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Resource for modelling with differential equations

  1. Aug 1, 2012 #1
    I'm looking for a good resource about modelling for differential equations. I've completed two courses on ODE's and PDE's, but they both lacked in the applications/modelling department.

    Can anyone recommend a good resource/book on modelling?
     
  2. jcsd
  3. Aug 2, 2012 #2
    A very nice but definitely not trivial book for modeling in biology is
    J.D. Murray – Mathematical Biology
     
  4. Aug 2, 2012 #3
    I've actually heard about that book before, but my interests have to do with engineering - particularly mechanical and materials engineering.
     
  5. Aug 3, 2012 #4
    Often when modeling mechanical systems or materials one ends up with differential algebraic (DAE) or partial differential equations (PDE).

    In case of DAEs the books of Hairer and Wanner contain some mechanical examples. You can find some of the examples at the hompage of Hairer
    http://www.unige.ch/~hairer/software.html.

    Unfortunately, I only model biological systems therefore I cannot really help you. (Nevertheless, I recommend the book from Murray because it is excellent written.)

    For fun, one of the craziest papers about modeling a biological system is from the famous R. Smith:

    WHEN ZOMBIES ATTACK!: MATHEMATICAL
    MODELLING OF AN OUTBREAK OF ZOMBIE
    INFECTION

    http://mysite.science.uottawa.ca/rsmith43/Zombies.pdf

    It is very well written and idependently(!) of the topic you get a very good idea how modeling with differential equations works.
     
  6. Aug 15, 2012 #5
    Modeling using ODEs and PDEs is abundantly necessary in engineering.

    Solid deformation mechanics
    Heat Transfer
    Fluid Mechanics
    Diffusion
    Chemical Reaction engineering
    Thermodynamics
    Transport Phenomena
    Continuum Mechanics
    Quantum mechanics

    Problems in all these areas should be part of the basic engineering curriculum. Modeling comes in when you are applying physical principles to describe the behavior of a physical system. The ODEs and PDEs capture the description of the physical system in terms of the language of mathematics. You then have to solve the equations to understand and predict in advance the behavior of the physical system.
     
  7. Aug 18, 2012 #6
    I use two so-called 'computer algebra systems' and they are quite outstanding. Student, and Home versions are available. One is 'Mathematica' which is a huge 4.5Gbyte system, and the other is Maple - much smaller but very powerful. The only drawback is that they are relatively expensive - but remember you usually get what you pay for - in systems like that.
     
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