|
|
Meaning and calculation of the mathematical constant
Geršl, David ; Dobrovský, Ladislav (referee) ; Dosoudilová, Monika (advisor)
This bachelor thesis discusses the meaning and methods for calculating the mathematical constant . The theoretical part focuses on the history of the methods for calculating this constant, while the most important ones, such as calculating by integral calculus or power series, are derived in detail in separate chapters. The practical part deals with the computational complexity of individual formulas and their subsequent comparison.
|
|
|
The solving of ordinary differential equations by means of the infinite series method.
Dražková, Jana ; Štoudková Růžičková, Viera (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the solving of ordinary differential equations by means of the infinite series methods, in particular, the power series and the Fourier series. The aim of this thesis is to find the solution of the initial value problem for ordinary differential equations by use of the power series and compare this approach to traditional analytic methods. Further, the thesis deals with the solving of the second order linear ordinary differential equations with a periodic forcing term via the Fourier series method.
|
|
|
Meaning and calculation of the mathematical constant
Geršl, David ; Dobrovský, Ladislav (referee) ; Dosoudilová, Monika (advisor)
This bachelor thesis discusses the meaning and methods for calculating the mathematical constant . The theoretical part focuses on the history of the methods for calculating this constant, while the most important ones, such as calculating by integral calculus or power series, are derived in detail in separate chapters. The practical part deals with the computational complexity of individual formulas and their subsequent comparison.
|
|
|
Nekonečné funkční řady a jejich aplikace
STUDENÁ, Lucie
The Theses deals with infinite function series, mainly its special type power series, and their applications. The introduction of the Theses summrizes history of infinity series from Archimedes to modern mathematicians. The first part of the Theses, which is more theoretical,concerns with convergence of function series and attributes of convergence, derivation and integration term by term, algebraic operations of power series and also representation of functions by Taylor series. The second part deals with mathematical applications of power series calculation of function values, determination of limits, calculation of integrals and also power series solutions to first and second order ordinary differential equations.
|
|
|
Exponential function and Mayer expansion
Nagy, Oliver ; Zahradník, Miloš (advisor) ; Loebl, Martin (referee)
Title: Exponential function and Mayer expansion Author: Oliver Nagy Department: Department of Mathematical Analysis Supervisor: doc. RNDr. Miloš Zahradník, CSc., Department of Mathematical Analysis Abstract: The unifying topic of this thesis is cluster expansion in statistical phy- sics. It is divided into three chapters. In the first one we present the necessary mathematical apparatus - selected topics from combinatorics, graph theory and theory of generating functions. The second one is an introduction to cluster expan- sion and abstract polymer model. Finally, in the third chapter we show a new resummation method for partition function of hard-core repulsive abstract poly- mer model. In this resummation we make use of cancellations of terms in partition function to rewrite the sum of clusters to a sum of quilted clusters, or alternati- vely as a sum of "bunches". The methods we use in this final chapter are original and may lead to some new results. Keywords: binomial and multinomial formula; power series; inclusion-exclusion principle; cluster expansion. iii
|
|
|
The solving of ordinary differential equations by means of the infinite series method.
Dražková, Jana ; Štoudková Růžičková, Viera (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the solving of ordinary differential equations by means of the infinite series methods, in particular, the power series and the Fourier series. The aim of this thesis is to find the solution of the initial value problem for ordinary differential equations by use of the power series and compare this approach to traditional analytic methods. Further, the thesis deals with the solving of the second order linear ordinary differential equations with a periodic forcing term via the Fourier series method.
|
guest ::
