F1031 Mathematics a step ahead

Faculty of Science
autumn 2017
Extent and Intensity
2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Supervisor
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 18. 9. to Fri 15. 12. Wed 13:00–14:50 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
    recommended 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
Teaching methods
lectures, seminars
Assessment methods
two short written tests
Language of instruction
Czech
Follow-Up Courses
The course is also listed under the following terms Autumn 2014, Autumn 2015, Autumn 2016.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2017/F1031

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