MATH 462: Mathematical Modeling

Winter 2006

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Professor :
David Gammack
Office: 1855 East Hall
Tel: 734-647-5367
Email: gammackatumich
Web: home

462 Class times :
M/W/Fr
11-12.00pm : DENN 130

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Office Hours Textbook Description Syllabus Objectives Homework Exams Handouts
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Evaluate Me

Office Hours


Office Hours will be held in :
Monday: 2-3pm Math Lab (basement East Hall)
Wednesday: 12-1pm 1855 East Hall
Friday: 10-11am 1855 East Hall
If you can't make office hours, talk to me after class and we can set up an alternate time.

Textbook

There is no set text. I would suggest that the first three are all solid introductions to modeling. Strogatz's book is probably more focussed on the math than the modeling. The final book is the best intro to non-linear differential equations I've read.

Haberman: Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow.
Beltrami: Mathematics for Dynamic Modeling.
Strogatz: Nonlinear Dynamics and Chaos, with Applications to Physics, Biology, Chemistry, and Engineering.
Jordan and Smith: Nonlinear Ordinary Differential Equations

Try for cheap copies.

Course Description


Introductory survey of applied mathematics with emphasis on modeling of physical, mechanical and biological problems in terms of differential equations. Formulation, analysis, and interpretation of the results will be the theme of the course. We will study analysis techniques common in dynamical systems such as linearization theory, Liapunov functions and phase plane.

Syllabus

Download syllabus: this is an approximation!

Objectives of the course

  • Concepts of Modeling
  • Dimensions, Units, Dimensional Analysis
  • Differential equations
  • Formulation of models from basic principles
  • Concepts of equilibria and stability
  • Nonlinearity, limit cycles, bifurcations
  • Chaos
  • Computation with matlab
  • Parameter estimating techniques
  • Interpretation of results

    Learning Objectives and Instructor Expectations
    Although mathematical modeling can be rather difficult, I will present the course material in as simple a manner as possible. More theoretical aspects, such as proofs, will not be presented but I will present in detail the mathematical techniques needed for mathematical modeling. Applications will be emphasized and will come from areas of Physics, Engineering, Medicine, and the Life Sciences. I will try to accommodate any specific needs of students: time and ease of topic permitting.

    Homework

    Follow links in the table below to obtain a copy of the homework in Adobe Acrobat (.pdf) format.

    (Fun)
    Homework
    Homework #1 (.pdf)Sols:(Page1)(Page2)(Page3)
    Homework #2 (.pdf)Sols:(Page1)(Page2)
    Homework #3 (.pdf)Sols:(here)
    Homework #4 (.pdf)Sols:(here)
    Homework #5 (.pdf)Sols:(here)
    Homework #6 (.pdf)
    Homework #7 (.pdf)
    Homework #8
    Homework #9
    Homework #10

    (Fun)
    Homework
    Homework #1 (.pdf)
    Homework #2 (.pdf)



    Group 1
    Darren Galligan
    Mike Kagan
    Bobby Counihan
    Vikas Reddy

    Group 2
    Amy Skrzypchak
    Brad Osinski
    Joe Stack
    Richard Tang

    Group 3
    Jacqui Milton
    Mike
    Kate
    Stephanie Bercaw

    Group 4
    Frantisek Sobolic
    Nicole Smith
    Kate Green
    Effendi Dufford

    Group 5
    Marc Sherman
    Stephanie Royer
    Luay
    Sean

    Group 6
    Roma Moza
    Rohin Moza
    Ming Young
    Natalioe Wowk

    Group 7
    Gillian Todd
    Benin Fitzpatrick
    Adam Konner
    Sunny An

    Group 8
    Kai-Hsiung Tsao
    Yakun Mu
    Chris Marsh
    Alexandra Lecorps

    Meetings

    List of group meeting times Adobe Acrobat (.pdf) format.

    Group
    Meetings
    Thurs 3.00
    Thurs 3.20
    Friday 2.10
    Friday 2.30
    Friday 3.00
    Friday 3.20
    Mon 3.00
    Mon 3.20 Group 5
    Mon 3.40
    Tues 1.15 Group 7
    Tues 1.35
    ??



    Exams


    There will be two midterms, no final.



    Grades


    Homework assignments will count towards ~30% of your grade, the two exams will count for ~30% of the grade. The remaining will come from a project that will be assessed as the semester progresses.

    Handouts

    Get The Paper from this Journal Now
    You need to get Volume 60, Issue 5, called "Continuous and Discrete Math Models of Tumor-induced Angiogenesis".


    DDEshere

    2nd Group HWsuggestions

    2nd mid termExam-like-questions

    March 6Exam-like-questions

    Feb 15Methods

    Mon 6 FebIntro

    Mon 6 FebIntro

    Fri 3 FebIntro

    Fri 3 FebIntro

    Fri 3 FebIntro

    Fri 3 FebIntro

    Fri 3 FebIntro

    Fri 3 FebIntro

    Fri 3 FebIntro

    Matlab ODE2Intro

    Matlab Intro

    Notes 1 here

    Notes 2 here

    Notes 3 here

    Taylor Series here