Calculus 1

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

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

Requirements:

No prerequisities.

Syllabus of lectures:

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 graph of functions.

Syllabus of tutorials:

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.

Study Objective:

The goal of this course is to manage basic techniques of computing limits of sequences, limits of real functions of one real variable and of differential calculus.

Study materials:

Apostol: Mathematical Analysis, Addison Wesley, 1974.

W. Rudin: Principles of Mathematical Analysis. McGraw-Hill, Mexico, 1980.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Matematické inženýrství - Matematické modelování (compulsory course of the specialization)
• BS Matematické inženýrství - Matematická fyzika (compulsory course of the specialization)
• BS Matematické inženýrství - Aplikované matematicko-stochastické metody (compulsory elective course)
• BS Informatická fyzika (compulsory elective course)
• BS Aplikace softwarového inženýrství (compulsory course of the specialization)
• BS jaderné inženýrství B (compulsory course of the specialization)
• BS Dozimetrie a aplikace ionizujícího záření (compulsory elective course)
• BS Experimentální jaderná a částicová fyzika (compulsory elective course)
• BS Inženýrství pevných látek (compulsory elective course)
• BS Diagnostika materiálů (compulsory elective course)
• BS Fyzika a technika termojaderné fúze (compulsory elective course)
• BS Fyzikální elektronika (compulsory elective course)