Course: Continuum Mechanics 1

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Course title Continuum Mechanics 1
Course code KMA/MK1
Organizational form of instruction Lecture + Seminar
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 3
Language of instruction Czech
Status of course Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Vodák Rostislav, RNDr. Ph.D.
  • Fürst Tomáš, RNDr. Ph.D.
  • Horák Jiří, doc. RNDr. CSc.
Course content
A. Linear algebra prerequisites. B. Differential calculus prerequisites. C. Integral calculus for applications: 1. Why we need the Lebesgue integral. 2. Interchanging limits, sums, and integrals. 3. Substitution and the Fubini Theorem. 4. Curve integrals and potential. 5. Surface integrals and the Divergence Theorem. 6. Surface integrals and the Stokes Theorem. D. Elasticity primer

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Semestral Work - 40 hours per semester
  • Attendace - 39 hours per semester
  • Homework for Teaching - 10 hours per semester
Learning outcomes
Understand the mathematical tools for continuum description
Application Apply differential and intergral calculus of functions of several variables to flow modeling and elasticity
Prerequisites
Classical calculus.

Assessment methods and criteria
Oral exam, Seminar Work

Credit: course work. Exam (combined): written test - examples, oral exam.
Recommended literature
  • C. Truesdell. (1975). A first course in rational mechanics (v ruštině). Izdatelstvo Mir, Moskva.
  • D. E. Carlson. (1972). Linear Thermoelasticity Encyclopedia of Physics VIa/2. Springer-Verlag Berlin.
  • G. Duvaut, J. L. Lions. (1976). Inequalities in Mechanics and Physics. Springer, Berlin.
  • J. Haslinger, I. Hlaváček, J. Nečas, J. Lovíšek. (1982). Riešenie variačných nerovností v mechanike. ALFA Bratislava.
  • J. Nečas, I. Hlaváček. (1983). Úvod do matematické teorie pružných a pružně plastických těles. SNTL, Praha.
  • M. E. Gurtin. (1981). An Introduction to Continuum mechanics. Academic Press, New York.
  • M. E. Gurtin. (1972). The linear theory of elasticity, Encyclopedia of Physics, VIa. Springer-Verlag, Berlin.
  • P. G. Ciarlet. (1986). Mathematical Elasticity, Volume I.: Three-dimensional elasticity. Elsevier Amsterdam.
  • P. G. Ciarlet. (1997). Mathematical Elasticity, Volume II.: Theory of plates. Elsevier Amsterdam.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science General Physics and Mathematical Physics (2014) Physics courses 1 Summer