SA_N_APM Applied mathematics and physics

Institute of Technology and Business in České Budějovice
winter 2023
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
Timetable of Seminar Groups
SA_N_APM/P01: Mon 14:50–16:20 B5, Mon 14:50–16:20 E5, D. Smetanová
SA_N_APM/S01: Mon 16:30–18:00 B5, D. Smetanová
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: Trajectories of sedimenting particles of the solid state, asteroid, spiral and helix.
  • 6. Some geometrically and physically defined curves II: Loxodroma, catenary, strophoid and various transitions.
  • 7. Moment of inertia of bodies. Flywheels and their practical use. Free flywheel, Maxwell flywheel, Cardan hinge. Heavy flywheel, its precession and nutation.
  • 8. Gyroscopic phenomena of transport machines in a turn (plane, ship, rocket). Gyroscopic phenomena in two-wheeled and one-wheeled vehicles. Disc and projectile flight stabilization.
  • 9. Functionals and their applications: cooling power plant towers.
  • 10. Issues surrounding fluid flow; Bernoulli's energy theorem, Euler and Navier-Stokes equation of motion.
  • 11. Potential scalar field, its properties and gradient.
  • 12. Vortex and non-vortex vector fields. Vector field rotor. Theorem of Stokes and Thompson. Flow and divergence of a vector field. Gauss' theorem
  • 13. Transmission of signals by optical fiber. Optical signal processing. Transmission of information through the atmosphere and other dielectric environments. The principle of satellite Earth observation.
Literature
  • HALLIDAY, D. et al., 2020, Principles in Physics, John Wiley & Sons Inc, ISBN 9781119454014
  • REKTORYS, K., 1998, Solving Ordinary and Partial Boundary Value Problems in Science and Engineering (Applied and Computational Mechanics) ISBN 978-0849325526
  • 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
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.
  • Enrolment Statistics (recent)
  • Permalink: https://is.vstecb.cz/course/vste/winter2023/SA_N_APM