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.
Credit Awarded
3 hours
Course Materials
Textbook
- The course uses a free textbook that can be found here: A First Course in Linear Algebra, K. Kuttler, Lyryx version 2023-B (publisher: Lyryx with Open Texts). An alternative resource is Linear Algebra and its Applications, D. Lay, S. Lay, and J. McDonald, fifth edition.
MyOpenMath
- The course uses the MyOpenMath platform for online homework. 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 Homogeneous systems Rank |
|
Week 3
|
Applications of linear systems Matrix operations Matrix inverses |
|
Week 4
|
More on matrix inverses Linear transformations |
|
Week 5 |
More on linear transformations Review for exam 1 Exam 1 LU factorization |
|
Week 6
|
Determinants |
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Week 7
|
Span Linear independence Subspaces Bases Dimension |
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Week 8
|
More on bases Null space and column space Rank-nullity theorem |
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Week 9
|
Eigenvalues and eigenvectors Review for exam 2 Exam 2 |
|
Week 10
|
Diagonalization Markov chains |
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Week 11
|
Dot product Orthogonality Gram-Schmidt |
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Week 12
|
QR factorization Orthogonal projection Least-squares solutions |
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Week 13
|
Orthogonal Diagonalization Review for exam 3 Exam 3 Singular values |
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Week 14
|
Singular value decomposition applications of the SVD The matrix exponential (time permitting) |
|
Week 15 |
Review for final exam |
|
Week 16
Finals Week |
Final Exam |