Course detail

# Mathematics 2

FAST-BA002Acad. year: 2023/2024

Antiderivative, indefinite integral, its properties and methods of calculation. Newton integral, its properties and calculation. Definition of Riemann integral. Applications of integral calculus in geometry and physics - area of a plane figure, length of a curve, volume and surface of a rotational body, static moments and the centre of gravity.

Functions in two and more variables. Limit and continuity, partial derivatives, implicit function, total differential, Taylor expansion, local minima and maxima, relative maxima and minima, maximum and minimum values of a function; directional derivative, gradient. Tangent to a 3-D curve, Tangent plane and normal to a surface.

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Students will achieve the subject's objectives. They will get an understanding of the basics of integral calculus of functions of one variable, know how to integrate elementary functions and apply these (length of a curve, volume and surface area of a rotational body, static momentums and centre of gravity). Students will acquaint themselves with the basic concepts of the calculus of functions of two and more variables. They will be able to calculate partial derivatives of functions of several variables. They will get an understanding of the total differential of a function and its geometrical meaning. They will also learn how to find local and global minima and maxima of two-functions. They will get acquainted with directional derivatives of functions of several variables and their calculation.

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Basic literature

Jirásek, F., Čipera, S., Vacek, M., Sbírka řešených příkladů z matematiky I, SNTL Praha 1986. (CS)

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