Course: Calculus I

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Course title Calculus I
Course code UMB/564
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Frequency of the course In each academic year, in the winter semester.
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
Lecturer(s)
  • Křivan Vlastimil, prof. RNDr. CSc.
  • Kalová Jana, doc. RNDr. Ing. Ph.D.
Course content
1. Numbers: Natural numbers, Peano axioms, rational numbers, real and complex numbers 2. Mappings: countable and uncountable sets, supremum and infimum 3. Functions: Review of elementary functions, powers, power function, operations with functions, inverse functions, inverse trigonometric functions 4. Limits: One-sided limits, Tangent Lines and Rates of Change, Limit Properties, Computing Limits, Limits Involving Infinity 5. Continuity: Definition, One-sided continuity, Upper and Lower Bound Theorem, Bolzano theorem 6. Derivatives: Definition, Interpretation of the Derivative, Differential 7. Differentiation Formulas: Product and Quotient Rule, Derivatives of elementary functions, Chain Rule, Implicit Differentiation, Higher Order Derivatives 8. Applications of Derivatives: Critical Points, Minimum and Maximum Values, Increasing and Decreasing Functions, Inflection points, Concavity, the Second Derivative Test) 9. Mean Value Theorem, Optimization Problems, L'Hospital's Rule and Indeterminate Forms, Linear Approximations, Newton's Method

Learning activities and teaching methods
Monologic (reading, lecture, briefing)
  • Class attendance - 56 hours per semester
  • Preparation for classes - 112 hours per semester
Learning outcomes
To develop basic concepts of differential calculus.
Students will learn basics of differential calculus of single variable.
Prerequisites
Level at the state high school exam in mathematics is expected.

Assessment methods and criteria
Student performance assessment

1. Regular attendance during lectures and labs 2. Score at least 50% from tests written during the course 3. Score at least 50% from homeworks
Recommended literature
  • J. Kopáček. Matematická analýza nejen pro fyziky I. MATFYZPRESS, 2004. ISBN 80-86732-25-8.
  • V. Jarník. Diferenciální počet I. Academia Praha, 1984.
  • V. Křivan. Přednášky z matematické analýzy I.. 2018.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Physics (1) Category: Physics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Informatics for future teachers (1) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Applied Mathematics (2010) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mechatronics (1) Category: Special and interdisciplinary fields 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (2012) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Physics for future teachers (1) Category: Physics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Chemistry (1) Category: Chemistry courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Physics (2012) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Biophysics (1) Category: Physics courses - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Biophysics (1) Category: Physics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Measuring and Computer Technology (1) Category: Electrical engineering, telecommunication and IT 1 Recommended year of study:1, Recommended semester: Winter