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Lecturer(s)
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Chytrý Vlastimil, doc. PhDr. Ph.D.
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Zdráhal Tomáš, doc. RNDr. CSc.
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Course content
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1. Numerical sequence and its limit, sum of numerical series. Convergence and divergence of sequences and series. 2. Elementary functions and their graphs (polynomial, rational, power, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic, inverse hyperbolic). 3. Limit and continuity of function. Heine theorem. Properties of continuous functions. 4. Derivative of a function, its geometric and physical interpretation. Basic rules for differentiation, derivatives and differentials of higher order. Function increment theorem and its application. 5. Local and global extremes. Inflection points of the function, graph asymptotes, graphs of functions. 6. Extreme value theory and applications. 7. Antiderivative (primitive) functions, calculation of basic types of indefinite integrals (integration by parts and substitution methods). 8. Riemann integral, calculation of a definite integral, mean value of integral. 9. Geometric and physical applications of a definite integral (curve length, volume and surface of rotating bodies, center of gravity, angular momentum and inertia). Differential Equations - introduction and elementary methods of their solution. 10. Functional sequences, power series, differentiation and integration of power series. 11. Matrices, determinants, matrices of linear mappings. Eigenvalues and eigenvectors, quadratic form. Systems of linear equations and their solutions.
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Learning activities and teaching methods
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- unspecified
- 50 hours per semester
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Learning outcomes
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Objectives: 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 one variable with emphasis on technical applications.
Students will acquire basic knowledge of infinitesimal calculus in the sense that they will be able to solve special problems and problems of the real world by means of differential and integral calculus of functions of one variable.
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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
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Recommended literature
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Budinský, B., Charvát, J. Matematika I, SNTL, Alfa Praha. 1987.
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K. Rektorys a spol. Přehled užité matematiky I, II, SNTL Praha, 1988.
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Mezník, J., Karásek, J., Miklíček, J. Matematika pro strojní fakulty I, SNTL Praha. 1992.
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