Jaquette, Jonathan

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New Jersey Institute of Technology Digital Commons @ NJIT Mathematical Sciences Syllabi NJIT Syllabi Fall 2023 MATH 613-001, Fall 2023: Advanced Applied Mathematics I, Fall 2023: Modeling Jonathan Jaquette Follow this and additional works at: https://digitalcommons.njit.edu/math-syllabi Recommended Citation Jaquette, Jonathan, "MATH 613-001, Fall 2023: Advanced Applied Mathematics I, Fall 2023: Modeling" (2023). Mathematical Sciences Syllabi. 226. https://digitalcommons.njit.edu/math-syllabi/226 This Syllabus is brought to you for free and open access by the NJIT Syllabi at Digital Commons @ NJIT. It has been accepted for inclusion in Mathematical Sciences Syllabi by an authorized administrator of Digital Commons @ NJIT. For more information, please contact digitalcommons@njit.edu. MATH 613: Advanced Applied Mathematics I: ModelingFall 2023 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, orany form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students areobligated to report any such activities to the Instructor.Please note that it is my professional obligation and responsibility to report any academic misconduct to theDean of Students Office. Any student found in violation of the code by cheating, plagiarizing or using any onlinesoftware inappropriately will result in disciplinary action. This may include a failing grade of F, and/orsuspension or dismissal from the university. If you have any questions about the code of Academic Integrity,please contact the Dean of Students Office at dos@njit.edu.COURSE INFORMATIONCourse Description: Concepts and strategies of mathematical modeling are developed by investigation ofcase studies in a selection of areas. Consistency of a model, nondimensionalization and scaling, regular andsingular effects are discussed. Possible topics include continuum mechanics (heat and mass transfer, fluiddynamics, elasticity), waves, kinetics, population dynamics, traffic flow, and the Sommerfeld problem.Number of Credits: 3Prerequisites: MATH 331 and MATH 337, or departmental approval.Course-Section and Instructors:Course-Section InstructorMath 613-001 Professor J. JaquetteOffice Hours for All Math Instructors: Fall 2023 Office Hours and EmailsRequired Textbook:Title Introduction to the Foundations of AppliedMathematicsAuthor Mark HolmesEdition 2ndPublisher Springer1ISBN # 97830302426029783030242619University-wide Withdrawal Date: The last day to withdraw with a W is Monday, November 13, 2023. It willbe strictly enforced.COURSE CONTENT & OBJECTIVESConcepts and strategies of mathematical modeling are developed by investigation of case studies in aselection of areas. Consistency of a model, nondimensionalization and scaling, regular and singular effects arediscussed. Possible topics include continuum mechanics (heat and mass transfer, fluid dynamics, elasticity),vibrating strings, population dynamics, traffic flow, and the Sommerfeld problem.By the end of the course, students will be able to:● Solve quantitative problems in applied math.● Critically read graduate textbooks, summarize the major points, and discuss the finer details.● prepare and deliver 15 minute presentations on applied mathematics and modeling.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:Presentations (8) and Participation (2) 10%Homework 25%Midterm Exam 30%Final Exam 35%Your final letter grade will be based on the following tentative curve.A 84 - 100 C+ 60 - 69B+ 77 - 83 D 50 - 59B 70 - 76 F 0 - 49Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you readand fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.Working in Groups: I highly recommend finding a friend or two in this class and studying together! It makesdoing homework more enjoyable (or less miserable?), and helps you learn difficult material. Even if you thinkyou know everything, explaining concepts to someone else will help you master the material.That said, the homework you turn in must be your own. Don’t just copy someone else’s work -- be it someoneelse in the class or someone online. If you get a significant idea or assistance from a classmate or an outside2source, BE SURE to reference them. Citing your sources is one of the best way to avoid representing other’swork as your own. While group work is great for preparing presentations and doing homework, the work you doon the midterm/final exams should be all your own.Seminar Format: This course is a seminar and, unlike a traditional course, almost all of the talking in ourmeetings is done by the students. The main work of the seminar meeting will be presentations on selectedtopics, discussion of the readings and presentations, discussion of student generated questions, andpresentation and discussion of homework problems. I'd like the seminar atmosphere to be lively but notintimidating. The goal of the group should be to push everyone's understanding. If something isn't clear, weneed to stop and clarify.In this format, the seminar members will be expected to have mastered all the basic background materialbefore seminar, and the seminar meeting will be devoted to reinforcing, extending and enhancing yourknowledge of the seminar topics. Students presenting material in any given week must thoroughly prepare thosepresentations in advance. Students not presenting material should still study all of the material to be presentedin advance so that they may ask good questions and participate fully in the discussions. If you are unable toattend class for any reason, please contact me as soon as possible.Meeting Organization: Below is an example agenda for one week’s seminar:Monday Class:• Brief summary of the week’s reading (5 min)• Student presentations (40-60 min)• Discussion of students’ prepared questions on the reading (15-30 min)Thursday Class:• Plan which problems to discuss (5 min)• Discussion of homework problems (65 min)• Closing, and planning for the next week (5-10 min)Reading Questions: Each week there will be about 25 pages from the book that everyone should read byMonday.By Monday morning (before noon!), each student must email me a list of at least 3 questions they had from thereading. My suggestion would be to compile your list of questions as you are reading the week’s material.In class on Monday we will go around the room. Each person will pose one of their questions and the group willdiscuss. If there is time remaining we will discuss any further questions/topics the group finds to be of interest.Presentations: Many seminars will include short presentations prepared by students. I'll ask for volunteers forpresentations the week before. Presentations may include discussing a section from our text or another book,readings from journals, or examples relating to the week’s reading.Each presentation should be 10-15 minutes and leave 5 minutes for questions. You should not go overtime; I willset a timer. Each student is expected to present at least once before the midterm, and once after the midterm.In weeks that you are giving a presentation, you are REQUIRED to talk to me in office hours before hand todiscuss your talk outline/ask questions about the material/etc.Homework Problems: Each week there will be homework problems to accompany the reading. You are stronglyencouraged to work together on problems.At the beginning of each Thursday seminar we'll decide who will lead the discussion on which homeworkproblems. You'll let me know the problems you feel most comfortable with and I'll respect your preferences.3Difficult problems we can all work on together.A writeup of the week’s homework problems will be due Friday morning, late work will be penalized. Timemanagement is key! Your write up should be mostly be complete by class on Thursday.Exams: There will be one midterm exam held in class during the semester and one comprehensive final exam.Exams are held on the following days:Midterm Exam October 26, 2023Final Exam Period December 17 - December 23, 2023The final exam will test your knowledge of all the course material taught in the entire course. Make sureyou read and fully understand the Math Department's Examination Policy. This policy will be strictlyenforced.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 during all class times.ADDITIONAL RESOURCESFurther 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.Accommodation of Disabilities: The Office of Accessibility Resources and Services (OARS) offers long term andtemporary accommodations for undergraduate, graduate and visiting students at NJIT.If you need an accommodation due to a disability, please contact the Office of Accessibility Resources andServices at oars@njit.edu, or visit Kupfrian Hall 201 to discuss your specific needs. A Letter of AccommodationEligibility from the office authorizing student accommodations is required.For further information regarding self identification, the submission of medical documentation andadditional support services provided please visit the Office of Accessibility Resources and Services (OARS)website at:https://www.njit.edu/accessibility/Important Dates (See: Fall 2023 Academic Calendar, Registrar)Date Day EventSeptember 4, 2023 Monday Labor DaySeptember 5, 2023 Tuesday First Day of ClassesSeptember 11, 2023 Monday Last Day to Add/Drop ClassesNovember 13, 2023 Monday Last Day to Withdraw4November 21, 2023 Tuesday Thursday Classes MeetNovember 22, 2023 Wednesday Friday Classes MeetNovember 23 toNovember 26, 2023Thursday andSaturdayThanksgiving Recess - ClosedDecember 13, 2023 Wednesday Last Day of ClassesDecember 14, 2023 Thursday Reading Day 1December 15, 2023 Friday Reading Day 2December 17 toDecember 23, 2023Sunday to Saturday Final Exam PeriodCourse Outline(This is a tentative schedule of material)Week Mon Thurs Topic Reading1 --- 9/7 Introduction & Dimensional Analysis Ch 12 9/11 9/14 Dimensional Analysis Ch 13 9/18 9/21 Perturbation Methods Ch 24 9/25 9/28 Kinetics Ch 35 10/2 10/5 Kinetics Ch 36 10/9 10/12 Diffusion Ch 47 10/16 10/19 Diffusion Ch 48 10/23 10/26 Diffusion / Midterm Ch 49 10/30 11/2 Traffic Flow Ch 510 11/6 11/9 Traffic Flow Ch 511 11/13 11/16 Continuum Mechanics, 1d Ch 612 11/20 11/21 Elastic Materials Ch 713 11/27 11/30 Continuum Mechanics, 3d Ch 814 12/4 12/7 Fluids Ch 915 12/11 --- Review ---Updated by Professor J. Jaquette - 9/6/2023Department of Mathematical Sciences Course Syllabus, Fall 20235

MATH 613-001, Fall 2023: Advanced Applied Mathematics I, Fall 2023: Modeling

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MATH 613-001, Fall 2023: Advanced Applied Mathematics I, Fall 2023: Modeling

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