Math 451-H04: Methods of Applied Mathematics II (Capstone II)
Spring 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: Small teams of students conduct research projects under the guidance of faculty members who perform applied research. Effective From: Spring 2009.
Number of Credits: 3
Prerequisites: Math 450H with a grade of C or better.
Course-Section and Instructors
| Course-Section |
Instructor |
| Math 451-H04 |
Professor L. Kondic |
Office Hours for All Math Instructors: Spring 2018 Office Hours and Emails
Course Materials:
- M. Wessling, Two dimensional stochastic modeling of membrane fouling, Separation and Purification Technology, 24, 375 (2001).
- I. Griffiths, A. Kumar, P. Stewart Designing asymmetric multilayered membrane filters with improved performance, J. Membrane Science, 511, 108 (2016).
- U. Beuscher, Modeling Sieving Filtration using Multiple Layers of Parallel Pores, Chem. Eng. Technology, 33, 1377 (2010);
- Sanaei, P., Richardson, G.W., Witelski, T. Cummings, L.J., Flow and fouling in a pleated membrane filter, J. Fluid Mech. 795, 36 (2016).
- Sanaei, P., Cummings, L.J., Flow and fouling in membrane filters: Effects of membrane morphology, J. Fluid Mech. 818, 744 (2017).
University-wide Withdrawal Date: The last day to withdraw with a W is Monday, April 2, 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 and Presentations |
70% |
| Final Report and Presentation |
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.
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: Spring 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: Spring 2018 Academic Calendar, Registrar)
| Date |
Day |
Event |
| January 16, 2018 |
T |
First Day of Classes |
| January 22, 2018 |
M |
Last Day to Add/Drop Classes |
| March 11 - 18, 2018 |
Su - Su |
Spring Recess - No Classes/ University Closed |
| March 30, 2018 |
F |
Good Friday - No Classes/ University Closed |
| April 2, 2018 |
M |
Last Day to Withdraw |
| May 1, 2018 |
T |
Friday Classes Meet - Last Day of Classes |
| May 2 - 3, 2018 |
W - R |
Reading Days |
| May 4 - 10, 2018 |
F - R |
Final Exam Period |
Course Outline
Deterministic and Stochastic Modeling of Porous Media Flow
Project 1: Stochastic Modeling of Membrane Fouling
- Develop further Monte-Carlo based simulation of fouling of membrane pores.
- Explore the influence of pore geometry on fouling.
- Employ appropriate statistical coarse-grained approaches to compare the results of Monte-Carlo simulations to existing continuum results.
Project 2: Modeling Multilayered Filtering
- Use the electrical circuit analogy to further develop models for multilayered filtering
- Compare the results to the existing ones found in literature and discuss possible improvements.
Project 3: Modeling Filtration Using Parallel Pores
- Develop further random fouling model, including development of appropriate statistical methods for results interpretation.
- Discuss how the results compare with the existing ones and possible improvements.
Project 4: Modeling Filtration
- Work towards development of extensions of the existing branching model.
- Discuss how branching and connectivity of the pores influences filter performance.
Note: Each project includes development of the web page on which the main results will be presented, and the developed software linked, as appropriate.
Updated by Professor L. Kondic - 1/13/2018
Department of Mathematical Sciences Course Syllabus, Spring 2018
