This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

This is a collection of notes for a one-semester course in linear algebra taught at San Jacinto College (Houston, Texas). The notes are suited for a first course in linear algebra taken by students who have completed one year of single-variable calculus. Unlike most traditional linear algebra textbooks, these notes begin with the ideas of vector spaces and linear functions (transformations). Since functions play a central role in calculus, this approach should seem more natural to students. Systems of linear equations and matrix theory are presented afterward as consequences of the preceding material. The result is an economical (only 175 pages) treatment of the main themes of linear algebra along with a few applications of the theory to geometry, economics, and cryptography.