for the vector calculus, emphasis should be given on an intuitive feel for the tools rather than on mere computations, which the students have had some exposure to in Math 251. For example, some discussion should be devoted to why the determinant appears in the change of variables formula for integration.

## MATH 311: Weekly Schedule

Note: This is a fall or spring schedule. In summer, this schedule is accelerated by 50% in order to accommodate a 10-week session.

Text: MATH 311 Linear Algebra and Vector Calculus at Texas A&M - Leon & Colley
A = 1st half of book
B = 2nd half of book

• Week 1 Linear Systems

• Sections A1.1, A1.2.
• Week 2 Matrix Algebra, Determinants

• Sections A1.3, A1.4, A2.1.
• Week 3 Determinants, Review of (Cross Product, Planes, Coordinates)

• Sections A2.2, Review( B1.4, B1.5, B1.7 ).
• Week 4 Vector Spaces, Review for Exam

• Sections A3.1, A3.2.
• Week 5 Bases

• Sections A3.3, A3.4, A3.5.
• Week 6 Change of Basis, Linear Transformations (Do Exer. A4.1 #20,21; Assign #16,22,24)

• Sections A3.6, A4.1, A4.2.
• Week 7 Linear Transformations

• Sections A4.2, A4.3, Review for exam
• Week 8 Inner Products

• Sections Exam 1 (Oct.21), A5.1, A5.2.
• Week 9 A5.3.,

• Sections Review( B3.1, B3.2, B3.3, B3.4 ).
• Week 10 Review of (Multiple Integrals), Change of Variables

• Sections Review( B5.1, B5.2, B5.3, B5.4 ), B5.5.
• Week 11 Line Integrals, FTC, Green's Theorem

• Sections B6.1, B6.2, B6.3.
• Week 12 Parametric Surfaces, Surface Integrals, Stokes' & Gauss' Theorems

• Sections B7.1, B7.2, B7.3.

• Week 13 Catch-up
• Week 14 Review for Exam, Exam 2 (Dec.4)
• Week 14 Review for Final.

• Last week of class has redefined days. See Important Dates for more details.