Course: Mathematics 1

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Course title Mathematics 1
Course code KMA/MAT1
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 6
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)
  • Andres Jan, prof. RNDr. dr hab. DSc.
  • Pavlačka Ondřej, RNDr. Ph.D.
  • Fišer Jiří, RNDr. Ph.D.
  • Ženčák Pavel, RNDr. Ph.D.
Course content
1. Mathematical preliminaries: Numbers, algebraic expressions, algebraic equations and inequalities. 2. Combinatorics and fundamentals of probability theory and statistics. 3. Linear algebra: Vectors, matrices, determinants, systems of linear equations (Frobenius Theorem and the Cramer's Rule). 4. Sequences, limits of sequences, infinite series. 5. Functions (real functions of a single real variable): The notion of functions, inverse functions, composition of functions. 6. Elementary functions: Exponential, logarithmic, circular and antitrigonometric functions. 7. Limit and continuity of a function. 8. Fundamentals of differential calculus: Derivative and its geometrical and physical meanings, differential, properties of functions.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 52 hours per semester
  • Homework for Teaching - 20 hours per semester
  • Preparation for the Course Credit - 40 hours per semester
  • Preparation for the Exam - 65 hours per semester
Learning outcomes
Understand the basics of mathematical analysis, linear algebra and statistical analysis.
Comprehension Understand the basics of mathematical analysis, linear algebra and statistical analysis.
Prerequisites
Grammar school mathematics.

Assessment methods and criteria
Written exam, Dialog

Credit: Passing two written tests (i.e. obtaining at least half of the possible points in each test). Exam: Oral exam.
Recommended literature
  • B. Budinský, J. Charvát. (1990). Matematika I. SNTL, Praha.
  • Bartch H. J. (1983). Matematické vzorce. SNTL, Praha.
  • E. Calda, V. Dupač. (1999). Matematika pro gymnázia. Kombinatorika, pravděpodobnost, statistika. Prométheus, Praha.
  • J. Kopáček. (2002). Matematická analýza pro fyziky. Matfyzpress.
  • Kolda S., Krajňáková D., Kimla A. (1990). Matematika pro chemiky II. SNTL Praha.
  • Kolda S., Krajňáková D., Kimla A. (1989). Matematika pro chemiky I. SNTL Praha.
  • R. A. Adams. (1991). Calculus: A Complete Course. Addision-Wesley Publishers Limited.
  • Tebbutt P. (1995). Basic Mathematics for Chemists. John Wiley & Sons, Chichester.
  • V. Kotvalt. (2003). Základy matematiky pro biologické obory. Karolinum, Praha.


Study plans that include the course
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