# Math 337-H02: Linear Algebra - HonorsSpring 2019 Course Syllabus

NJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.

## Course Information

Course Description: Topics enhance those of Math 337 and concepts are studied in detail. Matrices, determinants, systems of linear equations, vector spaces, linear transformations, eigenvalues, eigenvectors, and related topics.

Number of Credits: 3

Prerequisites: Math 112H with a grade of B or better or Math 112 with a grade of A.

Course-Section and Instructors

Course-Section Instructor
Math 337-H02 Professor J. Bechtold

Office Hours for All Math Instructors: Spring 2019 Office Hours and Emails

Required Textbook:

 Title Linear Algebra and its Applications Author Lay Edition 5th Publisher Pearson ISBN # 978-0321982384

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, April 8, 2019. It will be strictly enforced.

## Course Goals

### Course Objectives

• Learn about matrices, determinants, applications to solving linear system of equations, matrix factorization, eigenvalues and eigenvectors, Gram-Schmidt process.
• Cover relevant applications in economics, science and engineering to illustrate the utility of learning these topics.
• Use mathematical software, in problem solving, to allow the solution of more complex problems and provide visualization of the same.

### Course Outcomes

• Prepare students for further study in theoretical courses such as differential and difference equations and least squares analyses.
• To enable students to use linear algebra use for numerical solvability of many problems.
• Students are prepared for applying linear algebra to many practical applications in fields like economics, computer science, physics, engineering, archeology, demography, relativity, etc.

## Policies

DMS Course Policies: All DMS students must familiarize themselves with, and adhere to, the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly.

Grading Policy: The final grade in this course will be determined as follows:

 Homework and Quizzes 22% Common Midterm Exam I 22% Common Midterm Exam II 22% Final Exam 34%

Your final letter grade will be based on the following tentative curve.

 A 85 - 100 C 65 - 69 B+ 80 - 84 D 60 - 64 B 75 - 79 F 0 - 59 C+ 70 - 74

Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.

Exams: There will be two midterm exams held during the semester and one comprehensive final exam. Note: Honors Midterm Exams will be held during normal class hours the Thursday after Non-Honors Common Exams. The Non-Honors Common Exam schedule is as follows:

 Common Midterm Exam I February 27, 2019 Common Midterm Exam II April 17, 2019 Final Exam Period May 10 - 16, 2019

The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.

Makeup Exam Policy: To properly report your absence from a midterm or final exam, please review and follow the required steps under the DMS Examination Policy found here:

Cellular Phones: All cellular phones and other electronic devices must be switched off and put away during all class times.

Math Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Spring 2019 Hours)

Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.

If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at lyles@njit.edu. The office is located in Fenster Hall Room 260. A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.

For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:

Important Dates (See: Spring 2019 Academic Calendar, Registrar)

Date Day Event
January 22, 2019 T First Day of Classes
February 1, 2019 F Last Day to Add/Drop Classes
March 17 - 24, 2019 Su - Su Spring Recess - No Classes, NJIT Open
April 8, 2019 M Last Day to Withdraw
April 19, 2019 F Good Friday - No Classes, NJIT Closed
May 7, 2019 T Friday Classes Meet/ Last Day of Classes
May 8 & 9, 2019 W & R Reading Days
May 10 - 16, 2019 F - R Final Exam Period

# Course Outline

*Application Sections in Red

Week Subjects Section and Recommended Exercises
1 Systems of Linear Equations 1.1: 2, 4, 10, 15, 18, 24, 29
Row Reduction and Echelon Form 1.2: 2, 4, 8, 11, 13, 18, 20
Vector equations 1.3: 2, 5, 9, 11, 13, 17, 24
2 Matrix Equations 1.4: 2,4,5,9,17
Solutions of Linear Systems 1.5: 1,4,6,8,11,15,23
3 Application to Chemistry (brief) 1.6: 7,9
Linear Independence 1.7: 1,4,6,7,14,16,31
Linear Transformations 1.8: 2,4,7,9,13,15
4 Matrix form of Linear Transformations 1.9: 5,7,10,15,18,22
Matrix Operations 2.1: 4,7,9,16,23
Inverse of a Matrix 2.2: 3,6,9,26,29,32
5 Invertible Matrices 2.3: 2,6,9,11,13,14,41
LU Factorization 2.5: 2,4,5,8,11,15,17
6 Exam Review
Common Midterm #1 Wednesday - FEBRUARY 27, 2019
Application to Computer Graphics (brief) 2.7: 1,2,5
Introduction to Determinants 3.1: 3,8,9,12,22,24,25,28
7 Properties of Determinants 3.2: 1,4,6,9,21,22,25,26
Cramer's Rule 3.3: 2,5,8,11,16
Vector Spaces and Subspaces 4.1: 8,24,30,38
8 Null Spaces and Columns Spaces 4.2: 2,4,14,20,24
Linear Maps 4.3: 4,5,10,14,15,21
Dimension of a Vector space 4.5: 2,4,6,9,13,15,18
9 Rank 4.6: 1,2,5,9,13,17,18
Application to Markov Chains (Brief) 4.9: 2,4,6, 8,10
10 Eigenvalues and Eigenvectors 5.1: 3,7,9,13,15,17,20
The Characteristic Equation 5.2: 4,7,9,13,15,16,20,21
11 Exam Review
Common Midterm #2 Wednesday - APRIL 17, 2019
Diagonalization 5.3: 2,4,6,7,8,12,17,21
Complex Eigenvalues 5.5: 4,5,13,14
12 Inner Product, Length, and Orthogonality 6.1: 1,8,10,12,14,15,16,20
Orthogonal Sets 6.2: 1,4,8,12,16,1720,23
Orthogonal Projections 6.3: 2,4,6,8,10,12,14,16
13 The Gram-Schmidt Procedure 6.4: 1,4,8,9,12
Inner Product Spaces 6.7: 1,2,4,6,8
Diagonalization of Symmetric Matrices 7.1: 1-10,14,17,22,26
Exam Review

# MATLAB Projects for M337: Linear Algebra, Spring 2019

Visit the textbook website for supplementary materials including a guide to getting started with Matlab. For additional help, the math department has Matlab TA’s. Click for locations and times when they are available.

The first thing you need to do is to install the LayData toolbox on the computer where you will be using it. Here are the steps. I will assume that you have Matlab installed or are using Matlab on a campus PC.

Lower Triangular Matrices March 11, 2019 Problem (1c) and (2b) ask you to prove a result about lower triangular matrices. If you have trouble doing this in general, try it first with $$2\times2$$ lower triangular matrices, then $$3\times3$$ until you see the pattern. For general Matrices, try using the $$\Sigma$$ notation for the $$(i,j)$$ entry of a matrix product.