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41	Přirozený výklad komplexních čísel / A natural explanation of complex numbers Sedlák, Jan January 2021 (has links) The thesis is concerned with the introduction of complex num- bers. This topic is often perceived by pupils and students as very mysterious. This is often due to excessive formality, to which more time is devoted than to the illustrative geometrical concept of complex numbers. As a result, the important theorems achieved by complex numbers in the field of mathema- tics are consequently skipped. This thesis focuses on an illustrative geometric view on the field of complex numbers that will facilitate the understanding of related undergraduate curriculum. The text is written for readers at the upper grades of high school and first years of college. Examples are also included to create a coherent text useful for teaching and self-study. 1
42	Compatible discretizations for Maxwell equations He, Bo 22 September 2006 (has links) No description available. differential forms chains and cochains Whitney forms de Rham diagram gauging compatible discretization Hodge operator Hodge decomposition Euler's formula FDTD FEM Galerkin duality primal and dual pure Neumann boundary condition mixed FEM
43	Trigonometry: Applications of Laws of Sines and Cosines Su, Yen-hao 02 July 2010 (has links) Chapter 1 presents the definitions and basic properties of trigonometric functions including: Sum Identities, Difference Identities, Product-Sum Identities and Sum-Product Identities. These formulas provide effective tools to solve the problems in trigonometry. Chapter 2 handles the most important two theorems in trigonometry: The laws of sines and cosines and show how they can be applied to derive many well known theorems including: Ptolemy¡¦s theorem, Euler Triangle Formula, Ceva¡¦s theorem, Menelaus¡¦s Theorem, Parallelogram Law, Stewart¡¦s theorem and Brahmagupta¡¦s Formula. Moreover, the formulas of computing a triangle area like Heron¡¦s formula and Pick¡¦s theorem are also discussed. Chapter 3 deals with the method of superposition, inverse trigonometric functions, polar forms and De Moivre¡¦s Theorem. Sum Identities Difference Identities Double-Angle Identities Product-Sum Identities Sum-Product Identities Ceva's Theorem Menelaus's Theorem Ptolemy's Theorem Law of Sines Law of Cosine Euler Triangle Formula Inverse Trigonometric Functions Euler's Formula De Moivre's Theorem Pick's Theorem Weitzenbock's Inequality Heron' Formula Polar Coordinates Angle Bisector Formula Brahmagupta's Formula Median Formula Stewart's Theorem Parallelogram Law
44	Adaptive Mesh Redistribution for Hyperbolic Conservation Laws Pathak, Harshavardhana Sunil January 2013 (has links) (PDF) An adaptive mesh redistribution method for efficient and accurate simulation of multi dimensional hyperbolic conservation laws is developed. The algorithm consists of two coupled steps; evolution of the governing PDE followed by a redistribution of the computational nodes. The second step, i.e. mesh redistribution is carried out at each time step iteratively with the primary aim of adapting the grid to the computed solution in order to maximize accuracy while minimizing the computational overheads. The governing hyperbolic conservation laws, originally defined on the physical domain, are transformed on to a simplified computational domain where the position of the nodes remains independent of time. The transformed governing hyperbolic equations are recast in a strong conservative form and are solved directly on the computational domain without the need for interpolation that is typically associated with standard mesh redistribution algorithms. Several standard test cases involving numerical solution of scalar and system of hyperbolic conservation laws in one and two dimensions are presented in order to demonstrate the accuracy and computational efficiency of the proposed technique. Adaptive Mesh Redistribution Multigrid Methods Hyperbolic Conservation Laws Numerical Grid Generation Numerical Mesh Generation Mesh Partial Differential Equation Adaptive Mesh Redistriution Method Adaptive Mesh Redistribution Algorithms Computational Fluid Dynamics Mesh Redistribution Algorithms Mesh Adaptation Inviscid Burger's Equation Euler's Equations Fluid Dynamics
45	Řešení stability prutových konstrukcí / Stability solution of framed structures Baxant, Radek January 2015 (has links) This diploma thesis deals with the subject of slenderness bars’ stability assessment, especially in the steel structures. Before the assessment of bars in the frame constructions, we search for the influence of the computational model’s settings on the final result. The initial geometrical imperfections are examined on the model of Euler’s bar. The influence of the rigidity of girders on the poles’ buckling length is examined on the basic frame construction. The buckling lengths are assessed in the comparison with the figures we got from the statistical tables and the computational software. The influence of construction’s initial tilt and its replacement by the system of outer forces is examined on the frame structure. Three-hinged frame structure with variable cross-section member is designed then and the influence of non-linear calculations on the inner forces is studied. In the complex frame assessment, the influence of the number of parts of variable cross-section member on the bars’ buckling length is examined.

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