Math 310: Applied Linear Algebra

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

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:

Sample Exams and Material

Course Schedule

The following is a typical 15-week Fall or Spring semester schedule for MATH 310. During the Summer sessions, the schedule is condensed into 8 weeks.
Sections labelled * are optional and may be omitted by the instructor.
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