MATH 310: Applied Linear Algebra

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Contents

COURSE DESCRIPTION

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

TEXTBOOK

Linear Algebra and it's Applications, Addison-Wesley 5th edition, David C. Lay, Steven R. Lay, Judy J. McDonald, ISBN 978-0-321-98261-4, 0-312-98261-4

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).

This is a suggested course schedule. Individual sections may vary somewhat in their precise content and schedules. The * sections can be omitted.

Week 1. August 24-28, 2015
§ 1.1 Linear Systems § 1.2 Row Reduction and Echelon Forms § 1.3 Vector Equations
Week 2. August 31 - September 4, 2015
§ 1.4 The Matrix Equation Ax=b § 1.5 Solution Sets of Linear Systems § 1.6* Applications of Linear Systems
Week 3. September 9 - 11, 2015
§ 1.7 Linear Independance § 1.8 Linear ransformations
Week 4. September 14 - 18, 2015
§ 1.9 Matrix of a Linear Transformation § 1.10* Linear Models in Business, Science, and Engineering § 2.1 Matrix operations
Week 5. September 21 - 25, 2015
§ 2.2 Inverse of a Matrix § 2.3 Characterization of Invertible Matrices and § 2.4* Patitioned Matrices § 2.5 Matrix Factorization
Week 6. September 28 - October 2. 2015
§ 3.1 Introduction to Determinants Test 1 § 3.2 Properties of Determinants
Week 7. October 5 - 9, 2015
§ 3.3 Cramer's Rule, Volume and Linear Transformations § 4.1 Vector spaces and subspaces § 4.2 Null Spaces, Column Spaces, and Linear Transformations
Week 8. October 12 - 16, 2015
§ 4.3 Linearly independent sets; Bases § 4.4 Coordinate System § 4.5 The Dimension of a Vector Space
week 9. October 19 - 23, 2015
§ 4.6 Rank § 4.7 Change of basis § 5.1 Eigenvectors and Eigenvalues
Week 10.October 26 - 30, 2015
§ 5.2 The Characteristic Equation § 5.3 Diagonalization § 5.4 Eigenvectors and Linear Transformations
Week 11.November 2 - 6, 2015
Appendix B - Review of complex numbers § 5.5 Complex Eigenvalues § 4.9 Applications to Markov Chains
Week 12.November 9 - 13, 2015
§ 5.7 Applications to Differential equations Test 2 § 6.1 Inner product, length and orthogonality
Week 13.November 16 - 20, 2015
§ 6.2 Orthogonal Sets § 6.3 Orthogonal Projections § 6.4 The Gram-Schmidt Process
Week 14.November 23 - 25, 2015
§ 6.5 Least-Squares Problems § 6.6 Application to Linear Models.
Week 15.November 30 - December 4, 2015
§ 6.7 Inner Product Spaces § 7.1 Diagonalization of Symmetric Matrices § 7.4* The Singular Value Decomposition
Week 16.November December 7 - 11
Final Exam