### Contents

### 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 MATH310 and MATH320.

### PREREQUISITES

Grade of C or better in MATH 181.

### 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 may choose to use either a print copy or an ebook on Vital Source.

### STUDENTS WITH DISABILITIES

Students with disabilities who require special accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS). Students who need exam accommodations must contact ODS in the first week of the term to arrange a meeting with a Disability Specialist. Please contact ODS at (312)-413-2183 (voice) or (312)-413-0123 (TTY).

### RELIGIOUS HOLIDAYS

Religious holidays: Students who wish to observe their religious holidays shall notify the faculty member by the tenth day of the semester of the date when they will be absent unless the religious holiday is observed on or before the tenth day of the semester. In such cases, the student shall notify the faculty member at least five days in advance of the date when he/she will be absent.

### GRADING

10% Quizzes

10% Homework

20% Midterm 1 (held in class)

20% Midterm 2 (held in class)

40% Final Exam

Note: The date for the final exam is set by the university. The schedule can be found here.

### GRADES

The overall scores will be converted to grades as follows:

85%+ A

70%+ B

55%+ C

40%+ D

In addition individual instructors may choose to lower these boundaries for their section if deemed necessary to ensure fairness across different sections (so, for example, 85% will always result in an A grade, but it may be that an A grade is given to some students with slightly lower scores).

### ATTENDANCE

Attendance in person at lectures, quizzes and exams is mandatory in this course. Each instructor will determine the precise policy for their section.

### CALCULATORS

Quizzes and exams are to be taken without calculators.

### COURSE TOPICS

MATH 310 is a semi-coordinated course. Each section will have separate midterms and final exams, but will aim to cover the following topics (the * sections may be omitted).

§ 1.1 Linear Systems

§ 1.2 Row Reduction and Echelon Forms

§ 1.3 Vector Equations

§ 1.4 The Matrix Equation Ax=b

§ 1.5 Solution Sets of Linear Systems

§ 1.6 Applications of Linear Systems

§ 1.7 Linear Independence

§ 1.8 Linear Transformations

§ 1.9* The Matrix of a Linear Transformation

§ 1.10 Linear Models in Business, Science, and Engineering

§ 2.1 Matrix Operations

§ 2.2 The Inverse of a Matrix

§ 3.1 Introduction to Determinants

§ 3.2 Properties of Determinants

§ 3.3 Cramer's Rule, Volume and Linear Transformations

§ 2.8 Subspaces of R^n

§ 2.9 Dimension and Rank

§ 4.9 Applications to Markov Chains

§ 5.1 Eigenvectors and Eigenvalues

§ 5.2 The Characteristic Equation

§ 5.3 Diagonalization

§ 5.5* Complex Eigenvalues

§ 5.7 Applications to Differential Equations

§ 6.1 Inner Product, Length and Orthogonality

§ 6.2 Orthogonal Sets

§ 6.3 Orthogonal Projections

§ 6.4 The Gram-Schmidt Process

§ 6.5 Least-Squares Problems

§ 6.6 Application to Linear Models

§ 7.1 Diagonalization of Symmetric Matrices

§ 7.2 Quadratic Forms

§ 7.3* Constrained Optimization

§ 7.4 Singular Value Decomposition

### RECOMMENDED PROBLEMS

§ 1.1: 1, 3, 5, 7, 9, 11, 15, 21, 23, 31

§ 1.2: 1, 2, 3, 9, 10, 13, 17, 19, 21, 23

§ 1.3: 1, 5, 9, 11, 13, 15, 17, 19, 22, 25

§ 1.4: 1, 5, 7, 9, 11, 13, 15, 23, 24, 25 (verify the matrix product!)

§ 1.5: 1, 3, 5, 11, 15, 17, 23, 24, 29, 31

§ 1.7: 1, 3, 7, 9, 17, 21, 22, 23, 27, 28, 33, 34, 35, 36, 37

§ 1.8: 3, 5, 9, 13, 14, 15, 16, 17, 21, 22

§ 1.9: 1, 3, 5, 11, 17, 19, 23, 24, 25, 27

§ 1.10: 1, 4, 5, 7, 9

§ 2.1: 1, 5, 7, 9, 11, 12, 15, 16, 20, 23

§ 2.2: 1, 3, 5, 7, 9, 10, 11, 13, 17, 18, 26, 29 and 30 (check using Theorem 4), 31, 35

§ 3.1: 1, 3, 9, 13, 15, 25, 27, 29, 39, 40

§ 3.2: 1, 3, 4, 5, 9, 15, 19, 21, 25, 27, 28, 33, 34, 36, 39

§ 3.3: 1, 5, 7, 11, 17, 18, 19, 21, 23, 27, 29, 30

§ 2.8: 1, 3, 5, 7, 9, 11, 13, 17, 20, 21, 22, 23

§ 2.9: 1, 3, 5, 11, 13, 17, 18, 19, 23, 24

§ 4.9: 1, 3, 5, 7, 9, 10, 11, 13

§ 5.1: 1, 3, 5, 7, 13, 15, 17, 21, 22, 25, 27, 31

§ 5.2: 1, 3, 5, 7, 9, 13, 15, 17, 21, 22

§ 5.3: 1, 3, 7, 9, 11, 13, 15, 17, 19, 21, 22, 23

§ 5.5: 1, 3, 5, 7, 9, 13, 15, 25

§ 5.7: 1, 3, 4, 5, 7, 9, 11, 13

§ 6.1: 1, 3, 5, 7, 11, 13, 15, 17, 19, 20, 27, 30

§ 6.2: 1, 3, 7, 9, 11, 13, 17, 23, 24, 27

§ 6.3: 1, 3, 5, 7, 9, 11, 21, 22

§ 6.4: 1, 3, 5, 7, 9, 11, 17, 18

§ 6.5: 1, 3, 9, 11, 17, 18

§ 6.6: 1, 3, 5, 9

§ 7.1: 1, 3, 5, 7, 9, 11, 13, 16, 17, 19, 21, 23

§ 7.2: 1, 3, 5, 9, 11, 21, 23, 24, 27, 28

§ 7.3: 1, 3, 7, 9

§ 7.4: 1, 3, 7, 11, 15, 18