Math 310: Applied Linear Algebra
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Course Information
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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, but encouraged for the MyMathlab and written homework.
Credit Awarded
3 hours
Course Materials
Textbook
- Linear Algebra and its 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 will have access to an electronic copy of this book when you register for MyMathLab.
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
Course Schedule
Sections | Topics |
---|---|
Week 1
Sec 1.1-1.2 |
Systems of Linear Equations Row Reduction and Echelon Forms Direction Fields |
Week 2 Sec 1.3-1.5 |
Vector Equations The Matrix Equation Ax=b Solution Sets of Linear Systems |
Week 3
Sec 1.6-1.8 |
Applications of Linear Systems Linear Independence Introduction to Linear Transformations |
Week 4
Sec 1.10, 2.1, 2.2 |
Linear Models in Business, Science and Engineering Matrix Operations The Inverse of a Matrix |
Week 5 Midterm 1 and Sec 2.5 |
Review and Exam 1 Matrix Factorization |
Week 6
Sec 2.7 |
Applications to Computer Graphics |
Week 7
Sec 2.8, 2.9 |
Subspaces of R^n Dimensions and Rank |
Week 8
Sec 3.1-3.3 |
Introduction to Determinants Properties of Determinants Cramer's Rule, Volume and Linear Transformation |
Week 9
Sec 5.1-5.3 |
Eigenvectors and Eigenvalues The Characteristic Equation Diagonalization |
Week 10
Exam 2 and Sec 4.9 |
Review and Midterm Exam 2 Applications to Markov Chains |
Week 11
Sec 4.9, 5.7 |
Applications to Markov Chains (continued) Applications to Differential Equations |
Week 12
Sec 6.1-6.3 |
Inner Product, Length and Orthogonality Orthogonal Sets Orthogonal Projections |
Week 13
Sec 6.4-6.6 |
The Gram-Schmidt Process Least Squares Solutions Applications to Linear Models |
Week 14
Sec 7.1-7.3 |
Diagonalizations of Symmetric Matrices Quadratic Forms Constrained Optimization |
Week 15 Sec 7.4 and Review |
Singular Value Decomposition Review for Final Exam |
Week 16
Finals' Week |
Final Exam |