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Lecturer(s)
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Zdráhal Tomáš, doc. RNDr. CSc.
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Černohlávek Vít, Ing. Ph.D.
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Course content
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Numerical sequences and series Numerical sequence and its limit, the sum of numbers. Convergence and divergence of sequences and series. Real functions of one variable Elementary functions (polynomial, rational angle, power, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic, hyperbolometrické). Limit and continuity. Heine's theorem. Properties of continuous functions. Differential calculus of real functions of one real variable Derivative of a function, its geometrical and physical interpretation. Basic rules for differentiation, derivatives and differentials of higher order. Theorem on the growth function and its applications. Local and global extremes. Function inflection points, asymptotes graph, graph of a function. Application tasks to extremes functions. Integral calculus of real functions of one real variable Primitive functions, the calculation of the basic types of indefinite integrals (method of integration by parts and substitution methods). Definite Riemann integral, integral mean value. Geometric and physical applications of the definite integral (length of curve, volume and surface of revolution, center of gravity, momentum and inertia). Functional sequences and series Functional sequence, Taylor polynomial. Power series, differentiation and integration of power series. Taylor series, the development of elementary functions into Taylor series.
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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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Mathematics from the university point of view continues on the secondary school mathematics and contains above all the differential and integral calculus, analytic geometry and linear algebra. The knowledge gained here are prerequisite for vocational subjects studied at the Faculty of Mechanical Engineering, J. E. Purkyně University, therefore not to mere knowledge of mathematical substance, but also skills in the field of applications especially on technical issues. In Mathematics I, it is primarily a problem for functions of one variable.
Competence in the fundamentals of mathematics, students will be able to solve tasks and problems differential and integral calculus of functions of one variable and finally realizes connections with physical and technological applications.
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Prerequisites
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Knowledge and skills from the Mathematics preparatory course.
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Assessment methods and criteria
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unspecified
A necessary condition for obtaining credit is at least 70% attendance at seminars. In addition, credit will be given only if the student succeeds in at least 70% of tests and assignments.
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Recommended literature
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Budinský, B., Charvát, J. Matematika I, SNTL, Alfa Praha. 1987.
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Mezník, J., Karásek, J., Miklíček, J. Matematika pro strojní fakulty I, SNTL Praha. 1992.
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