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

   Additional References

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

Academic Integrity
  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,
  please ask for clarification.
  A one page(two sided) HANDWRITTEN crib sheet will be allowed for each
  exam.

  Link to homework:

  Foundations of Applied Mathematics_2011.htm




  Syllabus                                3 of 3                                2.5.2013

								
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