One semester course on linear algebra. Assuming a basic acquaintance with vectors and matrices, the course goes on to study matrix theory in greater depth as well as some of its applications. Topics include Gauss elimination, LU factorization, row, column and null spaces and their dimensions, orthogonality, Gram-Schmidt method, QR factorization, determinants, eigenvalues, symmetric and Hermitian matrices and linear transformations. Applications include Markov chains, linear differential and difference equations, method of least squares, principle axes for conic sections, etc.
Applied Linear Algebra, by Olver and Shakiban. We will cover many, but not all, of the topics in the book. This is only possible because some of the material should already be familiar from previous courses. Specifically, you should already know about matrix multiplication, determinants of small matrices, and probably at least heard of eigenvalues. Since the class meets only once a week, you will have to work hard on your own outside class.
There will be grades for quizzes and three midterm exams. All exams and quizzes are open book/notes, calculators allowed.
Quizzes 25 % Midterm Exams (25% each) 75 % For general policy statements about grades and academic honesty, go to: Grading Policy Statement, Student Conduct Statement .
Midterm I Wednesday, February 17 Midterm II Wednesday, March 31 Midterm III Wednesday, May 5
Homework will be assigned but not collected. Instead there will be weekly quizzes consisting of problems very similar to the homework problems. If you can do the homework problems you should have no trouble with the quizzes. One quiz score will be dropped to allow for an absence or just a "bad day." To see the assignments, click on the link above.
Week Topic Reading 1/20 Gauss elimination, PA=LU 1.2-1.4 1/27 Inverses, LDL^T, lin. systems, determinants 1.5,1.6,1.8,1.9 2/3 Vector spaces, span, lin.indep, basis, dim. 2.1-2.4 2/10 Fund. Subspaces, Fund.Theorem 2.5 2/17 Midterm I 2/24 Inner prods., norms, pos. def. mat., compl.sq. 3.1-3.5 3/3 Minimization, least squares 4.1-4.4 3/10 Orthog. bases, Gram-Schmidt, orth.matrices 5.1-5.3 3/17 Spring Break 3/24 Orthog. poly., orth. projection, orth. subspaces 5.4-5.6 3/31 Midterm II 4/7 Linear transformations 7.1-7.3 4/14 Eigenvalues, diagonalization 8.1-8.3, 9.1 4/21 Orthog. diagonalization, singular values 8.4-8.5 4/28 Linear iteration, Markov chains 10.1, 10.4 5/5 Midterm III
Here are two do-it-yourself computer labs to see how Matlab can be used to numerically solve linear algebra problems. The links below allow you to download the instructions for the labs which can be done on any computer running Matlab. This is purely for enrichment -- no grades.