### MATH 471 Linear Algebra II (01) [16F]

MANHATTAN COLLEGE - DEPARTMENT OF MATHEMATICS

MATH 471 LINEAR ALGEBRA II FALL 2016

Dr. Kathryn Weld OFFICE: RLC 201 I

PHONE: (718) 862-7251 email: kathryn.weld@ manhattan.edu

OFFICE HOURS: M,R 3:00-4:00, W: 4-5 PM, and by appointment.

TEXT: David C. Lay, Linear Algebra and Its Applications (4th/e), Pearson. + MyMathLab

Catalog Course Description:

A continuation of the topics introduced in MATH 241 with emphasis on orthogonality, inner product spaces, eigenvalues and eigenvectors, diagonalization, quadratic forms, and numerical linear algebra. Fall. Prerequisite: MATH 272.

Learning Outcomes:

1. Understanding of eigenvalues, eigenvectors and diagonalization

2. Vector Spaces and Linear Transformations

3. Inner Products, the Gram-Schmidt Process

4. Diagonalizations of symmetric matrices

6. The Singular Value Decomposition

TOPICS TO BE COVERED:

Chapter 4:

• Vector Spaces,

• Basis,

• Linear Transformations,

• Matrix representations,

• Coordinate Systems and Change of Basis,

• Applications to Difference Equations,

• Markov Chains.

Chapter 5:

• Review of Eigenvectors and Eigenvalues, the Characteristic Equation

• Diagonalization

• Eigenvectors and Linear Transformations

• Complex Eigenvalues

• Discrete Dynamical Systems and differential equations

Chapter 6:

6.1: Inner Product, Length, and Orthogonality

6.2: Orthogonal Sets

6.3: Othogonal Projections

6.4: The Gram-Schmidt Process

6.7: Inner Product Spaces (as time permits)

Chapter 7:

7.1: Diagonalization of Symmetric Matrices

7.3: Constrained Optimization

7.4: The Singular Value Decomposition

Choice of:

Chapter 8:

8.1: Affine Combinations

8.2: Affine Independence

Chapter 10:

10.1: Introduction and Examples

Other topics: dual spaces, etc., as times permits

Tentative Exam Schedule

Wed. 9/28/16

R. 10/27/16

Wed. 11/30/16

Final Exam: During Exam Period

Mid term exams 57% (19% each)

Final 22 %

Class Participation 5%

Fall 2016 Important Dates

Monday - August 29 - Classes Begin

Friday - September 2 - Late Registration and Add/Drop Ends

Monday - September 5 - Labor Day - College Closed

Monday - October 10 - Columbus Day - College Closed

Tuesday - October 11 - Monday Schedule – WE WILL NOT HAVE CLASS

Monday - October 17 - Mid-Term Grades Due

Monday - November 1 - Spring 2016 Web Registration Begins

Friday - November 18 - Last Day to Withdraw from a Fall 2015 Course

Wednesday, November 23 - Friday, November 25 - Thanksgiving Holiday - No Classes

Friday - December 9 - Last Day of Classes

Monday - Saturday - December 12 - 17 - Final Exam Period

Make-up exams: Barring a documented emergency, or an athletic or academic commitment, there will be no make up exams. You must notify me ahead of time, except in the case of an emergency.

Class participation: You will be expected to attend and participate in class: ask questions on current homework, volunteer answers, work with other students, come for help when you need it, etc.

Special Accommodations: Please let me know if you need untimed tests, a note taker, or other support by the end of the second week at the very latest. These accommodations must be documented at the Specialized Resource Center, Miguel 301B.

Calculators: A graphing calculator is not required for successful completion of this course. You will be allowed to use a graphing calculator without CAS: TI-89 and TI-92 are not allowed on tests. Memory must be cleared before the exam. No devices that connect with the internet are allowed on the exam.

Academic Integrity: Cheating is not allowed and will be reported. Unless otherwise indicated, all tests, quizzes, labs, and graded homework should be done by each individual. Please see :http://manhattan.edu/community-standards-and_student-code-conduct

email, moodle: Assignments, announcements, etc. will appear on moodle and, email will be sent to the address listed on moodle.

Attendance: Attendance is mandatory. Four or more unexcused absences must be reported to the dean of your school. If you are late, please notify the teacher at the end of the class.

Kathryn Weld