TMA4195 Mathematical Modelling - Fall 2014

Continuation Exam / kontinuasjonseksamen August 2015:

• Type: Oral exam.
• Date: Thursday August 13, 2015.
• Room: 734 SB 2 (same floor as department office)
• Office hours: None.
• To take this exam you must:
  1. have failed or missed the exam in December 2014
  2. register in StudWeb
  3. send me an email to get a time-slot – at least one week in advance
• Exam schedule Thursday August 13, 2015:

• 10.06.2015: Continuation Exam August 2015 - Thursday August 13, 2015. See above.

• 19.12.
• Comments on the exam:
  • The overall impression is that it was easy to collect points, but difficult to collect all the points in each problem.
  • Almost no one failed, but almost everyone lost some points on many problems.
  • Mistakes that many or even most students made:
    • Problem 1: Did not mention Buckinham's Pi theorem.
    • Problem 2: Just stated the boundary layer scale without discussion or checking whether it was consistent or not.
    • Problem 3: Did not state the bifucation points.
    • Problem 5: Only one student could derive correctly the ODEs from the law of mass action etc. (see solutions).
    • Problem 6a: Did not argue why integral=0 implies integrand=0 (see solutions).
    • Problem 6b: Did not mention that scaled variables and their derivatives are order 1.
    • Problem 6c: No one got more than half score here. If you did not follow my hint, it was easy to choose a wrong approach, more so than I expected beforehand.
      • Attempt 1: Derivation from (2): This is incorrect.
        • Problem: This leads to an incorrect equation. This equation coincides with the correct equation only if h_xx=0, which again would follow if you could assume also that the Laplace equation holds. In the latter case, all solutions are linear and not very relevant. All the relevant solutions have been lost. To find the relevant solutions you can not assume that the Laplace equation holds. Another approach is needed, one that allows for h_xx different from 0.
      • Attempt 2: Derivation using control volume where upper boundary is z=h(x,t). Difficult, but could work.
        • Problem: The domain is not fixed and it is not a material region. You would need some generalization of Reynold (that you likely do not know…) for the derivation to be correct. Many students make mistakes two times, mistakes that cancel out in such a way that the final answer is correct… but not the derivation.
      • Solution: 1D model suggested in the hint, see the solutions (only one student really tried this).

• 15.12.
  • Exam problems and solutions
    • This year's exam problems and solutions can be found here and here.
  • Project comments and grades
    • See 'Modling project' in the left menu.
  • God jul/Merry Christmas to all of you!

• 25.11.
  • Reference group meeting 25.11.
    • See 'Reference group' in the left menu for a short summary.
  • Final curriculum
    • See 'Curriculum' under 'General information' in the left menu.
  • Exam language:
    • English only (lectures and all written material has been in English).
      You may answer in English or Norwegian as you like.
  • Slides:
    • All slides of 2014 can be found here.
  • Last week of teaching: (Week 47)
    • we looked at previous relevant exam problems,
      • Exam 2009: Problem 3; Exam 2010: Problem 1,2,3; Exam 2013: Problem 5.
  • Office hours:

• 14.10.
  • Boundary value problems for conservation laws
    • Not covered by compendium.
    • Seperate note on Boundary value problems for conservation laws, see Notes in the left menu.
• 15.09.
  • Week 39:
    • Self-study of population models
      • Read chapter on Dynamic Population Models in compendium.
      • Extra homework problems in Exercise 6.
      • Relevant for the exam …

• Læringsmål/learning outcome: see here.
• First lecture: Tuesday, August 19.
• First problem session: Monday August 25

• Questions? Check the extensive course web pages first (see left menu).

Solving exercises is an integral part of this course! Make sure that you do the homework problems.

• Problem sets will be available Wednesdays before the problem session - or earlier.
• Solutions will be available Fridays after problem session.

Other homework:

• 2.9.: Read slides on kidney modeling
• 2.9.: Repeat if necessary: solutions of linear 1st and 2nd order ODEs, homogeneous and inhomogeneous equations.
• 9.9.: Read if necessay about linear ODEs, critical points and stability (Kreyszig (9th or 10th ed.) chp. 4.3-4.5).
• 15.9.: Read slides on quencing reaction (see 'Notes' in left menu).
• 18.9.: Read slides on equilibrium points, stability, and aggregation of amoebae (see 'Notes' in left menu)
• 7.10.: Read yourselves Krogstad section 3.2.
• 14.10.: Review the solution of the heat equation using Fourier transform
  • e.g. Kreyszig Advanced Engineering Mathematics 9th ed. sec. 12.6