Course detail

# Mathematics

FCH-BC_MATEAcad. year: 2021/2022

The subject is about calculus of real function of one real variable and its use.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

Department

Learning outcomes of the course unit

Knowledge, abilities and competence of students is expected to be seen in following areas:

a) calculation of limits, differentials and integrals of real functions of one real variable

b) finding course of a real function of one real variable

c) understanding importance of limits, differentials, indefinite and definite integral

d) knowledge of basic applications of calculus

e) knowledge of basic commands of suitable mathematical software and ability to use it for calculations

f) solving simple physics and chemistry related tasks found in specialized courses

a) calculation of limits, differentials and integrals of real functions of one real variable

b) finding course of a real function of one real variable

c) understanding importance of limits, differentials, indefinite and definite integral

d) knowledge of basic applications of calculus

e) knowledge of basic commands of suitable mathematical software and ability to use it for calculations

f) solving simple physics and chemistry related tasks found in specialized courses

Prerequisites

Knowledge of mathematics at the secondary school level is assumed.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Theoretical knowledge, examples of solutions and applications of tasks are presented in lectures. Seminars are used to practise selected tasks and their applications. Students can study from recommended literature, which will be available in LMS Moodle.

Assesment methods and criteria linked to learning outcomes

Students take two tests during the semester. During both tests computer with suitable mathematical software is available. Students can gain up to 15 points from each test. The condition for recognizing both tests is to get at least 8 points from each of them. As long as students have satisfactory result on both tests and do not have an unexcused absence they will able to take final exam. If any of the tests is unsatisfactory and it is not retaken during the semester, student has to retake this test. Finally, each student has to take an exam. This exam has written part (for up to 50 points) and oral part (for up to 20 points). Classification is made using ECTS scale.

Course curriculum

Week 1: Lecture - Basic concepts (sets, Cartesian product, binary relation, function, inverse function). Real function of one real variable and its properties.

Seminar - Sets, Cartesian product, binary relation, function, inverse function.

Week 2: Lecture - Elementary functions (polynomials, exponential function, goniometric functions) their domains and basic properties.

Seminar - Domain of real function of one real variable.

Week 3: Lecture - Limits, differential and its geometric meaning, basic rules for differentiation.

Seminar: Calculation of limits and derivatives.

Week 4: Lecture - Higher degree derivatives. L'Hospital's rule. Meaning of first derivative in geometry, physics and chemistry.

Seminar: Calculation of limits using L'Hospital's rule. Derivatives and their applications.

Week 5: Lecture - Course of a function.

Seminar: Course of a function.

Week 6: Lecture - Calculation of limits in mathematical software. Graph of real function of one real variable.

Seminar - Course of a function with use of mathematical software.

Week 7: Lecture - Zero points of function, first and second derivative. Solving non-linear equations.

Seminar - Test n. 1 - Differential calculus of real functions of one real variable and its applications (with the possibility of using appropriate mathematics software) - 15 points

Week 8: Lecture - Primitive function and indefinite integral.

Seminar - Calculation of indefinite integrals.

Week 9: Lecture - Integration of functions.

Seminar - Calculation of indefinite integrals.

Week 10: Lecture - Definite integral and its geometric meaning. Calculation of definite integrals.

Seminar - Calculation of definite integrals. Area of a shape.

Week 11: Lecture - Calculation of indefinite and definite integrals in mathematical software.

Seminar - Calculation of indefinite and definite integrals with use of mathematical software.

Week 12: Lecture - Application of definite integrals. Use of integrals in physics and chemistry.

Seminar - Test n. 2 - Integral calculus of real functions of one real variable and its applications (with the possibility of using appropriate mathematics software) - 15 points.

Week 13: Lecture - Final lecture. Summary of calculus.

Seminar - Correction tests.

Seminar - Sets, Cartesian product, binary relation, function, inverse function.

Week 2: Lecture - Elementary functions (polynomials, exponential function, goniometric functions) their domains and basic properties.

Seminar - Domain of real function of one real variable.

Week 3: Lecture - Limits, differential and its geometric meaning, basic rules for differentiation.

Seminar: Calculation of limits and derivatives.

Week 4: Lecture - Higher degree derivatives. L'Hospital's rule. Meaning of first derivative in geometry, physics and chemistry.

Seminar: Calculation of limits using L'Hospital's rule. Derivatives and their applications.

Week 5: Lecture - Course of a function.

Seminar: Course of a function.

Week 6: Lecture - Calculation of limits in mathematical software. Graph of real function of one real variable.

Seminar - Course of a function with use of mathematical software.

Week 7: Lecture - Zero points of function, first and second derivative. Solving non-linear equations.

Seminar - Test n. 1 - Differential calculus of real functions of one real variable and its applications (with the possibility of using appropriate mathematics software) - 15 points

Week 8: Lecture - Primitive function and indefinite integral.

Seminar - Calculation of indefinite integrals.

Week 9: Lecture - Integration of functions.

Seminar - Calculation of indefinite integrals.

Week 10: Lecture - Definite integral and its geometric meaning. Calculation of definite integrals.

Seminar - Calculation of definite integrals. Area of a shape.

Week 11: Lecture - Calculation of indefinite and definite integrals in mathematical software.

Seminar - Calculation of indefinite and definite integrals with use of mathematical software.

Week 12: Lecture - Application of definite integrals. Use of integrals in physics and chemistry.

Seminar - Test n. 2 - Integral calculus of real functions of one real variable and its applications (with the possibility of using appropriate mathematics software) - 15 points.

Week 13: Lecture - Final lecture. Summary of calculus.

Seminar - Correction tests.

Work placements

Not applicable.

Aims

Subject's goal is to introduce students to differentials and integrals of real functions of one real variable. Students will learn basic calculations and they will be able to use suitable mathematical software for them.

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

Seminars will be held for two hours every week in specialized IT classroom. Attendance on seminars is mandatory and will be checked. Lectures will be held for two hours every week. Attendance on lectures is recommended but not mandatory.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BARTSCH, Hans-Jochen. Matematické vzorce. Praha: SNTL – Nakladatelství technické literatury, 1983. 04-020-83. (CS)

-POLCEROVÁ, Marie. MATLAB počítačová cvičení z matematiky pro chemické aplikace. Brno: Fakulta chemická, Vysoké učení technické v Brně, 2018. (CS)

TOMICA, Rudolf. Cvičení z matematiky I. Brno: Katedra matematiky a deskriptivní geometrie, Vojenská akademie Antonína Zápotockého, 1974. S-2254/I. (CS)

-POLCEROVÁ, Marie. MATLAB počítačová cvičení z matematiky pro chemické aplikace. Brno: Fakulta chemická, Vysoké učení technické v Brně, 2018. (CS)

TOMICA, Rudolf. Cvičení z matematiky I. Brno: Katedra matematiky a deskriptivní geometrie, Vojenská akademie Antonína Zápotockého, 1974. S-2254/I. (CS)

Recommended reading

Not applicable.

Classification of course in study plans

- Programme BPCP_ECHBM Bachelor's 1 year of study, winter semester, compulsory
- Programme BKCP_ECHBM Bachelor's 1 year of study, winter semester, compulsory