Math 310: Applied Linear Algebra
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Course Information Heading link
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Course Prerequisites
Grade of C or better in MATH 181 (Calculus II)
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 MATH 310 and MATH 320 (Linear Algebra I).
Calculators not permitted on exams or quizzes.
Credit Awarded
3 hours
Course Materials
Textbook
- The courses uses a free textbook that can be found here.
A First Course in Linear Algebra, K. Kuttler, Lyryx Version 2023-A. (publisher: Lyryx with Open Texts)
MyOpenMath
- The course uses the MyOpenMath platform for online homework and quizzes. No purchase for this is required.
Linear Algebra Internet Resources
- Lots of interesting material (including video lectures on many topics) can be found on the MIT open course linear algebra site.
- The Mathematics Archives maintains an excellent guide to Web Sites related to Linear Algebra.
- Mathematics Archives – Topics in Mathematics – Linear Algebra
- The Linear algebra toolkit. Contains a number of tools that show computations of linear algebra in action.
- See also the Glossary file in the link below.
Sample Exams and Material Heading link
Course Schedule Heading link
| Sections | Topics |
|---|---|
|
Week 1
|
Systems of linear equations Row reduction and echelon Forms |
|
Week 2 |
Solutions of linear Equations Rank and homogeneous systems Applications of linear systems |
|
Week 3
|
Matrix operations Matrix inverses |
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Week 4
|
Further properties of the inverse of a matrix LU Decomposition |
|
Week 5 |
Review and Midterm 1 Determinants |
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Week 6
|
Applications of the determinant Vectors, length and dot product |
|
Week 7
|
Spanning set of vectors Linear independence Subspaces and Bases |
|
Week 8
|
Dimension Column Space and null Space Rank-nullity theorem |
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Week 9
|
Review and Midterm 2 Orthogonality |
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Week 10
|
Gram-Schmidt Orthogonal projections Least squares solutions |
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Week 11
|
Linear transformations Eigenvectors and eigenvalues |
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Week 12
|
Diagonalization |
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Week 13
|
Markov chains Orthogonal Diagonalization |
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Week 14
|
Singular Value Decomposition |
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Week 15 |
Applications of Singular Value Decomposition Review |
|
Week 16
Finals' Week |
Final Exam |