Description:

Basic calculus (real analysis, functions of one real variable, differential calculus).

Contents:

1. Basics of mathematical logic, equations and inequalities, goniometric functions, exponential and logarithmic functions, sums and products, induction.
2. Sets and mappings.
3. Real and complex sequence - limit, basic properties, limits of special sequences, number "e" and exponential function, some elementary functions.
4. Limit and continuity of functions of one real variable - basic properties.
5. Derivative of functions - basic properties.
6. Basic theorems of differential calculus. 7. Constructing graphs of functions.

Seminar contents:

1. Basic properties of functions and mappings.
2. Supremum, Infimum.
3. Limits of sequences.
4. Acculumation points.
5. Limits of real functions.
6. Continuity.
7. Derivative, graphs of real functions.

Recommended literature:

Recommended references:
[1] Apostol: Mathematical Analysis, Addison Wesley, 1974.
[2] W. Rudin: Principles of Mathematical Analysis. McGraw-Hill, Mexico, 1980.

Keywords:

differential calculus, real function, real variable, continuity, limit, derivative

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