Academic year 2023/2024 |
Supervisor: | doc. Mgr. Zdeněk Opluštil, Ph.D. | |||
Supervising institute: | ÚM | |||
Teaching language: | Czech | |||
Aims of the course unit: | ||||
The course aim is to acquaint the students with the theoretical basics of the above mentioned mathematical disciplines necessary for further study of engineering courses and for solving engineering problems encountered. Another goal of the course is to develop the students' logical thinking. | ||||
Learning outcomes and competences: | ||||
Students will acquire basic knowledge of mathematical disciplines listed in the course annotation and will be made familiar with their logical structure. They will learn how to solve mathematical problems encountered when dealing with engineering tasks using the knowledge and skills acquired. Moreover, they improve their skills in mathematical software, which can be used to solving problems. | ||||
Prerequisites: | ||||
Differential and integral calculus of functions in one variable. | ||||
Course contents: | ||||
The course takes the form of lectures and seminars dealing with the following topics: Real functions of two and more variables, Partial derivatives - total differentials, Applications of partial derivatives - maxima, minima and saddle points, Lagrange multipliers, Taylor's approximation and error estimates, Double integrals, Triple integrals, Applications of multiple integrals, Methods of solving ordinary differential equations A significant part of the course is devoted to applications of the studied topics. The acquired knowledge is a prerequisite for understanding the theoretical foundations in the study of other specialized subjects. |
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Teaching methods and criteria: | ||||
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures. | ||||
Assesment methods and criteria linked to learning outcomes: | ||||
COURSE-UNIT CREDIT REQUIREMENTS: |
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Controlled participation in lessons: | ||||
Attendance at lectures is recommended, attendance at seminars is required. The lessons are planned on the basis of a weekly schedule. Missed seminars may be made up of the agreement with the teacher supervising the seminar. | ||||
Type of course unit: | ||||
Lecture | 13 × 3 hrs. | optionally | ||
Exercise | 11 × 3 hrs. | compulsory | ||
Computer-assisted exercise | 2 × 3 hrs. | compulsory | ||
Course curriculum: | ||||
Lecture | 1. Function in more variables, basic definitions, and properties. Limit of a function in more variables, continuous functions. Partial derivative. |
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Exercise | The first week: calculating improper integrals, applications of the Riemann integral. Following weeks: seminars related to the lectures given in the previous week. | |||
Computer-assisted exercise | Seminars in a computer lab have suitable mathematical software as computer support. Obligatory topics correspond to the course syllabus. | |||
Literature - fundamental: | ||||
1. Thomas G.B. - Finney R.L.: Calculus and Analytic Geometry, 7th edition | ||||
2. Sneall D.B. - Hosack J.M.: Calculus, An Integrated Approach | ||||
3. Hartman, P.: Ordinary Differential Equations. New York: John Wiley & Sons, 1964. | ||||
4. Rektorys K. a spol.: Přehled užité matematiky I,II (SNTL Praha, 1988) | ||||
5. Kurzweil, J.: Obyčejné diferenciální rovnice, Praha, SNTL, 1978. | ||||
Literature - recommended: | ||||
6. Karásek J.: Matematika II (skriptum VUT) | ||||
7. Čermák, J., Nechvátal, L.: Matematika III, Brno, 2016. | ||||
8. Děmidovič B. P.: Sbírka úloh a cvičení z matematické analýzy | ||||
9. Thomas G.B., Finney R.L.: Calculus and Analytic Geometry (7th edition) |
The study programmes with the given course: | |||||||||
Programme | Study form | Branch | Spec. | Final classification | Course-unit credits | Obligation | Level | Year | Semester |
B-ENE-P | full-time study | --- no specialisation | -- | Cr,Ex | 7 | Compulsory | 1 | 1 | S |
B-PDS-P | full-time study | --- no specialisation | -- | Cr,Ex | 7 | Compulsory | 1 | 1 | S |
B-PRP-P | full-time study | --- no specialisation | -- | Cr,Ex | 7 | Compulsory | 1 | 1 | S |
B-STR-P | full-time study | STR Engineering | -- | Cr,Ex | 7 | Compulsory | 1 | 1 | S |
B-VTE-P | full-time study | --- no specialisation | -- | Cr,Ex | 7 | Compulsory | 1 | 1 | S |
Faculty of Mechanical Engineering
Brno University of Technology
Technická 2896/2
616 69 Brno
Czech Republic
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