# Course syllabus B-MAT2I - Mathematics 2 (FEEIT - WS 2019/2020)

**Information sheet**ECTS Syllabus

Slovak

**English**

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

Faculty: | |||||||||||||

Course unit code: | B-MAT2I | ||||||||||||

Course unit title: | Mathematics 2 | ||||||||||||

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

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

Recommended semester/trimester: | -- item not defined -- | ||||||||||||

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

Prerequisites for registration: | passed Mathematics 1 (B-MAT1I) | ||||||||||||

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 multivariable calculus and basic skills allowing them to work with the concepts derivatives and integrals.
•An understanding of the gradient, directional derivatives, and linear approximation. •The ability to compute derivatives using the chain rule or total differentials. •The ability to solve optimization problems involving several variables, with or without constraints. •The ability to compute double integrals. An understanding of the physical interpretation of these integrals. •The ability to set up and compute multiple integrals in rectangular and polar coordinates. •An understanding of change of variables in multiple integrals. | |||||||||||||

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

1. Vector space. Representation of functions of two and three variables.
2. Limits and continuity of a function of several variables. 3. Partial derivatives, directional derivative, gradient. The chain rule. 4. Tangent plane, differential and differentility. 5. Local extrems of the function of several variables. 6. second partial derivatives and second differential. 7. Taylor's theorem and expansion of the function of two variables. Applications. 8. Optimization of constrained functions. 9. The notion of double integral. Definition and basic properties. 10. Repeated integration, Fubini theorem. 11. Substution in double integrals. Transformation to polar coordinates. 12. Applications. | |||||||||||||

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

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

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

As a prerequisity Mathematics 1 is neeeded | |||||||||||||

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

Assessed students in total: 1485
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Name of lecturer(s): | RNDr. Mária Kečkemétyová, PhD. (examiner, instructor, lecturer) doc. RNDr. Boris Rudolf, PhD. (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.*