**Math 450H**: Methods of Applied Mathematics I (Capstone I)

*Fall 2017 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 2017 Office Hours and Emails

**Course Materials**: There is no mandatory text for this section. The following books and materials will be used:

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

**Office Hours for All Math Instructors**: Fall 2017 Office Hours and Emails

**University-wide Withdrawal Date**: The last day to withdraw with a **W** is **Monday, November 6, 2017**. 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 Through the Semester** |
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.

**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 2017 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 2017 Academic Calendar, Registrar)

Date |
Day |
Event |

September 5, 2017 |
T |
First Day of Classes |

September 11, 2017 |
M |
Last Day to Add/Drop Classes |

November 6, 2017 |
M |
Last Day to Withdraw |

November 21, 2017 |
T |
Thursday Classes Meet |

November 22, 2017 |
W |
Friday Classes Meet |

November 23 - 26, 2017 |
R - Su |
Thanksgiving Break - University Closed |

December 13, 2017 |
W |
Last Day of Classes |

December 14, 2017 |
R |
Reading Day |

December 15 - 21, 2017 |
F - R |
Final Exam Period |

# Course Outline

**Modeling in fluid mechanics**

Part I: Thin film instabilities in novel geometries;

**Part II: Stochastic modeling of porous media flow**

Introduction |

Introduction to asymptotic methods in applied mathematics. |

Continuum fields and fluid mechanics: An introduction. |

Application of asymptotic methods to fluid mechanics. |

Overview of nonlinear partial differential equations (PDE’s). |

Part I |

**Theoretical Component**:
- Development of PDE-based models for gravity driven thin film flows.
- Linear stability analysis. |

**Computational component**:
- Introduction to scientific computing.
- Overview of finite-difference based methods for solving PDE’s.
- Application of finite-difference methods to the nonlinear PDE’s relevant to thin film flows.
- Simulations of thin film flows in simple geometries. |

**Experimental Component**:
- Setting up of experiments involving gravity driven thin films. |

Part II |

**Theoretical Component**:
- Application of asymptotic methods to fluid mechanics: Darcy’s formulation and porous media flow.
- Introduction to basic PDE-based approaches to flow through membranes and filtering. |

**Computational component**:
- Introduction to stochastic methods.
- Introduction to Monte-Carlo simulations.
- Development of Monte-Carlo type of simulations of membrane flow and filtering. |

*Updated by Professor L. Kondic - 8/29/2017*

*Department of Mathematical Sciences Course Syllabus, Fall 2017*
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