### Csikja, Rudolf

csikja

@math.bme.hu Differenciálegyenletek feladatgyűjtemény [pdf]
Wednesday, 17:00–18:30

H607

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

- 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.

Some possible topics

- Equilibria in nonlinear systems, Chapter 8 in [2]
- Applications in Biology, Chapter 11 in [2]
- Applications in Circuit Theory, Chapter 11 in [2]
- Applications in Mechanics, Chapter 11 in [2]
- Discrete Dynamical Systems, Chapter 15 in [2]
- Analysis of nonlinear pendulum by perturbation methods
- Neuron models
- Sate feedback control
- PID control
- Optimal control