This is supplemental course information, designed to give you a fuller picture of the course and an expanded look at the topics covered. This is an unofficial document. The USC Course Catalog is the binding description of all university courses. Information such as books, materials covered, and the order of topics is subject to change. Please consult instructor for this semseter to get more upto date course information.
Catalog Data:
441 Applied Linear Algebra for Engineering (3, Fa,Sp,and Sm)
Introduction to linear algebra and matrix theory and their underlying concepts. Application to engineering problems.
Prerequisite: MATH 445 (Mathematics of Physics and Engineering II).
Text book:
Linear Algebra and Its Applications, Strang, Harcourt Brace Jovanovich, 1988.
Course Coordinators:
S. W. Golomb, Professor of Electrical Engineering
Topics:
1. Matrices and Gaussian Elimination including matrix and vector notation, and matrix manipulations.
2. Vector Spaces and Linear Equations: including subspaces, linear independence, basis and dimension.
3. Orthogonality: including inner products, projections, least-squares approximation and Gram-Schmidt Orthogonalization.
4. Determinants: including properties, formulae and applications.
5. Eigenvalues and Eigenvectors: including applications to difference and differential equations. Study of Hermitian matrices and of positive definite forms.
6. Singular Value Decomposition.
Course Objectives:
To make the students comfortable with formulating engineering problems in terms of vectors and matrices and then using matrix and vector space properties to solve the problem.
Course Outcomes:
The students will be able to:
1. Understand vector and matrix notation.
2. Be able to find the general solution to a system of linear equations.
3. Understand vector space concepts such as linear independence, basis and dimension.
4. Relate questions concerning linear independence and dimension to matrix properties.
5. Understand geometric concepts such as orthogonality, projections and angle.
6. Solve the least-squares approximation problem and carry out Gram-Schmidt orthogonalization.
7. Become familiar with determinants and their properties and apply the theory to solve equations and to compute areas and volumes.
8. Be able to find the eigenvalues and eigenvectors of a matrix and use these to solve problems such as linear difference equations, linear difference equations (using the state-space approach).
9. Understand Singular Value Decomposition and its relationship to the pseudo inverse and to least-squares approximation.
Prepared by: P. Vijay Kumar Date: Sep. 16, 2002
