470-2111/02 – Mathematical Analysis 2 (MA2)
Gurantor department | Department of Applied Mathematics | Credits | 4 |
Subject guarantor | doc. Mgr. Petr Vodstrčil, Ph.D. | Subject version guarantor | doc. Mgr. Petr Vodstrčil, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 1 | Semester | summer |
| | Study language | English |
Year of introduction | 2015/2016 | Year of cancellation | 2021/2022 |
Intended for the faculties | FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Students will learn about differential calculus of more-variable real functions.
In the second part students will get the basic practical skills for working with fundamental concepts, methods and applications of integral calculus of more-variable real functions.
Teaching methods
Lectures
Tutorials
Summary
This subject contains following topics:
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differential calculus of two and more-variable real functions,
integral calculus of more-variable real functions or differential equations (according to the version)
Compulsory literature:
BOUCHALA, Jiří; KRAJC, Bohumil. Introduction to Differential Calculus of Several Variables, 2022
http://am.vsb.cz/bouchala
BOUCHALA, Jiří; VODSTRČIL, Petr; ULČÁK, David. Integral Calculus of Multivariate
Functions, 2022
http://am.vsb.cz/bouchala
Recommended literature:
Way of continuous check of knowledge in the course of semester
During the semester we will write two tests.
E-learning
Other requirements
There are not defined other requirements for student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
- More-variable real functions. Partial and directional derivatives,
differential and gradient.
- Taylor's theorem.
- Extremes of more-variable real functions.
- Definition of double integral, basic properties. Fubini theorems for
double integral.
- Transformation of double integral, aplications of double integral.
- Definition of triple integral, basic properties. Fubini theorems for triple
integral.
- Transformation of triple integral, aplications of triple integral.
Exercises:
- More-variable real functions. Partial and directional derivatives,
differential and gradient.
- Taylor's theorem.
- Extremes of more-variable real functions.
- Definition of double integral, basic properties. Fubini theorems for double
integral.
- Transformation of double integral, aplications of double integral.
- Definition of triple integral, basic properties. Fubini theorems for triple
integral.
- Transformation of triple integral, aplications of triple integral.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction