Math 310: Applied Linear Algebra
Left
Course Prerequisites
Grade of C or better in MATH 181 (Calculus II)
Course Description
Matrices, Gaussian elimination, vector spaces, LUdecomposition, orthogonality, GramSchmidt 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 Kuttle, , Lyryx Version 2021A. Publisher Lyryx with Open Texts
MyOpenMath
 The courses 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.
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 
Week 4

Further properties of the inverse of a matrix LU Decomposition 
Week 5 
Review and Midterm 1 Determinants 
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 Ranknullity theorem 
Week 9

Review and Midterm 2 Orthogonality 
Week 10

GramSchmidt Orthogonal projections Least squares solutions 
Week 11

Linear transformations Eigenvectors and eigenvalues 
Week 12

Diagonalization 
Week 13

Markov chains Orthogonal Diagonalization 
Week 14

Singular Value Decomposition 
Week 15 
Applications of Singular Value Decomposition Review 
Week 16
Finals' Week 
Final Exam 