Course: Mathematical Analysis 1

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Course title Mathematical Analysis 1
Course code KMA/MAF1
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 7
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Burkotová Jana, Mgr. Ph.D.
  • Fürst Tomáš, RNDr. Ph.D.
  • Tomeček Jan, doc. RNDr. Ph.D.
  • Fišer Jiří, RNDr. Ph.D.
  • Ligurský Tomáš, RNDr. Ph.D.
  • Kouřilová Pavla, Mgr. Ph.D.
Course content
1. Introduction: On the structure of mathematics, sets, basic logic. 2. Sequences: The notion of limits, theorems on limits, boundedness and convergence. 3. Functions: The notion of functions, continuity, properties of continuous functions, limits, limits of composite functions, elementary functions. 4. Differentiation: Relation to limits and continuity, the differential of a function, mean value theorems, Taylor's polynomials, L'Hospital's rule. 5. Integration: Motivation, Newton's formula and the relation to differentiation, primitive functions, integration by parts, integration by substitution, integration of rational functions, more on integration techniques, the Riemann integral and the proof of Newton's formula. 6. Applications: Length, surface, volume, center of gravity, moment of inertia, numerical methods.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 78 hours per semester
  • Preparation for the Course Credit - 40 hours per semester
  • Preparation for the Exam - 60 hours per semester
  • Homework for Teaching - 30 hours per semester
Learning outcomes
Understand differential calculus of functions of a single real variable
Comprehension Understand the mathematical tools of differential and integral calculus of functions of a single variable.
Prerequisites
Grammar school mathematics

Assessment methods and criteria
Oral exam, Written exam

Credit: the student has to pass two written tests (i.e. to obtain at least half of the possible points in each test).
Recommended literature
  • J. Kopáček. (2005). Matematická analáza pro fyziky I. Matfyzpress, Praha.
  • J. Veselý. (2001). Matematická analýza pro učitele I. Matfyzpress.


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 (1) Physics courses 1 Winter
Faculty of Science Molecular Biophysics (2015) Physics courses 1 Winter
Faculty of Science Optics and Optoelectronics (1) Physics courses 1 Winter
Faculty of Science Applied Physics (1) Physics courses 1 Winter
Faculty of Science Nanotechnology (1) Special and interdisciplinary fields 1 Winter
Faculty of Science Computer Physics (1) Physics courses 1 Winter
Faculty of Science Biophysics (2015) Physics courses 1 Winter