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, two midterm exams and a final exam. All exams and quizzes are open book/notes, calculators allowed. For a general university policy statement about grades, academic honesty and workload, go to: University Grading Policy Statement.
|Midterm Exams (20 % each)||40 %|
|Final Exam||40 %|
|Midterm I||Wednesday, February 21|
|Midterm II||Wednesday, April 4|
|Final||Wednesday, May 9|
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.
|1/17||Gauss elimination, PA=LU||1.2-1.4|
|1/24||Inverses, LDL^T, lin. systems, determinants||1.5,1.6,1.8,1.9|
|1/31||Vector spaces, span, lin.indep, basis, dim.||2.1-2.4|
|2/14||Inner products, norms||3.1-3.3|
|2/28||Pos. def. matrices, comp.square, complex vs||3.4-3.6|
|3/7||Minimization, least squares||4.1-4.4, 6.1|
|3/21||Orthog. bases, Gram-Schmidt, orth.matrices||5.1-5.3|
|3/28||Orthog. poly., orth. projection, orth. subspaces||5.4-5.6|
|4/18||Eigenvalues, diagonalization||8.1-8.3, 9.1|
|4/25||Orthog. diagonalization, singular values||8.4-8.5|
|5/2||Linear iteration, Markov chains, Google||10.1, 10.4|
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.