✩ Language: English

✩ Place: Czech Technical University in Prague, Prague, Czech Republic

✩ Category: Theory + Labs

✩ Credits: 7 credits

✩ Classes: Tuesday 9.15 – 10.45 (Lecture) ★ Wednesday 9.15 – 10.45 (Lecture) ★ Wednesday 11.00 – 12.30 (Practice)

✩ When: Winter Term 2026 – 2027 (September 21 – January 10, 2027)

✩ Syllabus

• Lectures
  • The real line, elementary functions and their graphs, shifting and scaling.
  • Limits and continuity, tangent, velocity, rate of change. 
  • Derivative of functions, properties and applications.
  • Mean value theorem, L’Hospital’s rule. 
  • Higher derivatives, Taylor polynomial.
  • Local and global extrema, graphing of functions.
  • Indefinite integral, basic integration methods.
  • Integration of rational functions, more techniques of integration.
  • Definite integral, definition and properties, Fundamental Theorems of Calculus.
  • Improper integrals, tests for convergence. Mean value Theorem for integrals, applications.
  • Sequences of real numbers, numerical series, tests for convergence.
  • Power series, uniform convergence, the Weierstrass test.
  • Taylor and Maclaurin series.
• Tutorials
  • The real line, elementary functions and their graphs, shifting and scaling.
  • Limits and continuity, tangent, velocity, rate of change.
  • Derivative of functions, properties and applications.
  • Mean value theorem, L’Hospital’s rule. 
  • Higher derivatives, Taylor polynomial.
  • Local and global extrema, graphing of functions.
  • Indefinite integral, basic integration methods.
  • Integration of rational functions, more techniques of integration.
  • Definite integral, definition and properties, Fundamental Theorems of Calculus.
  • Improper integrals, tests for convergence. Mean value Theorem for integrals, applications.
  • Sequences of real numbers, numerical series, tests for convergence.
  • Power series, uniform convergence, the Weierstrass test. 
  • Taylor and Maclaurin series.

✩ Evaluation system

★Lectures: attendance is not mandatory, but highly recommended. 

★Practice: attendance is mandatory, 2 absences are tolerated.

★Midterms: During the labs of Week 6 and Week 11 – 45 minutes and 3 problems

★Homeworks: 10 accepted homeworks is one of the requirements for zápočet (assessment).

★Zápočet (assesment): In order to obtain zápočet (needed for the final exam), students are required to actively participate in the labs, hand in the assigned homeworks and obtain a sufficient score (at least 9 points out of 20) in the midterms. If the score obtained in a test is not sufficient, extra homework will be assigned and the test will be repeated at the end of the course.

★Final exam: it is composed of written and oral part. The written final exam will be in January-February (the dates will be announced later), it will consist of six problems (one about theory) to be solved in 90 minutes. The oral final exam is optional, it is used to improve the grade up to ten points. Questions about theory will be asked (definitions, theorems, proofs). In order to pass the exam a minimum of 50 points in the written test is required, students with more then 60 points in the written part of the exam will be allowed to improve their grade with the oral part of the exam.

★Grading: the grade is calculated as follows (this is the grade from the final exam only!):

➤0 – 49 points: F

➤ 50 – 59 points: E

➤ 60 – 69 points: D

➤ 70 – 79 points: C 

➤ 80 – 89 points: B

➤ 90 – 100 points: A

❖ You have at most 3 attempts to pass the final exam, each is entirely independent.

❖ Repeating the exam is obvious in case you fail, but you can also refuse a grade when you are not happy with it, then you are assigned the grade F and you can try again (if you still have attempts left).

❖ The midterm and the final test are subject to the following rules: No textbooks, no notes, no calculators, no cellphones are allowed.