Potocki-Dul, M.

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New Jersey Institute of TechnologyDigital Commons @ NJITMathematical Sciences Syllabi NJIT SyllabiFall 2019MATH 222-029: Differential EquationsM. Potocki-DulFollow this and additional works at: https://digitalcommons.njit.edu/math-syllabiThis Syllabus is brought to you for free and open access by the NJIT Syllabi at Digital Commons @ NJIT. It has been accepted for inclusion inMathematical Sciences Syllabi by an authorized administrator of Digital Commons @ NJIT. For more information, please contactdigitalcommons@njit.edu.Recommended CitationPotocki-Dul, M., "MATH 222-029: Differential Equations" (2019). Mathematical Sciences Syllabi. 87.https://digitalcommons.njit.edu/math-syllabi/87MATH 222: Differential EquationsFall 2019 Course SyllabusNJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciencestakes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means thatthere must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or anyform of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are obligatedto report any such activities to the Instructor.COURSE INFORMATIONCourse Description: Methods for solving ordinary differential equations are studied together with physicalapplications, Laplace transforms, numerical solutions, and series solutions.Number of Credits: 4Prerequisites: Prerequisite: MATH 112 with a grade of C or better or MATH 133 with a grade of C or better.Course-Section and InstructorsCourse-Section InstructorMath 222-001 Professor I. CohanoschiMath 222-003 Professor M. MichalMath 222-009 Professor M. MichalMath 222-011 Professor A. BoseMath 222-013 Professor R. GoodmanMath 222-017 Professor J. Ratnaswamy Math 222-023 Professor M. Potocki-DulMath 222-029 Professor M. Potocki-DulMath 222-101 Professor J. RatnaswamyOffice Hours for All Math Instructors: Fall 2019 Office Hours and EmailsRequired Textbook:Title Elementary Differential Equations and BoundaryValue ProblemsAuthor Boyce and DiPrimaEdition 11thPublisher John Wiley & Sons, Inc.ISBN # 978-1119447399Website http://web.njit.edu/~goodman/Math222Additional Information: Some review materials are on the course homepage. Exam solutions, and MATLAB helpare also posted there.University-wide Withdrawal Date:The last day to withdraw with a W is Monday, November 11, 2019. It will bestrictly enforced.COURSE GOALSCourse ObjectivesStudents should (a) learn elementary analytical solution techniques for the solution of ordinary differentialequations (ODEs), (b) understand the solution structure of linear ODEs in terms of independent homogeneoussolutions and non-homogeneous solutions, and (c) interpret the solutions using plots and methods of calculus.Students should (a) understand by exposure to examples how systems and phenomena from science andengineering can be modeled by ODEs, and (b) how solution of such a model can be used to analyze or predict asystem’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 familiaritywith the solution of ODEs using MATLAB.Course OutcomesStudents 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 should be prepared for further study in science, technology, engineering, and mathematics.Course Assessment: The assessment of objectives is achieved through homework assignments and commonexaminations with common grading.POLICIESDMS Course Policies: All DMS students must familiarize themselves with, and adhere to, the Department ofMathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policiesvery seriously and enforces them strictly.Grading Policy: The final grade in this course will be determined as follows:Homework, Quizzes, and MATLAB 10%Common Midterm Exam I 20%Common Midterm Exam II 20%Common Midterm Exam III 20%Final Exam 30%Your final letter grade will be based on the following tentative curve.A 88 - 100 C 60 - 65B+ 83 - 87 D 45 - 59B 75 - 82 F 0 - 44C+ 66 - 74Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read andfully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.Homework and Quiz Policy: Weekly homework assignments are listed on the course outline. They are to behanded in according to your instructor's schedule. Each week, a 15-20 minute quiz will be given on the materialcovered in the previous week’s homework.MATLAB Assignments: There will be two MATLAB assignments. Some helpful material is on the coursehomepage. Math Department MATLAB TAs hold office hours. See here for details.Exams: There will be three common midterm exams held during the semester and one comprehensive commonfinal exam. Exams are held on the following days:Common Midterm Exam I September 25, 2019Common Midterm Exam II October 23, 2019Common Midterm Exam III November 20, 2019Final Exam Period December 14 - 20, 2019The time of the midterm exams is 4:15-5:40 PM for daytime students and 5:45-7:10 PM for evening students.The final exam will test your knowledge of all the course material taught in the entire course. Make sure youread 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 followthe required steps under the DMS Examination Policy found here:http://math.njit.edu/students/policies_exam.phpCellular Phones: All cellular phones and other electronic devices must be switched off and put away during allclass times.ADDITIONAL RESOURCESMath Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Fall 2019 Hours)Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporaryaccommodations 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 ofDisability Support Services at 973-596-5417 or via email at lyles@njit.edu. The office is located in Fenster HallRoom 260. A Letter of Accommodation Eligibility from the Disability Support Services office authorizing youraccommodations will be required.For further information regarding self identification, the submission of medical documentation and additionalsupport services provided please visit the Disability Support Services (DSS) website at:https://www.njit.edu/studentsuccess/accessibility/Important Dates (See: Fall 2019 Academic Calendar, Registrar)Date Day EventSeptember 3, 2019 T First Day of ClassesSeptember 13, 2019 M Last Day to Add/Drop ClassesNovember 11, 2019 M Last Day to WithdrawNovember 26, 2019 T Thursday Classes MeetNovember 27, 2019 W Friday Classes MeetNovember 28 - December 1, 2019 R - Su Thanksgiving RecessDecember 11, 2019 W Last Day of ClassesDecember 12 & 13, 2019 R & F Reading DaysDecember 14 - 20, 2019 Sa - F Final Exam PeriodCourse OutlineWeek +Dates Section # + Topic HW Problem NumbersWEEK 1:09/3- 09/61.1 Some Basic Models; Direction Fields 5, 6, 7, 11, 12, 191.2 Solutions of Some Differential Equations 1, 7 (should say ), 101.3 Classification of Differential Equations 1, 2, 4, 6, 9, 11, 12WEEK 2:09/9- 09/132.1 Linear Equations; Integrating Factors 6(c), 8(c), 10, 11, 13(b,c), 17, 18,21, 23, 24, 252.2 Separable Equations 2, 4, 6, 9, 122.3 Modeling with First Order Equations 2, 5, 7, 12, 14(a)WEEK 3:09/16-09/202.5 Autonomous Differential Equations and PopulationModels2, 4, 6, 8, 10, 112.7 Numerical Approximation; Euler’s Method 2REVIEW FOR EXAM 1WEEK 4:09/23-09/27COMMON EXAM 13.1 Homogeneous Equations with Constant Coefficients 3, 5, 6, 8, 10, 13, 15, 163.2 Solutions of Linear Homogeneous Equations: TheWronskian2, 4, 5, 7, 9, 14, 17, 19, 20, 21,23WEEK 5:9/30- 10/4Matlabassignment#1 due.3.3 Complex Roots of the Characteristic Equation 1, 2, 4, 5, 8, 12, 193.4 Repeated Roots; Reduction of Order 1, 5, 7, 9, 11, 12, 19, 22WEEK 6:10/7- 10/113.5 Nonhomogeneous Equations; UndeterminedCoefficients2, 4, 8, 13, 14, 16(a), 17(a), 21(a)3.6 Variation of Parameters 2, 6, 7, 9, 10, 12, 133.7 Mechanical and Electrical Vibrations 1, 2, 3, 4, 6, 7WEEK 7:10/14-10/183.7 Vibrations (Continued) 9, 11, 12, 133.8 Forced Vibrations 1, 4, 6REVIEW FOR EXAM 2WEEK 8: COMMON EXAM 210/21-10/25 5.1 Review of Power Series 15, 17, 18, 195.2 Series Solutions of Second Order Linear ODEs withNon-constant Coefficients; Solution Near an OrdinaryPoint3(a,b), 5(a,b),6(a,b),7(a,b)WEEK 9:10/28- 11/16.1 Definition of the Laplace Transform 3, 5, 10, 12, 16, 19, 20, 216.2 Solution of Initial Value Problems 1, 2, 3, 4, 6, 10, 16, 17WEEK 10:11/4- 11/86.3 Step Functions 1, 3, 5, 8, 10, 12,14, 156.4 ODEs with Discontinuous Forcing Functions 2, 3, 4, 7, 11, 146.5 Impulse Functions 1, 2, 7WEEK 11:11/11-11/156.6 The Convolution Integral 4, 5, 7, 8, 9, 147.1 System of First Order Linear ODEs 1, 3, 4, 7(a,b)REVIEW FOR EXAM 3WEEK 12:11/18-11/22COMMON EXAM 37.2 Review of Matrices 1, 2, 4, 7, 177.3 Review of Linear Algebraic Equations, Eigenvalues,and Eigenvectors (2x2)14, 15, 167.5 Homogeneous Linear Systems with ConstantCoefficients2b, 3b, 5b, 10, 11WEEK 13:11/25-11/277.6 Complex Eigenvalues 1b, 4b, 8, 11, 14, 2310.1 +supplementTwo-Point Boundary Value Problems + Supplement 1, 3, 5, 10, 14, 15, 18 + problemsfrom supplement10.2 Fourier Series + Supplement 1, 5, 6, 7, 13, 15, 16WEEK 14:12/2- 12/6Matlabassignment#2 due.10.2 Fourier Series (Continued) 19(a,b), 20(a,b), 22(a,b)10.4 +supplementEven and Odd Functions 2, 3, 4, 7, 9, 15, 16, 21, 23(a,b),27(a,b) + problems fromsupplementREVIEW FOR FINAL EXAM WEEK 15:12/9- 12/11REVIEW FOR FINAL EXAM FINAL EXAM PERIOD: DECEMBER 14 - 20, 2019Updated by Professor R. Goodman- August 30, 2019Department of Mathematical Sciences Course Syllabus, Fall 2019

MATH 222-029: Differential Equations

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MATH 222-029: Differential Equations

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