FC1022 Applied Mathematics 1

Faculty of Education
Autumn 2024
Extent and Intensity
0/0/3. 4 credit(s). Type of Completion: k (colloquium).
Teacher(s)
Mgr. Ivana Medková, Ph.D. (lecturer)
doc. RNDr. Petr Sládek, CSc. (lecturer)
Guaranteed by
doc. RNDr. Petr Sládek, CSc.
Department of Physics, Chemistry and Vocational Education – Faculty of Education
Contact Person: Jana Jachymiáková
Supplier department: Department of Physics, Chemistry and Vocational Education – Faculty of Education
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the subject is to acquire clear knowledge of the basics of higher mathematics. Emphasis is placed on the logical structure of this scientific discipline and on acquiring the knowledge and skills needed to master the physics course at university.
Learning outcomes
After completing the course, the student will acquire:
Knowledge: A comprehensive overview of knowledge on the topics Vectors, Differential and integral calculus of functions of one or more variables.
Skills: Be able to use basic definitions and sentences when solving simple and application problems. To understand the connection of the material being discussed with practical physical applications. Be able to perform a qualified estimation of values.
Attitudes: Acquire the values ​​of objectivity and the importance of scientific work.
Syllabus
  • I. Coordinates, vectors. 1. Cartesian coordinates on a straight line, in a plane and in space, polar coordinates. 2. Concept of vector, vector space, addition of vectors, scalar and vector product, concept of vector base.
  • II. Functions of one variable 1. Graph of a function, basic properties of functions, Some elementary functions.The concept of limits and connections. 2. Derivation of a function, investigation of the course of a function using derivatives. Differential of a function. 3. Concept of primitive function, indefinite integral. Calculation of the indefinite integral. Definite integral, its calculation, application.
  • III. Sequences and series. 1. Sequences. 2. Number series. Taylor's development.
  • IV. Functions of multiple variables. • 1. Concept of function of several variables, basic properties of functions. 2. Partial derivatives • 3. Fundamentals of the integral calculus of a function of several variables. • 4. Curve integrals I. and II. kinds. •
  • V. Fundamentals of differential equations. • 1. Concept of differential equation, initial and boundary conditions, general solution. • Linear differential equation of the 1st order •
Literature
    required literature
  • SLÁDEK, Petr and Václav VACEK. Matematika pro fyziky I a II. Elportál. Brno: Masarykova univerzita, 2009. ISSN 1802-128X. URL info
  • NOVÁK, Vítězslav. Diferenciální počet funkcí jedné reálné proměnné. 1. vyd. Brno: Masarykova univerzita v Brně, 2004, 158 s. ISBN 802103386X. info
  • NOVÁK, Vítězslav. Integrální počet v R. 3. vyd. Brno: Masarykova univerzita, 2004, 85 s. ISBN 8021027207. info
    recommended literature
  • JIRÁSEK, František, Eduard KRIEGELSTEIN and Zdeněk TICHÝ. Sbírka řešených příkladů z matematiky. 2. nezměn. vyd. Praha: SNTL - Nakladatelství technické literatury, 1981, 817 s. URL info
  • HÁJEK, Jiří. Cvičení z matematické analýzy : diferenciální počet v R. 2. vyd. Brno: Masarykova univerzita, 2003, 103 s. ISBN 802103260X. info
  • HÁJEK, Jiří. Cvičení z matematické analýzy : integrální počet v R. 1. vyd. Brno: Masarykova univerzita, 2000, 102 s. ISBN 8021022639. info
  • DULA, Jiří and Jiří HÁJEK. Cvičení z matematické analýzy : nekonečné řady. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1992, 76 s. ISBN 8021003855. info
  • DULA, Jiří and Jiří HÁJEK. Cvičení z matematické analýzy : obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 1998, 74 s. ISBN 8021019751. info
Teaching methods
lectures, exercises
Assessment methods
Colloquium, 3x written test, completing online worksheets
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is taught: every week.
Information on the extent and intensity of the course: 12 hodin.
Listed among pre-requisites of other courses
Teacher's information
For students on a foreign placement (ERASMUS, etc.): Course requirements will be individually set in the context of the courses taken during the foreign placement and in accordance with the objectives and learning outcomes of the study programme.
The course is also listed under the following terms Autumn 2023.
  • Enrolment Statistics (recent)
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