Course detail

# Mathematics 1

FEKT-BPC-MA1BAcad. year: 2021/2022

Basic mathematical notions. Function, inverse function, sequences. Differential calculus of one variable, limit, continuity, derivative of a function. Derivatives of higher orders, l´Hospital rule, behavior of a function. Integral calculus of fuctions of one variable, antiderivatives, indefinite integral. Methods of a direct integration. Integration by parts, substitution methods, integration of some elementary functions. Definite integral and its applications. Improper integral. Infinite number series, convergence criteria. Power series. Multiple integral, transformation of a multiple integral, applications.

Supervisor

Department

Learning outcomes of the course unit

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;

Prerequisites

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.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Brabec, B., Hrůza, B., Matematická analýza II, SNTL, Praha, 1986. (CS)

Edwards, C.H., Penney, D.E., Calculus with Analytic Geometry, Prentice Hall, 1993. (EN)

Fong, Y., Wang, Y., Calculus, Springer, 2000. (EN)

Goldstein, L.J., Lay, D.C., Schneider, D.I., Asmar, N.H., Calculus & Its Applications, Pearson, 2017. (EN)

Hoffmann, L., Bradley, G., Sobecki, D., Price, M., Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition, McGraw-Hill Education, 2012. (EN)

Kolářová, E: Maple. (CS)

Kolářová, E: Matematika 1 - Sbírka úloh. (CS)

Krupková, V., Fuchs, P., Matematika 1. (CS)

Lial, M.L., Greenwell, R.N., Ritchey, N.P., Calculus with Applications, Pearson, 2015. (EN)

Ross, K.A., Elementary analysis: The Theory of Calculus, Springer, 2000. (EN)

Švarc, S. a kol., Matematická analýza I, PC DIR, Brno, 1997. (CS)

Thomas, G.B., Finney, R.L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994. (EN)

Planned learning activities and teaching methods

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

Assesment methods and criteria linked to learning outcomes

Maximum 30 points during the semester for entering the excersize classes + homework + a test (11+4+15). To get the course-unit credit, student must gain at least 10 points and make the 2 obligatory homeworks.

The exam is only written exam for maximum 70 points.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

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.

Aims

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.

Specification of controlled education, way of implementation and compensation for absences

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.

#### Type of course unit

Fundamentals seminar

8 hours, compulsory

Teacher / Lecturer

Computer-assisted exercise

18 hours, compulsory

Teacher / Lecturer

eLearning

**eLearning:** opened course