Shirokoff, D.

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New Jersey Institute of TechnologyDigital Commons @ NJITMathematical Sciences Syllabi NJIT SyllabiFall 2019MATH 473-001: Intermediate DifferentialEquationsD. ShirokoffFollow 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 CitationShirokoff, D., "MATH 473-001: Intermediate Differential Equations" (2019). Mathematical Sciences Syllabi. 138.https://digitalcommons.njit.edu/math-syllabi/138MATH 473: Intermediate 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: Topics in the qualitative behavior of solutions of ordinary differential equations withapplications to engineering problems. Includes phase plane analysis, stability, dynamical systems, and chaos.Number of Credits: 3Prerequisites: MATH 222 with a grade of C or better and MATH 337 with a grade of C or better.Course-Section and InstructorsCourse-Section InstructorMath 473-001 (also 573) Professor D. ShirokoffOffice Hours for All Math Instructors: Fall 2019 Office Hours and EmailsRequired Textbook:Title Nonlinear Dynamics and Chaos with Applications to Physics,Biology, Chemistry and EngineeringAuthor S. StrogatzEdition 2ndPublisher Westview PressISBN # 978-0813349107RecommendedMaterials Additional papers will be provided by the instructor.Website We will use a Moodle page for Math 473.University-wide Withdrawal Date: The last day to withdraw with a W is Monday, November 11, 2019. It willbe strictly enforced.COURSE GOALSCourse Objective:Geometric analysis and characterization of ODEs via phase plane analysis. Sketching phase planes.Understanding of how (physical) parameters change the qualitative behavior of solutions to ODEs.Some physical understanding of instabilities, and how they arise from bifurcations.Linear stability analysis of nonlinear ODEs. Some understanding of special solutions (limit cycles) and how theyarise from fixed points (Hopf bifurcations).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 Class Participation 35%Midterm Exam 15%Project/ Presentation 20%Final Exam 30%Your final letter grade will be based on the following tentative curve.A 90 - 100 C 70 - 74B+ 85 - 89 D 60 - 69B 80 - 84 F 0 - 59C+ 75 - 79Attendance 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.Exams: There will be one midterm exam held during in class the semester and one final exam. Exams are heldon the following days:Midterm Exam Tuesday, October 22, 2019Final Exam Period December 14 - 20, 2019The 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: There will be NO MAKE-UP QUIZZES OR EXAMS during the semester. In the event anexam is not taken under rare circumstances where the student has a legitimate reason for missing the exam,the student should contact the Dean of Students office and present written verifiable proof of the reason formissing the exam, e.g., a doctor’s note, police report, court notice, etc. clearly stating the date AND time ofthe mitigating problem. The student must also notify the Math Department Office/Instructor that the exam willbe missed.Cellular Phones: All cellular phones and other electronic devices must be switched off during all class times.ADDITIONAL RESOURCESMath Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Fall 2019 Hours)Further Assistance: For further questions, students should contact their instructor. All instructors have regularoffice hours during the week. These office hours are listed on the Math Department's webpage for InstructorOffice Hours and Emails.All students must familiarize themselves with and adhere to the Department of Mathematical Sciences CoursePolicies, in addition to official university-wide policies. The Department of Mathematical Sciences takes thesepolicies very seriously and enforces them strictly.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 F 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 28-29, 2019 R-F Thanksgiving RecessDecember 11, 2019 W Last Day of  ClassesDecember 12, 13  2019  R & F Reading DaysDecember 14-20,  2019 F – R Final Exam PeriodCourse OutlineLecture Topic Assignment1 Introduction, overview, review of analytical and numerical methods of solving ordinarydifferential equations (ODEs)See coursewebsite2 Geometric methods for the qualitative analysis of ODEs. Fixed-points and stability. LinearStability analysis“3 Population growth “4 Bifurcations: saddle-node and transcritical “5 Bifurcations: pitchfork and imperfect “6 Flows on the circle: oscillations “7 Two-dimensional linear systems. “8 Classification of linear systems “9 Phase portraits. Topology of the phase-space “10 Fixed-points and linearization “11 Conservative and reversible systems “12 Limit cycles “13 Poincare-Bendixon theorem “14 Relaxation oscillators: multi-scale systems “15 Weakly nonlinear oscillators “16 Applications from the scientific literature “17 Bifurcations in two-dimensional systems: saddle-node, transcritical and pitchfork “:18 Hopf bifurcations “19 Global bifurcations “20 Quasi periodicity “21 Poincaré maps “22 Introduction to Chaos and strange attractors “23 One-dimensional maps “24 Liapunov exponents “25 Review (will be intercalated in between lectures as necessary)26 Midterm evaluation 27 Student presentations28 Student presentationsUpdated by Professor D. Shirokoff - 8/6/2019Department of Mathematical Sciences Course Syllabus, Fall 2019

MATH 473-001: Intermediate Differential Equations

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MATH 473-001: Intermediate Differential Equations

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