# Course syllabus B-MAT1I - Mathematics 1 (FEEIT - WS 2019/2020)

**Information sheet**ECTS Syllabus

Slovak

**English**

University: | Slovak University of Technology in Bratislava | ||||||||||||

Faculty: | Faculty of Electrical Engineering and Information Technology | ||||||||||||

Course unit code: | B-MAT1I | ||||||||||||

Course unit title: | Mathematics 1 | ||||||||||||

Mode of delivery, planned learning activities and teaching methods: | |||||||||||||

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Credits allocated: | 6 | ||||||||||||

Recommended semester/trimester: | Applied Informatics - bachelor (compulsory), 1. semester | ||||||||||||

Level of study: | 1. | ||||||||||||

Prerequisites for registration: | none | ||||||||||||

Assesment methods: | |||||||||||||

Written tests during the semester for 30 points. For credit at least 50% of total is needed. Final exam at the end of semester for 70 points. Sum of all points determines the final evaluation. For evaluation A at least 92 points is needed,for evaluation B at least 83 points is needed, for evaluation C at least 74 points is needed, For evaluation D at least 65 points is needed,for evaluation E at least 56 points is needed. | |||||||||||||

Learning outcomes of the course unit: | |||||||||||||

After completing this course, students should have developed an understanding of the fundamental concepts of single variable calculus and a range of skills allowing them to work effectively with the concepts of derivatives and integrals.
Students should demonstrate competency in the following skills: •Use rules of differentiation to differentiate functions. •Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions. •Apply differentiation to solve applied max/min problems. •Evaluate integrals by using the Fundamental Theorem of Calculus. •Evaluate integrals using techniques of integration, integration by parts, substitution, partial fractions. •Determine the convergence/divergence of an infinite series. | |||||||||||||

Course contents: | |||||||||||||

1. Function of a real variable. Properties of functions, odd and even functions, boundedness, maximum, minimum, supremum, infimum, inverse function.
2. Elementary functions, power function, exponential and logaritmic function, trigonometric and inverse trigonometric functions. 3. Limit and continuity of a function. Finite and infinite limits. Limits at infinity. 4. Continuity. Properties of continuous functions on a compact interval. 5. Derivative. Definition of derivative and basic rules. Geometrical interpretation of derivative, differential. 6. Monotonicity and local extrema. Lagrange's theorem 7. Higher derivatives. Convexity of a function. Local extrema and 2-nd derivative. L‘Hospital rule. 8. Sequence. Limit of a sequence. Arithmetic and geometric sequence. Recurrencies. 9. Series. Convergence of infinite series. geometric series. Tests for convergence of positive series. 10. Integration, basic ideas and definitions, elementary integrals, integration methods. 11. Integration of rational functions, partial fractions. 12. Definite integral, The fundamental theorem, integration methods and applications. | |||||||||||||

Recommended or required reading: | |||||||||||||

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Language of instruction: | slovak or english | ||||||||||||

Notes: | |||||||||||||

Courses evaluation: | |||||||||||||

Assessed students in total: 2053
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Name of lecturer(s): | RNDr. Karla Čipková, PhD. (examiner, instructor) - slovak, english RNDr. Elena Pastuchová, PhD. (examiner, instructor) - slovak, english doc. RNDr. Boris Rudolf, PhD. (instructor, lecturer, person responsible for course) - slovak, english | ||||||||||||

Last modification: | 6. 5. 2019 | ||||||||||||

Supervisor: | doc. RNDr. Boris Rudolf, PhD. and programme supervisor |

*Last modification made by RNDr. Marian Puškár on 05/06/2019.*