| Course Unit Code | 470-8722/01 |
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| Number of ECTS Credits Allocated | 6 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. |
| KRA04 | Mgr. Bohumil Krajc, Ph.D. |
| VOD03 | doc. Mgr. Petr Vodstrčil, Ph.D. |
| Summary |
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| The subject consists of the basic parts of the n-dimensional calculus theory and practice. |
| Learning Outcomes of the Course Unit |
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| Succesful student will gain deep and wide knowledge of the subject. |
| Course Contents |
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| Real functions of several variables. Euclidean spaces. Topological properties of subsets of Euclidean metric space. Limits and continuity. Partial derivative, the concept of directional derivatives. Total differential and the gradient function. Applications. Geometric interpretation gradient, outline methods steepest descent method. Discussion relationships between the fundamental concepts of calculus. Differentials of higher orders, Taylor polynomials, Taylor's theorem. Theorem of implicit function. Weierstrass theorem on the global extrema, local extrema. Criteria existence of local extreme. Constrained local extrema, Lagrange multipliers method. Search global extremes - practices. Riemann double integral, basic properties. Fubini phrases in double integrals. Substitution theorem for double integrals, applications of double integrals Riemann triple integrals, basic properties. Fubini theorems for integrals. Substitution theorem for integrals. Applications. First order differential equations, the theorem on the existence and uniqueness of the Cauchy problem. Linear differential equation 1 order, the equation with separated variables. |
| Recommended or Required Reading |
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| Required Reading: |
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Tom M. Apostol: Calculus, Volume 2, Multi-variable calculus and linear algebra with applications to differential equations and probability, Wiley, New York, 1969
W. E. Boyce, R. C. DiPrima: Elementary differential equations. Wiley, New York 1992 |
B. Budinský, J. Charvát: Matematika II. SNTL, Praha 1990
J. Charvát, M. Hála, V. Kelar, Z. Šibrava: Příklady k Matematice II, ČVUT, Praha 1999
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| Recommended Reading: |
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W. Rudin: Principles of Mathematical Analysis. McGraw-Hill Book Company, New York 1964
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Další prameny
J. Brabec, B. Hrůza: Matematická analýza II. SNTL, Praha 1986
P. Burda, J. Doležalová: Cvičení z matematiky IV (skripta VŠB-TUO)
N. Častová a kol.: Cvičení z matematiky III (skripta VŠB-TUO)
V. Dobrovská, K. Stach: Matematika II (Diferenciální počet funkce jedné a více proměnných). (skripta VŠB-TUO)
D. Píšová, E. Gardavská: Diferenciální počet funkcí více proměnných. (skripta VŠB-TUO)
K. Rektorys a kol.: Přehled užité matematiky. SNTL Praha
W. Rudin: Principles of Mathematical Analysis. McGraw-Hill Book Company, New York 1964
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| 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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| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 30 | 10 |
| Examination | Examination | 70 | 21 |