Description:

It is an introductory course to calculus of functions of one variable. It starts with limit and continuity of functions, derivative and its geometrical meaning and properties, graphing of functions. Then it covers indefinite integral, basic integration methods and integrating rational functions, definite integral and its applications. It concludes with introduction to Taylor series.

Contents:

1. The real line, elementary functions and their graphs, shifting and scaling.
2. Limits and continuity, tangent, velocity, rate of change.
3. Derivative of functions, properties and applications.
4. Mean value theorem, L'Hospital's rule.
5. Higher derivatives, Taylor polynomial.
6. Local and global extrema, graphing of functions.
7. Indefinite integral, basic integration methods.
8. Integration of rational functions, more techniques of integration.
9. Definite integral, definition and properties, Fundamental Theorems of Calculus.
10. Improper integrals, tests for convergence. Mean value Theorem for integrals, applications.
11. Sequences of real numbers, numerical series, tests for convergence.
12. Power series, uniform convergence, the Weierstrass test.
13. Taylor and Maclaurin series.

Seminar contents:

1. The real line, elementary functions and their graphs, shifting and scaling.
2. Limits and continuity, tangent, velocity, rate of change.
3. Derivative of functions, properties and applications.
4. Mean value theorem, L'Hospital's rule.
5. Higher derivatives, Taylor polynomial.
6. Local and global extrema, graphing of functions.
7. Indefinite integral, basic integration methods.
8. Integration of rational functions, more techniques of integration.
9. Definite integral, definition and properties, Fundamental Theorems of Calculus.
10. Improper integrals, tests for convergence. Mean value Theorem for integrals, applications.
11. Sequences of real numbers, numerical series, tests for convergence.
12. Power series, uniform convergence, the Weierstrass test.
13. Taylor and Maclaurin series.

Recommended literature:

1. M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994
2. P. Pták: Calculus II. ČVUT Praha, 1997.

https://math.fel.cvut.cz/en/people/vivipaol/MA12015.pdf

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar