Csikja, Rudolf

csikjadeletethis@math.bme.hu

Differenciálegyenletek feladatgyűjtemény [pdf]

Differential Equations with Computer (2019/20/2)

Wednesday, 17:00–18:30
H607

References

  1. S. Wolfram: an Elementary Introduction to the Wolfram Language
  2. M. W. Hirsch, S. Smale, R. L. Devaney: Differential Equations, Dynamical Systems & An Introduction to Chaos
  3. R. E. Maeder: Computer Science with Mathematica (R): Theory and Practice for Science, Mathematics, and Engineering
  4. S. Mangano: Mathematica Cookbook

Downloads

  1. Hands on notes: Introduction
  2. Introduction to Mathematica
  3. Calculus & More
  4. Exercices 1

Curriculum

Introduction
Demonstrating the capabilities of Wolfram Mathematica solving and analysing problems related to simple population dynamics models.
Introduction to Mathematica
Basic syntax and concepts. Numbers and arithmetics. Lists and list operations. Elementary functions. Plotting and graphics primitives.
Higher mathematics
Algebra, trigonometry. Differentiation, integration, infinite sums and finite approximations. Recursion. Solving equations. Linear algebra. Advanved Mathematica programming; rules, patterns, pure functions.
Solutions of differential equations
Parametric curves as solutions of ODEs. Symbolic solutions. Numeric methods and numeric solutions. Numeric solutions with parameters. Events and hybrid differential equations.

Projects

The topic of your project should be fixed no later than 26 March.

Some possible topics
  1. Equilibria in nonlinear systems, Chapter 8 in [2]
  2. Applications in Biology, Chapter 11 in [2]
  3. Applications in Circuit Theory, Chapter 11 in [2]
  4. Applications in Mechanics, Chapter 11 in [2]
  5. Discrete Dynamical Systems, Chapter 15 in [2]
  6. Analysis of nonlinear pendulum by perturbation methods
  7. Neuron models
  8. Sate feedback control
  9. PID control
  10. Optimal control
10 March, 2020