Course title  Calculus I 

Course code  UMB/CV564 
Organizational form of instruction  Lecture + Lesson 
Level of course  not specified 
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  unspecified 
Form of instruction  unspecified 
Work placements  unspecified 
Recommended optional programme components  None 
Lecturer(s) 


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: Onesided limits, Tangent Lines and Rates of Change, Limit Properties, Computing Limits, Limits Involving Infinity 5. Continuity: Definition, Onesided 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)

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 

Study plans that include the course 
Faculty  Study plan (Version)  Category of Branch/Specialization  Recommended semester 
