Course Unit Code | 470-8723/01 |
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Number of ECTS Credits Allocated | 4 ECTS credits |
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Type of Course Unit * | Compulsory |
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Level of Course Unit * | First Cycle |
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Year of Study * | First Year |
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Semester when the Course Unit is delivered | Summer Semester |
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Mode of Delivery | Face-to-face |
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Language of Instruction | Czech |
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Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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Name of Lecturer(s) | Personal ID | Name |
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| BOU10 | prof. RNDr. Jiří Bouchala, Ph.D. |
Summary |
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This subject contains 2 basic themes:
differential and integral calculus of multivariable real functions.
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Learning Outcomes of the Course Unit |
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Students will get basic practical skills for work with fundamental concepts, methods and applications of differential and integral calculus of multivariable functions. |
Course Contents |
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1. Differential calculus of multivariable functions
Real functions of several variables.
Limits and continuity.
Partial derivative, gradient and directional derivative, total differential.
Differentials of higher orders, Taylor polynomials, Taylor's theorem.
Implicit function theorem.
Local, constrained and global extrema. Lagrange multipliers method.
2. Integration of multivariable functions
Riemann double and triple integrals.
Fubini theorem.
Substitution theorem for double and triple integrals.
Applications of double and triple integrals. |
Recommended or Required Reading |
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Required Reading: |
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J. Stewart: Calculus, 2008 Thomson
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J. Kuben, Š. Mayerová, P. Račková, P. Šarmanová: Diferenciální počet funkcí více proměnných, http://mi21.vsb.cz/modul/diferencialni-pocet-funkci-vice-promennych
P. Vodstrčil, J. Bouchala: Integrální počet funkcí více proměnných, http://mi21.vsb.cz/modul/integralni-pocet-funkci-vice-promennych
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Recommended Reading: |
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W. Rudin: Principles of Mathematical Analysis. McGraw-Hill Book Company, New York 1964 |
B. Budinský, J. Charvát: Matematika II. SNTL, Praha 1990
J. Charvát, M. Hála, V. Kelar, Z. Šibrava: Příklady k Matematice II, ČVUT, Praha 1999 |
Planned learning activities and teaching methods |
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Lectures, Tutorials |
Assesment methods and criteria |
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Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing |
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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 30 | 10 |
Examination | Examination | 70 | 21 |