MA 303 (001) Fall 2023 Linear Analysis

Instructor: Chao Chen

Email: chao_chen@ncsu.edu (Please include course number in the subject.)

Times: TuTh 3:00PM - 4:15PM

Location: 3216 Broughton Hall

Office hours: SAS 4236, ThTh 1:00PM - 2:00PM and by appointment

Textbook: N. J. Rose, Introduction to Linear Analysis, Department of Mathematics, NC State University, 1999

Course Description

This course is about the analysis of discrete and continuous dynamical systems, or systems that change with time. Specific topics include

• linear difference equations of first and second order, compound interest and amortization

• linear differential equations of first and second order

• matrices and systems of linear equations, eigenvalues, diagonalization, systems of difference and differential equations.

Homework

• Homework assignments will be given weekly, and they will be collected on specified due dates after lectures (in the classroom).

Exams

Three midterm exams (during class time): September 14 (Thursday), October 19 (Thursday), and November 21 (Tuesday)

Final exam: December 12 (Tuesday) 3:30PM - 6:00PM

Grading

Numerical grade = homework (10%) + 3 x midterms (20%) + final (30%)

Letter grade

• 97 and above is A+, starting from 93 and below 97 is A, starting from 90 and below 93 is A-.

• Similar for the B, C, and D ranges.

• Anything below 60 is F.

Moodle

The Moodle page of this course is here.

Panopto

Lectures will be videotaped and made available via Panopto.

(Classroom attendance is recommended on the substance.)

Schedule

Week 1

• Aug. 22: Difference Equations

• AUg. 24: Difference Equations, Compound Interest

Week 2

• Aug. 29: Compound Interest

• Aug. 31: Mortgage Amortizations, 1st Order Difference Equation

Week 3

• Sep. 5: 1st Order Difference Equations

• Sep. 7: Complex Numbers

Week 4

• Sep. 12: Complex Numbers, Fibonacci Numbers

• Sep. 14: Midterm Test 1

Week 5

• Sep. 19: Wellness Day (no class)

• sep. 21: Properties of Solutions of 2nd Order Linear Difference Equations

Week 6

• Sep. 26: Homogeneous 2nd Order Linear Difference Equation

• Sep. 28: Non-homogeneous 2nd Order Linear Difference Equation

Week 7

• Oct. 3: Economic Model, Gambler's Ruin

• Oct. 5: Differential Equations

Week 8

• Oct. 10: Fall break (no class)

• Oct. 12: Separation of Variables

Week 9

• Oct. 16: 1st Order and 2nd Order Linear Differential Equations

• Oct. 19: Midterm Test 2

Week 10

• Oct. 24: Vectors and Matrices

• Oct. 26: Matrix Notation for Linear Systems, Properties of Solutions

Week 11

• Oct. 31: Elementary Operations

• Nov. 2: Solution of Linear Systems, Consistency of Linear Systems

Week 12

• Nov. 7: Matrix Algebra

• Nov. 9: Powers, Transposes, Inverses

Week 13

• Nov. 14: Inverses, Linear Dependence and Linear Independence

• Nov. 16: Midterm Test 3

Week 14

• Nov. 21: Determinants

• Nov. 23: Thanksgiving Holiday (no class)

Week 15

• Nov. 28: Eigenvalues, Eigenvectors

• Nov. 30: Systems of Differential Equations

Week 16

• Dec. 5: Solutions of Systems of Difference Equations

Academic integrity and honesty

Students are required to comply with the university policy on academic integrity found in the Code of Student Conduct 11.35.01 sections 8 and 9. Therefore, students are required to uphold the Pack Pledge: “I have neither given nor received unauthorized aid on this test or assignment.” Violations of academic integrity will be handled in accordance with the Student Discipline Procedures.

Please refer to the Academic Integrity web page for a detailed explanation of the University’s policies on academic integrity and some of the common understandings related to those policies.