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Riemann type integral in Banach spaces
Mrhal, Filip ; Lukeš, Jaroslav (advisor) ; Zajíček, Luděk (referee)
Title: Riemann type integral in Banach spaces Author: Filip Mrhal Department: Department of Mathematical Analysis Supervisor: Prof. RNDr. Jaroslav Lukeš, DrSc., Department of Mathematical Analysis Abstract: In this thesis we study some differences in the behaviours of the Ri- emann integral when integrating functions from any compact subinterval of real numbers to real numbers or to any Banach space. Especially, we outline that the Lebesgue theorem is no longer valid in relationship to functions with images in some Banach spaces. We show that for some well-known Banach spaces using counterexamples. Keywords: Riemann integral, Banach space, Lebesgue theorem 1
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Propedeutics of differential and integral calculi
Malachov, Martin ; Halas, Zdeněk (advisor) ; Slavík, Antonín (referee)
Propaedeutics of Differential and Integral Calculi Author: Ing. Martin Malachov Department: Department of Mathematics Education Supervisor: Zdeněk Halas, DiS., Ph.D. Department of Mathematics Education Keywords: propaedeutics, derivative, Riemann integral, applications Differential and integral calculi both are interesting and beautiful branches of mathematics with many interdisciplinary overlaps and significant and practi- cal applications. Learning as well as teaching of these topics is very difficult and demanding. In this thesis we show that the derivatives and integrals have much to offer in the high school education while the schooling can be eased and made attractive with intentional propaedeutics and knowledge of rich background of applications. First part of the thesis presents short contem- plation on the current state of teaching and literature, we focus on the urge for the propaedeutics of the differential and integral calculi revealed by us. We identify key terms that can be used to build useful preconcepts during the whole high school education, even in the elementary education. In the latter part of the thesis we offer teacher innovative texts and a rich set of origi- nal exercises that can be used for motivation, application and propaedeutics of the differential and integral calculi. We also present...
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Cavalieri's principle
Kreslová, Iva ; Halas, Zdeněk (advisor) ; Štěpánová, Martina (referee)
The Bachelor thesis deals with the development of key ideas important for formal formulating of Cavalieri's principle, its proof in general form and using Cavalieri's principle in determining the area of plane figures and volumes of solids. Determining of area and volumes using Cavalieri's principle is associated with the derivation of the well-known formulae for calculating area and volume.
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Riemann type integral in Banach spaces
Mrhal, Filip ; Lukeš, Jaroslav (advisor) ; Zajíček, Luděk (referee)
Title: Riemann type integral in Banach spaces Author: Filip Mrhal Department: Department of Mathematical Analysis Supervisor: Prof. RNDr. Jaroslav Lukeš, DrSc., Department of Mathematical Analysis Abstract: In this thesis we study some differences in the behaviours of the Ri- emann integral when integrating functions from any compact subinterval of real numbers to real numbers or to any Banach space. Especially, we outline that the Lebesgue theorem is no longer valid in relationship to functions with images in some Banach spaces. We show that for some well-known Banach spaces using counterexamples. Keywords: Riemann integral, Banach space, Lebesgue theorem 1
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The integral and substitution
ČLUPEK, Tomáš
This document introduces indefinite and definite integral. Also includes various substitution methods for calculation. Solved and unsolved examples of their usage are also attached.
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Using of the Riemannian integral for mathematical and physical calculus
MAREČEK, Ondřej
The theoretical part of the thesis includes introduction of Riemann integral and its qualities, introduction of function of more variables, introduction of double and triple Riemann integral and physical applications of integral. The practical part includes derivation of general area formulas for different shapes and volume formulas for different solids, in some examples there are shown different ways of solution. The practical part also includes the use of Riemann integral for the determination of centre of mass, of statical moments and moments of inertia of objects.
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