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Math 450H: Methods of Applied Mathematics I (Capstone I)
Fall 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: Combines mathematical modeling with physical and computational experiments conducted in the Undergraduate Mathematics Computing Laboratory. Effective From: Spring 2009.

Number of Credits: 3

Prerequisites: Math 331 with a grade of C or better, Math 337 with a grade of C or better, and Math 340 with a grade of C or better.

Course-Section and Instructors

Course-Section Instructor
Math 450-H01 Professor L. Kondic

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

Course Materials: There is no mandatory text for this section. The following books and materials are available in the library or will be provided by the instructo4:

  1. Lin and Segel: Mathematics Applied to Deterministic Problems in the Natural Sciences; ISBN: 0898712297
  2. Farlow: Partial Differential Equations for Scientists and Engineers; ISBN 048667620X
  3. D.J. Acheson, Elementary Fluid Dynamics, Oxford Applied Mathematics and Computing Science Series, 1990, ISBN-13: 978-0198596790
  4. K. W. Morton and D. F. Mayers, Numerical Solutions for Partial Differential Equations: An Introduction, Cambridge, 2005, ISBN-13: 978-0521607933j
  5. Selected research articles.

University-wide Withdrawal Date: The last day to withdraw with a W is Monday, November 12, 2018. It will be strictly enforced.

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:

Projects 30%
Quizzes 20%
Midterm Exam 20%
Final Exam 30%

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.

Makeup Exam Policy: To properly report their absence during a midterm or final exam, please review 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, Lower Level, Rm. G11 (See: Fall 2018 Hours)

Further Assistance: For further questions, students should contact their instructor. All instructors have regular office hours during the week. These office hours are listed on the Math Department's webpage for Instructor Office Hours and Emails.

All students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. The Department of Mathematical Sciences takes these policies very seriously and enforces them strictly.

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: Fall 2018 Academic Calendar, Registrar)

Date Day Event
September 4, 2018 T First Day of Classes
September 10, 2018 M Last Day to Add/Drop Classes
November 12, 2018 M Last Day to Withdraw
November 20, 2018 T Thursday Classes Meet
November 21, 2018 W Friday Classes Meet
November 22 - 25, 2018 R - Su Thanksgiving Recess
December 12, 2018 W Last Day of Classes
December 13 & 14, 2018 R & F Reading Days
December 15 - 21, 2018 Sa - F Final Exam Period

Course Outline

Introduction
Modeling in applied mathematics
Problem formulation and non-dimensionalization
Introduction to perturbation theory 
Examples: linear and nonlinear pendulum, projectile problem
Continuum Fields
Introduction to continuum fields with examples: fluid mechanics, elasticity theory
Laplace’s equation and related examples
Application of asymptotic methods to continuum fields
Overview of nonlinear partial differential equations (PDE’s): analytical methods
Overview of nonlinear partial differential equations (PDE’s): numerical methods
Case Study: Asymptotic Methods in Fluid Mechanics
Systematic asymptotic reduction of Navier – Stokes equation using order-of-magnitude estimates and small-parameter expansion
Numerical methods for nonlinear parabolic equations
Stability theory in fluid mechanics
Applications of stability theory: examples involving thin films
Self-similarity in fluid mechanics

Updated by Professor L. Kondic - 8/29/2018
Department of Mathematical Sciences Course Syllabus, Fall 2018