doc. RNDr. Edita Kolářová, Ph.D.

Department of Mathematics (UMAT)

After completing the course, students should be able to:

- estimate the domains and sketch the grafs of elementary functions;
- compute limits and asymptots for the functions of one variable, use the L’Hospital rule to evaluate limits;
- differentiate and find the tangent to the graph of a function;
- sketch the graph of a function including extrema, points of inflection and asymptotes;
- integrate using technics of integration, such as substitution, partial fractions and integration by parts;
- evaluate a definite integral including integration by parts and by a substitution for the definite integral;
- compute the area of a region using the definite integral, evaluate the inmproper integral;
- discuss the convergence of the number series, find the set of the convergence for the power series.
- compute double and triple integral without a transformation;
- using transformation compute double and triple integral without a transformation;

Students should be able to work with expressions and elementary functions within the scope of standard secondary school requirements; in particular, they shoud be able to transform and simplify expressions, solve basic equations and inequalities, and find the domain and the range of a function.

Not applicable.

Not applicable.

FONG, Y., WANG, Y., Calculus, Springer, 2000. (EN)
SMALL, D.B., HOSACK, J.M., Calculus (An Integrated Approach), Mc Graw-Hill Publ. Comp., 1990. (EN)
KRUPKOVÁ, V., FUCHS, P.,: Matematika 1 (CS)
KOLÁŘOVÁ, E., Matematika 1 - Sbírka úloh (CS)

Teaching methods include lectures, computer exercise and computing exercises with computer support.

Maximum 30 points during the semester (for two tests). To get the course-unit credit, student must gain at least 10 points.

The exam is only written exam for maximum 70 points.

Czech

Not applicable.

1. Sets, functions and the inverse function.
2. Limits and the continuity of the functions of one variable.
3. The derivative of the functions of one variable.
4. Local and absolute extrema of a function.
5. L'Hospital rule, graphing a function.
6. Antiderivatives, the per partes method and the substitution technique.
7. Integration of the rational and irrational functions.
8. Definite integral.
9. Aplications of the definite integral and the improper integral.
10. Number and power series.
11. Multiple integral.
12. Transformation of multiple integrals.
13. Applications of multiple integrals.

The main goal of the calculus course is to explain the basic principles and methods of higher mathematics that are necessary for the study of electrical engineering. The practical aspects of application of these methods and their use in solving concrete problems (including the application of contemporary mathematical software) are emphasized.

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

• Programme BPC-AMT Bachelor's, 1. year of study, winter semester, 7 credits, compulsory
  
• Programme BPC-SEE Bachelor's, 1. year of study, winter semester, 7 credits, compulsory
  

• Programme EEKR-CZV lifelong learning

  branch ET-CZV , 1. year of study, winter semester, 7 credits, compulsory
  

18 hours, compulsory

doc. RNDr. Edita Kolářová, Ph.D.
Mgr. Jiří Vítovec, Ph.D.