Math 310 - Syllabus for Applied Linear Algebra

MATH 310
APPLIED LINEAR ALGEBRA

SYLLABUS

This is an suggested course syllabus and weekly schedule.
Individual sections will vary somewhat in their precise content and schedules.

CATALOGUE DESCRIPTION: Matrices, Gaussian elimination, vector spaces, LU-decomposition, orthogonality, Gram-Schmidt process, determinants, inner products, eigenvalue problems, applications to differential equations and Markov processes. Credit is not given in both Mathematics 310 and 320.

CHAPTER 1: LINEAR EQUATIONS

Week 1. § 1.1 Linear Systems & Row Operations

§ 1.2 Gauss-Jordan Operation on Matrices

Week 2. § 1.3 Matrix algebra, multiplication (incl. transpose, inverse)

Week 3. § 1.4 Elementary matrices; LU-decomposition

§ 1.5 Partitioned matrices, as time permits

CHAPTER 2: DETERMINANTS

Week 4. § 2.1 Computation by elimination and/or cofactors

§ 2.2 Properties

§ 2.3 Cramer's rule

CHAPTER 3: VECTOR SPACES

Week 5. § 3.1 Examples

§ 3.2 Subspaces (how to verify), span

Week 6. § 3.3 Linear independence

§ 3.4 Basis and dimension

Week 7. § 3.5 Change of basis (coordinates, transition matrix)

§ 3.6 Row space & column space

CHAPTER 4: LINEAR TRANSFORMATIONS

Week 8. § 4.1 Linear transformations - definition & examples

§ 4.2 Matrix representation

§ 4.3 Similarity, look ahead to diagonalization in § 6.3

CHAPTER 5: ORTHOGONALITY

Week 9. § 5.1 Dot product

§ 5.2 Orthogonal subspaces

Week 10. § 5.3 Least squares, pseudo-inverses

§ 5.4 General inner product spaces, Cauchy-Schwarz inequality

Week 11. § 5.5 Orthonormal basis & projection

§ 5.6 Gram-Schmidt process & QR-factorization

CHAPTER 6: EIGENVALUES

Week 12. § 6.1 Definition: Eigenvalues and eigenvectors; example: Markov Matrices

§ 6.2 Linear differential systems

Week 13. § 6.3 Diagonalization, matrix exponential; "defective" (or non-diagonalizable) matrices

§ 6.4 Hermitian matrices: including symmetric matrices

Week 14. § 6.6 General quadratic forms ( as time permits)

§ 6.7 Positive definite matrices (as time permits)

Week 15. § 6.8 Nonnegative matrices (as time permits)

URL: http://www.math.uic.edu/math310/syllabus.html -- Updated August 16, 2002 by S. Smith

CHAPTER 1: LINEAR EQUATIONS
Week 1.	§ 1.1	Linear Systems & Row Operations
Week 1.	§ 1.2	Gauss-Jordan Operation on Matrices
Week 2.	§ 1.3	Matrix algebra, multiplication (incl. transpose, inverse)
Week 3.	§ 1.4	Elementary matrices; LU-decomposition
Week 3.	§ 1.5	Partitioned matrices, as time permits
CHAPTER 2: DETERMINANTS
Week 4.	§ 2.1	Computation by elimination and/or cofactors
	§ 2.2	Properties
	§ 2.3	Cramer's rule
CHAPTER 3: VECTOR SPACES
Week 5.	§ 3.1	Examples
Week 5.	§ 3.2	Subspaces (how to verify), span
Week 6.	§ 3.3	Linear independence
Week 6.	§ 3.4	Basis and dimension
Week 7.	§ 3.5	Change of basis (coordinates, transition matrix)
Week 7.	§ 3.6	Row space & column space
CHAPTER 4: LINEAR TRANSFORMATIONS
Week 8.	§ 4.1	Linear transformations - definition & examples
	§ 4.2	Matrix representation
	§ 4.3	Similarity, look ahead to diagonalization in § 6.3
CHAPTER 5: ORTHOGONALITY
Week 9.	§ 5.1	Dot product
Week 9.	§ 5.2	Orthogonal subspaces
Week 10.	§ 5.3	Least squares, pseudo-inverses
Week 10.	§ 5.4	General inner product spaces, Cauchy-Schwarz inequality
Week 11.	§ 5.5	Orthonormal basis & projection
Week 11.	§ 5.6	Gram-Schmidt process & QR-factorization
CHAPTER 6: EIGENVALUES
Week 12.	§ 6.1	Definition: Eigenvalues and eigenvectors; example: Markov Matrices
Week 12.	§ 6.2	Linear differential systems
Week 13.	§ 6.3	Diagonalization, matrix exponential; "defective" (or non-diagonalizable) matrices
Week 13.	§ 6.4	Hermitian matrices: including symmetric matrices
Week 14.	§ 6.6	General quadratic forms ( as time permits)
Week 14.	§ 6.7	Positive definite matrices (as time permits)
Week 15.	§ 6.8	Nonnegative matrices (as time permits)