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PřF:F1031 Mathematics a step ahead - Course Information

## F1031 Mathematics a step ahead

**Faculty of Science**

Autumn 2015

**Extent and Intensity**- 2/0. 2 credit(s). Type of Completion: z (credit).
**Teacher(s)**- prof. RNDr. Jana Musilová, CSc. (lecturer)
**Guaranteed by**- prof. RNDr. Jana Musilová, CSc.

Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science

Contact Person: prof. RNDr. Jana Musilová, CSc.

Supplier department: Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science **Timetable**- Mon 15:00–15:50 F2,02012, Mon 16:00–16:50 F4,03017
**Prerequisites**- Secondary school mathematics.
**Course Enrolment Limitations**- The course is offered to students of any study field.
**Course objectives**- Student continually obtains knowledge and practical skills of mathematical tools for the study of the discipline F1030 Mechanics and molecular physics (one week before a corresponding lecture of F1030). The obtained knowledge and skills are useful for the study of other disciplines of the fundamental course of general physics.
**Syllabus**- 1. Vector calculus.
- 2. Fundaments of infinitesimal calculus: scalar and vector functions, limits, derivatives -- from trajectories to accelerations.
- 3. Fundaments of infinitesimal calculus: integraton -- from accelerations to trajectories.
- 4. Approximation of values of functions by polynomials.
- 5. Mathematics of equations of motion I. (solution of simplest differential equations).
- 6. Mathematics of equations of motion II. (solution of simplest differential equations).
- 7. Functions of two and three variables, path integrals.
- 8. Functions of two and three variables, partial derivatives, total differential.
- 9. Multiple integration. Something about tensors.
- 10. Surface integral.
- 11. Integral theorems.
- 12. Once more path integrals and their dependence/independence on the integration curve.
- 13. Random quantities (discrete and continuous distribution and its basic charactgeristics).
- 14. Mathematical preparation for the exam of Mechanics and molecular physics (problems proposed by students).
- Note: The items corresponds to semestral weeks. The topics with the given number corresponds with that of Mechanics and molecular physics (F1030) with the same number.

**Literature**- MUSILOVÁ, Jana and Pavla MUSILOVÁ.
*Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis)*. první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012. 697 pp. ISBN 978-80-214-4071-5. info - MUSILOVÁ, Jana and Pavla MUSILOVÁ.
*Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I)*. Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009. 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info

*recommended literature*- MUSILOVÁ, Jana and Pavla MUSILOVÁ.
**Teaching methods**- lectures, seminars
**Assessment methods**- four short written tests
**Language of instruction**- Czech
**Follow-Up Courses****Further comments (probably available only in Czech)**- Study Materials

- Enrolment Statistics (Autumn 2015, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2015/F1031