Mathematical Modelling in Engineering

Course Description

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Forms of Teaching

Lectures

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Independent assignments

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Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Homeworks 0 % 40 % 0 % 0 %
Class participation 0 % 10 % 0 % 0 %
Seminar/Project 0 % 40 % 0 % 40 %
Mid Term Exam: Written 0 % 30 % 0 %
Final Exam: Written 0 % 30 %
Final Exam: Oral 10 %
Exam: Written 0 % 60 %
Exam: Oral 40 %
Comment:

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Week by Week Schedule

  1. Introduction to mathematical modelling. Dimensional analysis. Released energy in the Trinity test.
  2. Perturbation theory. Method of dominant balance.
  3. Systems of ordinary differential equations, state space, equilibrium points and linearisation.
  4. Epidemic modelling. SIR model.
  5. Herd immunity. Advanced epidemic models.
  6. Predator-Prey and Lotka-Volterra model.
  7. Hodgkin – Huxley and FitzHugh – Nagumo model.
  8. Midterm
  9. Einstein's explanation of Brown's motion. Fokker-Planck equation.
  10. Continuum modelling. Fields and potentials. Gaussian Law.
  11. Conservation Law. Heat propagation.
  12. Separation of variables and stationary solutions.
  13. Self-similar solutions. Fundamental solution and superposition principle.
  14. Reaction-diffusion equation.
  15. Final Exam

Study Programmes

University undergraduate
Free Elective Courses (5. semester)
Free Elective Courses (5. semester)

Literature

David J. Wollkind, Bonni J. Dichone (2018.), Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences, Springer
David F. Parker (2012.), Fields, Flows and Waves, Springer Science & Business Media

For students

General

ID 227564
  Winter semester
5 ECTS
L0 English Level
L1 e-Learning
45 Lectures
0 Seminar
0 Exercises
0 Laboratory exercises
0 Project laboratory

Grading System

85 Excellent
75 Very Good
60 Good
50 Acceptable