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