Numerical Methods

General data

Course ID:	1100-1ENMETNUM3
Erasmus code / ISCED:	11.3 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (unknown)
Course title:	Numerical Methods
Name in Polish:	Metody numeryczne
Organizational unit:	Faculty of Physics
Course groups:
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	(unknown)
Type of course:	obligatory courses
Prerequisites (description):	Learning basic numerical methods used in scientific calculations their pros and cons, as well as acquiring the ability to implement them in computer programs.
Mode:	Self-reading
Short description:	The course will be focused on basic numerical methods used in scientific computer aided computations.
Full description:	Numerical analysis, or numerical methods of solving mathematical problems, is probably as old as mathematics itself. The oldest known algorithms are dated 1800 BC, many more come from ancient Greece, and another group, named by their creators (Newton, Gauss, Euler, Lagrange) suggest outburst in XVIII century. With beginning of era of computers, the numerical methods are the basic methods of problem solving in all practical applications, from physics to social sciences, from engineering to medicine. Regardless of programming language, sophisticated libraries, graphical programs, every person using computer for numerical calculations. should be aware of certain limitations. Some of them come from the mathematical construction of the algorithm itself, but other are deeply bounded to the way the computers are performing floating point calculations. Lack of knowledge in that matter may result in some circumstances in a tragic situations (literally). Program: 1. How computers perform numerical calculations? What problems arises from this? 2. How do we construct algorithms? How to take care of their convergence and stability? 3. How to solve any equation, even such without analytical solution? 4. How to sort a deck of cards? How to fast sort a database of population? 5. How to find what was result of experiment, between known data points? 6. How to calculate differential and integral of any function? 7. Why physicist talk a lot about Monte Carlo? 8. How do the bacteria grow? How the population of rabbits and foxes change? Why it is difficult to restart nuclear reactor? The lecture will be accompanied by classes where students will write programs implementing and testing the algorithms. We will use two optional programming languages: C++ (with gnuplot for data visualization) and Python (with matplotlib). The final grade will depend on test (25%), and notes given by assistants for class activities (75%).
Bibliography:	D. Kincaid, W. Cheney "Numerical analysis" Brooks/Cole 1991 D. Kincaid, W. Cheney "Analiza numeryczna" Wydawnictwa Naukowo-Techniczne 2006 A. Ralston "Wstęp do analizy numerycznej" PWN
Learning outcomes:	After the course the student: 1. Knows basic numerical methods 2. Can implement algorithms in the form of a computer program
Assessment methods and assessment criteria:	The final grade will depend on test (25%), and notes given by assistants for class activities and homework (25%) and two exams taken during classes (25% each).

This course is not currently offered.

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