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Advanced mathematical tools for scientists, 7.5 credits

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The course syllabus was confirmed by the Faculty board for graduate studies 21 December 2020. The course is in the third cycle and amounts to 7.5 credits.
The course syllabus is formally approved in Swedish. This is a translation.

Learning outcomes

The aim of the course is to give synoptic knowledge of applied mathematics with focuson advanced problems in natural science and medicine. The course includes advanced use of mathematical software for research-related practical problem solving.

On completion of the course, participants shall be able to:

Knowledge and understanding

• Superficially account for the basics of tenor’s algebra
• Be familiar with calculus of variations
• Superficially account for numerical methods and their use for scientific applications

Skills and abilities

• use common formula manipulations for computing integrals and to solve differential
equations
• Use functions containing complex variables
• Operate with special functions, including Legendre, Chebyshev and Bessel functions
• Use statistical methods to analyse scientific data
• Use use programming languages to make interface to standard mathematical libraries

Judgement and approach

• Master independent planning and use of mathematical software for problem solving
and production of graphs
• Formulate and independently solve application problems using linear algebra in
matrix representation, including eigenvalues problems

Course content

The course is focused on advanced mathematical topics related to the research in the field of natural science. In particular, the course covers linear algebra, partial differentiation equations, special functions, variations, functions of complex variables, tensors, numerical methods, probability and statistics.

Teaching

Lectures: Theory and representative examples.
Exercises: Supervised tutorials with practical calculations and problem solving.
Computer labs: Supervised introduction to and exercises in using mathematical software.

Assessment

Assessment is based on a written exam for theory and written reports for the computer exercises.

Grading scale

Possible grades are Pass and Fail. To pass the course, the participant must pass the written exam and pass the computer exercises.

Language of instruction

The course is given in English.

Entry requirements

To be admitted to the course, general entry requirements should be fulfilled including 90 hp courses in science including MAT015 (Mathematics for scientists 1, 10 hp) or MAT131 (Mathematics 1-alfa, 10 hp) as well as either i) 45 hp finished courses in chemistry including KEM103 (Chemistry, 10 hp) or ii) 90 hp physics including FYS023 (Physics 3, general course, 20 hp). Corresponding prior knowledge, acquired in other ways, will also allow for admittance to the course.

Additional information

The course content corresponds to the second part of the previously given course “Chemist ́s modelling tools”, 15 hp

Course responsible teacher and unit/division

Valera Veryazov
Email: valera.veryazov@compchem.lu.se

Computational Chemistry, KILU

Do you have questions? Please contact FUstudierektor@kilu.lu.se