Course Syllabus by fjzhangweiyun

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```									Course Syllabus
Course Information
Foundations of Applied Mathematics      MATH 4700             Section 01
RPI Fall 2011               04 cr
MR          2:00PM-3:50PM         RCKTTS 211
Prerequisites or Other Requirements:
MATH 2400 or equivalent.

Instructor
Donald Drew                                      drewd@rpi.edu
Office Location: EATON 306                       (518) 276-6903
Office Hours: M 10:00AM-11:00AM

Teaching Assistant(s)
Name                    Office           Office Hours        Email Address
Sarah Farell            Amos Eaton       T 2-4               farels@rpi.edu
316E

Course Description
Mathematical formulation of models for various processes. Derivation of relevant
differential equations from conservation laws and constitutive relations. Use of
dimensional analysis, scaling, and elementary perturbation methods. Description
of basic wave motion. Examples from areas including biology, elasticity, fluid
dynamics, particle mechanics, chemistry, geophysics, and finance.

Course Text(s)
Text: Introduction to the Foundations of Applied Mathematics by M. H. Holmes

Mathematics Applied to Deterministic Problems in the Natural Sciences by Lin
and Segel

Mathematical models: mechanical vibrations, population dynamics, and traffic
flow: an
introduction to applied mathematics by R. Haberman

Introduction to Perturbation Methods by M. H. Holmes

Syllabus                               1 of 3                              2.5.2013
Course Goals / Objectives
Develop symbol manipulation, mathematical modeling, and proof skills.
Develop a thorough understanding of dimensional analysis and scaling.
Develop an understanding of conservation principles, and be able to derive
equations for conserved quantities.
Develop understanding of the first principles of continuum mechanics and be able
to derive continuum mechanics equations.
Build skills in simplifying and solving algebraic equations, ordinary differential
equations and partial differential equations.

Course Content
Approximate Schedule

Weeks 1, 2 Dimensional Analysis, Scaling
Weeks 3, 4 Regular Perturbations
Weeks 5, 6 Singular Perturbations

Exam 1

Weeks 7, 8 Chemical Kinetics
Weeks 9,10 Diffusion, Random Walks and Brownian Motion

Exam 2

Weeks 11,12 Traffic Flow and Waves
Weeks 13,14 Continuum Mechanics

Final Exam(during Finals Week)

Student Learning Outcomes
1. Develop symbol manipulation, mathematical modeling, and proof skills.
2. Develop a thorough understanding of dimensional analysis and scaling.
3. Develop an understanding of conservation principles, and be able to derive
equations for conserved quantities.
4. Develop understanding of the first principles of continuum mechanics and be
able to derive continuum mechanics equations.
5. Build skills in simplifying and solving algebraic equations, ordinary
differential equations and partial differential equations.

Syllabus                              2 of 3                               2.5.2013
Course Assessment Measures
Assessment                       Due Date            Learning Outcome #s
Homework                         every other week 1, 2, 3, 4, 5
Exam                             two per semester 1, 2, 3, 4, 5
Exam                             Finals week      1, 2, 3, 4, 5

Grading: Homework: 20%, Hour Exams either 40% or 60%, Final Exam
(comprehensive!) either 40% or 20%

Student-teacher relationships are built on trust. For example, students must trust
that teachers have made appropriate decisions about the structure and content of
the courses they teach, and teachers must trust that the assignments that students
turn in are their own. Acts, which violate this trust, undermine the educational
process. The Rensselaer Handbook of Student Rights and Responsibilities define
various forms of Academic Dishonesty and you should make yourself familiar
with these. In this class, all assignments that are turned in for a grade must
represent the student’s own work. In cases where help was received, or teamwork
was allowed, a notation on the assignment should indicate your collaboration. I
encourage you to work in small groups on the homework. However, each student
should turn in a written document that suggests some understanding of the
material, and is not a direct copy of anyone else’s paper. Of course, work on
examinations must be that of the student signing the paper. No cellphones or other
communications devices are allowed during exams. Submission of any
assignment that is in violation of this policy will result in a penalty of zero on the
assignment or exam and an academic integrity report to the Dean of Students.
If you have any question concerning this policy before submitting an assignment,
A one page(two sided) HANDWRITTEN crib sheet will be allowed for each
exam.