MATH 310: Applied Linear Algebra

Navigation:

Contents

COURSE 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.

TEXTBOOK

David C. Lay, Linear Algebra and Its Applications, 4th Edition, Addison-Wesley, 2012.

SCHEDULE

This is a suggested course schedule. Individual sections may vary somewhat in their precise content and schedules.

System Message: ERROR/3 (<string>, line 25)

Malformed table. Column span incomplete at line offset 13.

============== ========= =============================
**CHAPTER 1: LINEAR EQUATIONS IN LINEAR ALGEBRA**
------------------------------------------------------
Week 1.        |S| 1.1   Linear Systems
..             |S| 1.2   Row Reduction & Echelon Forms
..             |S| 1.3   Vector Equations
Week 2.        |S| 1.4   The Matrix Equation Ax=b
..             |S| 1.5   Solution Sets of Linear Systems
Week 3.        |S| 1.6   Applications of Linear Systems
..             |S| 1.7   Linear Independence
..             |S| 1.8   Linear Transformations
Week 4.        |S| 1.9   Matrix of Linear Transformation
..             |S| 1.10  Linear Models in Business, Science & Engineering
-------------------------------------------------------
**CHAPTER 2: MATRIX ALGEBRA**
-------------------------------------------------------
..             |S| 2.1   Matrix Operations
Week 5.        |S| 2.2   Inverse of a Matrix
..             |S|       First Exam
..             |S| 2.3   Characterization of Invertible Matrices
Week 6.        |S| 2.4   Partitioned Matrices
..             |S| 2.5   Matrix Factorization
..             |S| 2.7   Application to Computer Graphics
---------------------------------------------------------
**CHAPTER 3: DETERMINANTS**
---------------------------------------------------------
Week 7.        |S| 3.1   Introduction to Determinants
..             |S| 3.2   Properties of Determinants
..             |S| 3.3   Cramer's Rule, Volume & Linear Transformations
---------------------------------------------------------
**CHAPTER 4: VECTOR SPACES**
---------------------------------------------------------
Week 8.        |S| 4.1   Vector Spaces & Subspaces
..             |S| 4.2   Null Spaces, Column Spaces & Linear Transformations
Week 9.        |S| 4.3   Linear Independent Sets; Bases
..             |S| 4.4   Coordinate System
..             |S| 4.5   The Dimension of a Vector Space
Week 10.       |S| 4.6   Rank
..                       Second Exam
..             |S| 4.7   Change of Basis
----------------------------------------------------------
**CHAPTER 5: EIGENVALUES AND EIGENVECTORS
----------------------------------------------------------
Week 11.       |S| 5.1   Eigenvectors & eigenvalues
..             |S| 5.2   The Characteristic Equation
..             |S| 5.3   Diagonalization
Week 12.       |S| 5.4   Eigenvectors and Linear Transformations
..             |S| 5.5   Complex Eigenvalues
..             |S| 4.9   Applications to Markov Chains
Week 13.       |S| 5.7   Applications to Differential Equations
-------------------------------------------------------------
**CHAPTER 6: ORTHOGONALITY AND LEAST SQUARES
-------------------------------------------------------------
..             |S| 6.1   Inner product, Length and Orthogonality
..             |S| 6.2   Orthogonal Sets
Week 14.       |S| 6.3   Orthogonal Projections
..             |S| 6.4   The Gram-Schmidt Process
..             |S| 6.5   Least-Squares Problems
Week 15.       |S| 6.6   Applications to Linear Models
               |S| 6.7   Inner Product Space
               |S| 7.1   Diagonalization of Symmetric Matrices
============== ========= =============================

STUDENTS WITH DISABILITIES

Students with disabilities who require special accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS). Students who need exam accommodations must contact ODS in the first week of the term to arrange a meeting with a Disability Specialist.

Please contact ODS at (312)-413-2183 (voice) or (312)-413-0123 (TTY).