SA_N_APM Applied mathematics and physics

Institute of Technology and Business in České Budějovice
winter 2024
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Guaranteed by
prof. Ing. Radimír Novotný, DrSc.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Prerequisites
OBOR ( CAP )
Knowledge of basic mathematical calculus for universities.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to acquaint students with the possibilities of applications of functional mathematics, differential geometry and algebra in theoretical and applied physics, especially in engineering mechanics.
Learning outcomes
The student is able to orientate in differential geometry and algebra in theoretical and applied physics, especially in engineering mechanics.
Syllabus
  • 1. Geometrical and physical aspects and connections in infinitesimal calculus.
  • 2. Brief review and summary of basic concepts of functional mathematics; function, limit, derivative, indefinite and definite integral.
  • 3. Coordinate systems and forms of description of physical phenomena.
  • 4. Fundamentals of vector algebra with emphasis on geometric and physical applications. Tensor concept.
  • 5. Some geometrically and physically defined curves I.
  • 6. Some geometrically and physically defined curves II.
  • 7. Moment of inertia of bodies. Flywheels and their practical use.
  • 8. Gyroscopic phenomena of transport machines in a turn .
  • 9. Scalar and Vector Fields, gradient
  • 10. Divergence and Gauss – Ostrogradski Theorem
  • 11. Rotation and Stokes Theorem
  • 12. Transmission of signals by optical fibres
  • 13. The principle of satellite Earth observation.
Literature
    required literature
  • STRANG, G., Calculus, online https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf
  • HALLIDAY, D. et al., 2020, Principles in Physics, John Wiley & Sons Inc, ISBN 9781119454014
  • REKTORYS, K. Survey of Applicable Mathematics (Mathematics and Its Applications, 280/281) 2nd ed. 1994. Softcover reprint of the original 2nd ed. 1994 Edition, ISBN 978-9401583107
    recommended literature
  • REKTORYS, K., 1998, Solving Ordinary and Partial Boundary Value Problems in Science and Engineering (Applied and Computational Mechanics) ISBN 978-0849325526
Forms of Teaching
Lecture
Seminar
Tutorial
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Brainstorming
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Final exam11
Preparation for Lectures13 
Preparation for Seminars, Exercises, Tutorial2665
Preparation for the Final Test3838
Attendance on Lectures26 
Attendance on Seminars/Exercises/Tutorial/Excursion2626
Total:130130
Assessment Methods and Assesment Rate
Test – final 100 %
Exam conditions
Test - final 100%. Overall classification of the subject (30 - 0): A 100 - 90, B 89.99 - 84, C 83.99 - 77, D 76.99 - 73, E 72.99 - 70, FX 69.99 - 30, F 29.99 - 0.
Language of instruction
Czech
Teacher's information
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory, except of the lectures, for full-time students to attend 70 % lesson of the subjet in a semester.
The course is also listed under the following terms winter 2022, winter 2023.
  • Enrolment Statistics (winter 2024, recent)
  • Permalink: https://is.vstecb.cz/course/vste/winter2024/SA_N_APM