Required in stage
Optional in stage
First term
Second term
Both terms
Not organised
This year
Next year
Alternating years
External
Prerequisites
Taught by
Language of instruction
Duration
Identical coursesComputer aided Problem Solving in Physics (B-KUL-G0P36B)
Aims
Upon completion of this course, the student is able to make use of existing numerical and symbolic software (advanced techniques) to solve physics problems that are not analytically solvable. In that respect, the student develops a critical attitude towards the obtained results, and he learns to estimate their reliability without knowing the details about the methods used . To learn what is to be expected of numerical methods, the student has to fathom some basic numerical techniques.
Previous knowledge
The student must understand Dutch and master basic linear algebra and analysis. Ordinary and partial differential equations must be
known as tools to describe mathematical models. Experience with a higher programming language is necessary.
Order of Enrolment
Mixed prerequisite:
You may only take this course if you comply with the prerequisites. Prerequisites can be strict or flexible, or can imply simultaneity. A degree level can be also be a prerequisite.
Explanation:
STRICT: You may only take this course if you have passed or applied tolerance for the courses for which this condition is set.
FLEXIBLE: You may only take this course if you have previously taken the courses for which this condition is set.
SIMULTANEOUS: You may only take this course if you also take the courses for which this condition is set (or have taken them previously).
DEGREE: You may only take this course if you have obtained this degree level.
FLEXIBLE( G0N28A ) AND (FLEXIBLE( G0N84A ) OR SIMULTANEOUS( G0N84B ) OR SIMULTANEOUS ( G0Y42A ) OR FLEXIBLE( I0N19A ) OR FLEXIBLE (I0N19B) )
The codes of the course units mentioned above correspond to the following course descriptions:
G0N28A : Principles of Computer Programming
G0N84A : Differential Equations (No longer offered this academic year)
I0N19A : Differential Equations (No longer offered this academic year)
I0N19B : Differential Equations
G0N84B : Differential Equations
G0Y42A : Differential Equations and Complex Functions (No longer offered this academic year)
Is included in these courses of study
- Bachelor of Physics (Leuven) 180 ects.
- Bachelor of Geography (Leuven) (Minor Subject: Mathematics and Physics) 180 ects.
Activities
2 ects. Computer aided Problem Solving in Physics (B-KUL-G0P36a)
Content
We will focus on the condition of problems, the stability of algorithms and problems typically related to floating point calculations. Vector and matrix norms will be used for estimating errors. Students will learn that approximation methods are necessary for practical problems that cannot always be solved analytically. The approximation of curves (interpolation, least squares approximation) and derivatives are building blocks for a.o. methods for numerically solving ordinary and partial differential equations. In doing so, the numerical solution of a system of linear equations is often needed. Solving non-linear equations and approximating integrals is not only used as part of sophisticated numerical methods, but is often a goal in itself.
Phenomena that can be described as a stochastic process are often simulated with a computer by means of the so-called Monte Carlo methods. The student will be introduced to this through Monte Carlo integration and variants (variant reduction, quasi-Monte Carlo methods). The first steps to the Monte Carlo simulation will be made.
Students will be informed about the wide range of available mathematical software. In this course, however, only Matlab will be used.
Course material
Syllabus "Computergesteund probleemoplossen in de natuurkunde", published by Acco.
1 ects. Computer aided Problem Solving in Physics: Exercises (B-KUL-G0P37a)
Content
See G0P36a
Course material
See G0P36a.
Evaluation
Evaluation: Computer aided Problem Solving in Physics (B-KUL-G2P36b)
Explanation
The exam takes place in a PC classroom and consists of theory and exercises. The student will need to use the software used in the exercise sessions in order to answer a part of the exam question.