Felsőbb Mathematica
Oktató: Dr. Karsai János, egyetemi docens
Feltétel: bevezető Mathematica kurzus teljesítése (pl. Számítógéppel segített matematikai modellezés)
Óraszám: heti 2 óra számítógépes tanteremben
Értékelés: A hallgatók 3 db komplex projektet készítenek kis csoportokban. Ezek értékelése adja a végső osztályzatot.
Preliminary program:
Summary of basic concepts of the language of Mathematica
Structures, types, Head, Head operations,
Lists in more details, Sequences
Value setting, rules (immediate and delayed),
Patterns, type check in rules and functions
functions vs. expressions; pure form of functions in more details
Piecewise or conditional definition of functions, recursions
Formula manipulations, logic
summary of graphics structures
Elements of dynamic manipulations
List programming
Rule-based programming
Structure operations on lists: Map, Apply, Thread, Fold, ...
Rotating lists, and applications to problems in geometry and numerical algorithms
Operations over functions
Example: Derivative and D
Operations: InverseFunction, Composition, Operate, Through,..
Special function objects: Function, InterpolatingFunction, BooleanFunction, Transformations,....
Iteration, nesting
Recursion vs. iterations
Iterations, fixed points of mappings
Numerical applications: Newton iteration, gradient method, Euler method to solve ODE’s, etc,
Graphics programming structures and operations
Graphics and Graphics3D, GraphicsComplex
How the built-in plots work
Applications of structure and rule-based programming to graphics objects:
Some advanced applications to scientific and engineering visualizations: functions, vector fields and scalar fields
Iterative forms, fractal constructions, Generating trees, Sierpinsky triangles, the midpoint rule
Dynamic manipulations
Dynamic variables, dynamic operations
Control objects, gauges
Developing dynamic demonstrations
Programming paradigms in Mathematica: a systematic overview
Procedural programming
Functional programming
Rule-based programming
Applications to difference systems
Solving, visualizations
cobweb diagram, bifurcation diagram
Special tools in difference calculus
Discretization of ODE’s, PDE's
Advanced applications to differential equations
ODE summary, simple tools to solve and visualize ODE’s
Method of linearization
The phasemap and Ljapunov’s methods: a visual approach
Differential systems with impulse effect
Poincare maps
Elementary data handling, statistics (optional)
Experimental data, plotting data, data transformations
Curve fitting
Parameter fitting of differential equations
The "ModelFit" objects
Additional topics
Notebook design
Advanced notebook operations: options, option inspector
Stylesheet design, automatic numbering, hyperlinks, ...
Export, import: HTML, XML, MathML, TeX
Writing packages
Package design, a general overview
Structure-based functional programming
Using variable names as parameters
Handling options
