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Lecturer(s)
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Černohlávek Vít, Ing. Ph.D.
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Pitrová Veronika, RNDr. PhD., Ph.D.
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Course content
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1. Functions of several real variables. Limit and continuity. Derivative in direction, partial and total derivative. 2. Differentiation of function, total differential. Increment theorems, higher order derivatives, Taylor theorem. 3. Local, global and bound extremes. Implicit functions. 4. Vector spaces. Linear dependence and independence, basis and dimension, subspace of vector space. 5. Scalar, vector and mixed product of vectors. Orthogonal coordinate system. Gauss plane. 6. Vector function, scalar function, vector field. First order operations (gradient, divergence, curl). 7. Second order operations (Laplace operator and its meaning). 8. Riemann integral in two and three-dimensional space, basic properties. Methods of integration, Fubini's theorem. 9. Geometric and physical applications of multivariate integrals. Line and surface integrals. 10. Green, Gauss and Stokes theorem. The use of line and surface integrals in physics and technology. 11. Analytical geometry in plane and space. General and parametric equations of lines and planes, their mutual positions, distances and deviations. Conic sections, technical curves (cycloids, spirals). Quadrics.
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Learning activities and teaching methods
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unspecified, unspecified
- unspecified
- 50 hours per semester
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Learning outcomes
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The course is organized in the form of lectures (explanation of basic principles and theory) and seminars (focused on practical mastery of the subject). The aim of the course is to acquaint students with the basic principles of differential and integral calculus of functions of two and three variables with emphasis on technical applications.
Competence in the fundamentals of mathematics, students will be able to solve tasks and problems differential and integral calculus of functions on two and three variables and finally realizes connections with physical and technological applications.
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Prerequisites
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Successfully completed course Mathematics I.
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Assessment methods and criteria
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unspecified
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Recommended literature
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Budinský, B., Charvát, J. Matematika II, SNTL Praha. 1990.
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Černý, I. Úvod do inteligentního kalkulu 2. Academia, Praha, 2005.
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Dontová E. Matematika IV. ČVUT Praha, 1996.
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Kurzweil, J. Obyčejné diferenciální rovnice, TKI, SNTL Praha. 1978.
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Pytlíček J. Lineární algebra a geometrie. ČVUT Praha, 2007.
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