# Math 222: Differential EquationsSummer 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: Methods for solving ordinary differential equations are studied together with physical applications, Laplace transforms, numerical solutions, and series solutions.

Number of Credits: 4

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

Course-Section and Instructors

Course-Section Instructor
Math 222-031 Professor M. Potocki-Dul
Math 222-131 Professor M. Potocki-Dul

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

Required Textbook:

 Title Elementary Differential Equations and Boundary Value Problems Author Boyce and DiPrima Edition 10th Publisher John Wiley & Sons, Inc. ISBN # 978-0470458310

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

• Students should (a) learn elementary analytical solution techniques for the solution of ordinary differential
equations (ODEs), and (b) understand the solution structure of linear ODEs in terms of independent
homogeneous solutions and non-homogeneous solutions.
• Students should (a) understand by exposure to examples how systems and phenomena from science and
engineering can be modeled by ODEs, and (b) how solution of such a model can be used to analyze or predict
a system’s behavior. A key example is the damped, forced, simple harmonic oscillator.
• Students should understand the role of initial value problems for ODEs in examples from science engineering,
and should be introduced to the role of two-point boundary value problems and Fourier series.
• Students should understand an elementary method for the numerical solution of ODEs and have some
familiarity with the solution of ODEs using MATLAB.

### Course Outcomes

• Students have improved problem-solving skills, including knowledge of techniques for the solution of ODEs.
• Students have an understanding of the importance of differential equations in the sciences and engineering.
• Students are prepared for further study in science, technology, engineering, and mathematics.

Course Assessment: The assessment of objectives is achieved through homework assignments and common examinations with common grading.

## 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 15% Common Midterm Exam I 25% Common Midterm Exam II 25% Final Exam 35%

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

 A 88 - 100 C 60 - 66 B+ 81 - 87 D 45 - 59 B 74 - 80 F 0 - 44 C+ 67 - 73

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 common midterm exams held during the semester and one comprehensive common final exam. Exams are held on the following days:

 Common Midterm Exam I June 20, 2018 Common Midterm Exam II July 18, 2018 Final Exam August 6, 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.

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

Section Topic Homework
1.1 Some Basic Math Models; Direction Fields 8,10,17,18,23
1.3 Classification of Differential Equations 1,2,5,8,12
2.2 Separable Equations 2,4,7,9a,15a
2.1  Integrating Factors 2c,5c, 14,17
2.3 Modeling with First Order Equations 1,5(a), 7, 8
2.3 Modeling with First Order Equat. (cont.) 11, 12, 21
MATLAB PROJECT 1  ASSIGNED DUE  Week 6
3.1 Homogeneous Equations  with Constant Coefficients 3,6,8,10,13
3.1 Homogeneous Equations  with Constant Coefficients 17,20,22,24
3.2 Solution of Linear Homogeneous Equations, the Wronskian 2,4,8,12,17
3.2 Solution of Linear Homogeneous Equations, the Wronskian (cont.) 18,24,25,26
3.3 Complex Roots of the Characteristic Equation 3,5, 7,13,19
3.4 Repeated Roots 1,6,8,11,14
3.4 Reduction of Order 23,25,28
3.5 Nonhomog. Eqts., Undetermined Coefficients 3,4,7,14,17
REVIEW FOR EXAM 1
MIDTERM EXAM1
3.5 Nonhomog. Eqts., Undet. Coefficients (cont.) 19(a), 23(a), 26(a)
3.6 Variation of Parameters 1,5,9,11
3.6 Variation of Parameters (cont.) 13,15,19
3.7 Mechanical Vibrations    1,2,5,7,11,
3.7 Mechanical Vibrations (cont.) 12,17,18,24
5.2: Solutions to 2nd Order Linear Equations with Variable Coefficients: Ordinary Points  4(a,b), 6(a,b), 7(a,b)
5.4 Euler’s Equation; Omit SPs 1,3,4,12,17,20
6.1 Definition of the Laplace Transform 3,6,8,13,15
6.2 Solution of Initial Value Problems 1,2,3,7,8
6.2 Solution of Initial Value Problems (cont.) 13,21,24,29,30
6.3 Step Functions 2,15,17,20,21
REVIEW
MIDTERM EXAM 2
6.4 Differential Equations with Discontinuous Forcing Functions 2,3,5,7,9
6.5 Impulse Functions 1,2,5,6,9
6.6 The Convolution Integral 4,6,8,9,14
7.1 Introduction 2, 4, 5
7.3 Review of Linear Algebraic 16 , 17,18, 19
Equations, Eigenvalues, and Eigenvectors (2x2)
7.5 Homogeneous Linear Systems with Constant Coefficients 1(a),4(a),7(a),15,16
7.6 Complex Eigenvalues 2(a),10, 28(a,d)
10.1 Two-Point Boundary Value Problems 1,5,10,14,18
10.2 Fourier Series 1,5,13,15
10.2 Fourier Series (cont.) 16, 22(a,b), 24(a,b)
10.4 Even and Odd Functions 2,4,7,9 15,16
10.4 Even and Odd Functions (cont.) 21,23(a,b),27(a,b)
REVIEW FOR FINAL EXAM
FINAL EXAM

Updated by Professor M. Potocki-Dul - 5/21/2018
Department of Mathematical Sciences Course Syllabus, Summer 2018