This course introduces the central ideas of matrix theory and linear algebra. It emphasizes topics useful in other disciplines such as systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes.

This course is sophomore-junior level. The course website includes homework problems, projects, downloadable files, lab materials, lecture slides, course outline/syllabus, recommended books, and video lectures.

Professor Name: Gilbert Strang
Department: Mathematics
University: Massachusetts Institute of Technology

Textbooks:
Strang, G. Introduction to Linear Algebra, 3rd edition. Wellesley-Cambridge Press, 2003

Language: English

This course introduces students to linear algebra using MATLAB. Topics include: matrix and vector computations, linear equations and matrix algebra, LU and QR decomposition, determinants, eigenvalues and eigenvalues.

Professor Name: Prof. R. Goodman, Prof. C. Woodward
Department: Mathematics
University: Rutgers University

Textbooks:
Spence, L., Insel, A., & Friedberg, S. Elementary Linear Algebra: A Matrix Approach 2e. Prentice Hall, 2008.

Language: English

This course focuses on ordinary differential equations and some of their many applications. The course will take a multifaceted approach, including both analytic and numerical solution methods, as well as qualitative methods that enable us to discover properties of solutions without actually having a formula. Matrix algebra is a useful tool, and we will cover the parts of that subject which will be necessary for our use. MATLAB will be used throughout, both as a computational tool and as a remarkable aid to visualization.

Professor Name: John Polking, Joseph Masters, Carol Gwosdz, Joung Song
Department: Mathematics
University: Rice University

Textbooks:
Polking, J.C., Boggess, A. and Arnold, D. Differential Equations, Prentice Hall, 2001.
Arnold, D. and Polking, J.C. Using MATLAB in Ordinary Differential Equations. Prentice Hall, 1999.

Language: English

This course website contains links to an extensive set of MATLAB assignments that the author has created for the course, which covers linear algebra, finite Fourier transform, and wavelet analysis.

Language: English