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.
Math 613-001: Advanced Applied Mathematics I: Modeling
FALL 2010
Textbook: Mathematics Applied to Deterministic Problems in the Natural Sciences, by Lin and Segel; ISBN: 0-89871-229-7.
Additional References:
▪ Mathematics Applied to Continuum Mechanics, by Segel; ISBN: 0-486-65369-2.
▪ An Introduction to Partial Differential Equations, by J. D. Logan, Wiley 1994; ISBN 0-471-59916-6.
Course Description: This course focuses on utilizing techniques to develop concepts and strategies of mathematical modeling by investigation of case studies in a selection of areas. Consistency of a model, nondimensionalization and scaling, regular and singular effects are discussed. Possible topics include vibrating strings, continuum mechanics (heat and mass transfer, fluid dynamics, elasticity), population dynamics, traffic flow, and the Sommerfeld problem.
Prerequisites: Math 331 and Math 337, or departmental approval.
Grading Policy: The final grade in this course will be determined as follows:
▪ Homework: |
33% |
▪ Midterm Examination: |
33% |
▪ Final Examination: |
34% |
Drop Date: Please note that the University Drop Date November 1, 2010 deadline will be strictly enforced.
Homework Policy: Homework assignments will be handed out roughly every two weeks. Late assignments will not be accepted. As a substantial portion of your grade rests on your ability to do these problems, you are advised to start them EARLY and to come to office hours if you have questions.
Makeup Exam Policy: There will be No make-up EXAMS during the semester. In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate reason for missing the final exam, a makeup exam will be administered by the math department. In any case the student must notify the Math Department Office and the Instructor that the exam will be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note, police report, court notice, etc., clearly stating the date AND time of the mitigating problem.
Further Assistance: For further questions, students should contact their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.
Cellular Phones: All cellular phones and beepers must be switched off during all class times.
MATH DEPARTMENT CLASS POLICIES LINK
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. For DMS Course Policies, please click here.
M |
Labor Day Holiday ~ University Closed |
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M |
Last Day to Withdraw from this course |
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R-Su |
Thanksgiving Recess ~ University Closed |
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T |
Classes follow a Thursday Schedule |
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December 8, 2010 |
W |
Classes follow a Friday Schedule |
Course Outline:
Week |
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Course Topics |
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Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Week 12
Week 13
Week 14
Week 15 |
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I. |
Introduction to Applied Mathematics Units and Scales The Simple Pendulum The Projectile Problem |
II. |
Simple examples from mechanics |
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III. |
Two body problem Kepler’s Laws Orbits of planets | ||
IV. |
Poincare’s perturbation theory |
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V. |
Conservation Laws General Balance Law Flux Density | ||
VI. |
Traffic Flow Continuum Model Method of Characteristics |
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VII. |
Diffusion Equation Heat and Mass Flow Random Walk. Difference Equation and its limit | ||
VIII. |
Constitutive Relations |
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IX. |
Elementary Linear Stability Theory | ||
X. |
Wave Phenomena Derivation of 1D wave equation |
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XI. |
Travelling Wave Solutions Burgers Equation, kdv | ||
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Finals |
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Final EXAM WEEK: December 10-16, 2010 |
Prepared By: Prof. John Bechtold
Last revised: July 15, 2010