## C1472 Applied mathematics for biochemists - seminar

Faculty of Science
Spring 2020
Extent and Intensity
0/1/0. 1 credit(s) (plus extra credits for completion). Type of Completion: z (credit).
Teacher(s)
prof. RNDr. Jaroslav Koča, DrSc. (lecturer)
RNDr. Tomáš Raček (lecturer)
doc. RNDr. Radka Svobodová, Ph.D. (lecturer)
Mgr. Zdeněk Kříž, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jaroslav Koča, DrSc.
National Centre for Biomolecular Research - Faculty of Science
Supplier department: National Centre for Biomolecular Research - Faculty of Science
Prerequisites (in Czech)
NOW ( C1471 Applied mathematics for biochemists )
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of this course is to introduce the methods and approaches for solving the most common computational problems in chemistry, biochemistry and, more generally, in life sciences.
Learning outcomes
At the end of the course student will be able to describe and apply basic numerical methods on life science problems as well as evaluate their limits on particular examples.
Syllabus
• 1. Problems of floating point representation of real numbers.
• 2. Solution to linear systems (GEM drawbacks, LU decomposition, least squares method).
• 3. Vector algebra. Transformation of coordinates. Molecular modelling applications.
• 4. Dimensionality reduction and visualization of multidimensional data. Cluster analysis.
• 5. Random numbers a their generation. Monte Carlo methods.
• 6. Functions of two variables. Local extremes.
• 7. Numerical differentiation and integration.
• 8. Integration of functions of two variables, applications.
• 9. Introduction to optimization. Molecular geometry optimization.
• 10. Parameterization of computational methods in chemistry. Local vs. global optimization methods.
• 11. Differential equations and their application in chemistry.
• 12. Differential equations in molecular mechanics (analytical and numerical approaches).
Literature
• PÓTA, György. Mathematical problems for chemistry students. 1st ed. Amsterdam: Elsevier, 2006. viii, 250. ISBN 044452794X. info
• TURRELL, George. Mathematics for chemistry and physics. San Diego: Academic Press, 2002. xiv, 408. ISBN 0127050515. info
Teaching methods
Practical exercises.
Assessment methods
Continuous assessment.
Language of instruction
Czech