# Math 322: Differential Equations for ApplicationsSummer 2018 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: An applied science study using differential equations as the vehicle for comprehension of the unknown. Introduction to first-order differential equations and their applications to motion, cooling and electromechanical systems followed by higher order differential equations and their solutions. Study of methods of undetermined coefficients, variation of parameters, and many series and numerical methods. Includes Laplace transforms, matrix methods, and eigenvalue problems.

Number of Credits: 3

Prerequisites: MATH 112 with a grade of C or better or MATH 133 with a grade of C or better or MATH 238 with a grade C or better.

Course-Section and Instructors

Course-Section Instructor
Math 322-141 Professor K. Bosler

Office Hours for All Math Instructors: Summer 2018 Office Hours and Emails

Required Textbook:

 Title Differential Equations with Boundary-Value Problems, 9th + Enhanced WebAssign Author Dennis G. Zill and Warren S. Wright Edition 9th Publisher Pearson ISBN # 978-1337652483 (bound) 978-1337604901 (looseleaf) Notes Laptop Computer

Withdrawal Date: Please see the Summer 2018 Academic Calendar for the last day to withdraw based on the summer session you are registered for.

## Course Goals

### Course Objectives

• Derive solutions of separable and linear first-order differential equations.
• Interpret solutions of differential equation models in mechanics, circuits, &c.
• Derive solutions of linear second order equations or systems that have constant coefficents.
• Apply the Laplace transform to solve forced linear differential equations.
• Determine the behavior of solutions near critical points of planar systems.
• Express the solutions of analytic differential equations in power series.

### Course Outcomes

• Prepare students for further study in technological disciplines and more advanced mathematics courses.
• Students have an understanding of the importance of differential equations in the sciences and engineering.

## 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 15% Quizzes 10% Midterm Exam I 20% Midterm Exam II 20% Final Exam 35%

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

 A 90 - 100 C 70 - 74 B+ 85 - 89 D 60 - 69 B 80 - 84 F 0 - 59 C+ 75 - 79

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 common final exam. Exams are held on the following days:

 Midterm Exam I June 11, 2018 Midterm Exam II June 27, 2018 Final Exam July 16, 2018

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 during all class times.

## Additional Resources

Math Tutoring Center: Located in the Central King Building, Room G11 (Summer Hours: TBA)

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.  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: Summer 2018 Academic Calendar, Registrar)

Date Event
May 21, 2018 First Day of Classes
May 22, 2018 Last Day to Add/Drop Classes
May 28, 2018 University Closed for Memorial Day
June 25, 2018 Last Day of First Summer Session
July 4, 2018 University Closed for Independence Day
July 16, 2018 Last Day of Middle Summer Session
August 6, 2018 Last Day of Full and Second Summer Sessions

# Course Outline

Class Section Title Homework
1 (5/21) 1.1-1.2; 2.1-2.2 Introduction to Differential Equations, Solving Autonomous and Separable Equations  1.1: 22, 23
1.2: 4, 8, 12
2.1: 26
2.2: 8, 11, 27
2 (5/23) 2.3-2.4 First-Order Linear Differential Equations, Exact Equations 2.3: 3, 17, 23, 28, 35
2.4: 5, 10, 22, 27, 33
3 (5/30) 2.5-2.6; 9.1 Bernoulli Equations, Euler’s Methods 2.5: 18, 22, 25
2.6: 7
9.1: 7
4 (6/4) 9.2; 3.1 The Fourth-Order Runge Kutta Method and Applications of First-Order Linear Differential Equations 9.2: 9
3.1: 5, 19, 21, 27
5 (6/6) 3.2; 4.1-4.2 Applications of First-Order Nonlinear Differential Equations, Introduction to Higher-Order Equations 3.2: 2, 11
4.1: 15, 18, 27
4.2: 8
6 (6/11) 4.3 6:00-7:20: EXAM #1 4.3: 12, 22, 28, 32, 40
7:40-9:00: Homogeneous Equations with Constant Coefficients
7 (6/13) 4.4; 4.6 The Method of Undetermined Coefficients and Variation of Parameters 4.4: 5, 12, 20, 31
4.6: 3, 12, 21
8 (6/18) 5.1-5.2 Linear Initial-Value Problems and Linear Boundary-Value Problems 5.1: 6, 27, 37
5.2: 10, 15
9 (6/20) 6.1-6.2 A Review of Power Series and Series Solutions About Ordinary Points 6.1: 5, 12, 19
6.2: 6, 7
10 (6/25) 6.3; 7.1 Series Solutions About Singular Points and The Laplace Transform 6.3: 5, 16
7.1: 11, 20, 29, 37
11 (6/27) 7.2 6:00-7:20: EXAM #2 7.2: 5, 19, 23, 37, 39
7:40-9:00: The Inverse Laplace Transform
12 (7/2) 7.3-7.4; App B Properties of the Laplace Transform and a Crash-Course in Matrix Algebra 7.3: 9, 16, 26
7.4: 6, 10, 19, 26, 36
App. B: 31, 50, 54, 56
13 (7/9) 8.1-8.2 Homogeneous Systems of Linear Differential Equations 8.1: 2, 5, 7, 8, 18
8.2: 1, 8, 14, 29, 43
14 (7/11) 8.3 Non-Homogeneous Systems of Linear Differential Equations 8.3: 3, 7
Review for Final Exam
15 (7/16) N/A FINAL EXAM N/A

Updated by Professor K. Bosler - 5/22/2018
Department of Mathematical Sciences Course Syllabus, Summer 2018