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This book discusses discrete geometric analysis, especially topological crystallography and discrete surface theory for trivalent discrete surfaces. Topological crystallography, based on graph theory, provides the most symmetric structure among given combinatorial structures by using the variational principle, and it can reproduce crystal structures existing in nature. In this regard, the topological crystallography founded by Kotani and Sunada is explained by using many examples. Carbon structures such as fullerenes are considered as trivalent discrete surfaces from the viewpoint of discrete geometric analysis. Discrete surface theories usually have been considered discretization of smooth surfaces. Here, consideration is given to discrete surfaces modeled by crystal/molecular structures, which are essentially discrete objects. .

Geometry, Differential. --- Discrete mathematics. --- Differential Geometry. --- Applications of Discrete Mathematics. --- Discrete Mathematics. --- Cristal·lografia matemàtica --- Carboni --- Compostos de carboni --- Estructura molecular --- Models matemàtics --- Superfícies (Matemàtica) --- Geometria discreta

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This book explains that diffusion, osmosis, dissolution, evaporation, and heat loss all preferentially affect small bodies due to their high surface/volume ratios. Because surface area increases as the square of length, but volume (and mass) increase as the cube, large objects have low surface/volume ratios and small objects have high surface/volume ratios. This simple physical constraint governs much of the physical world. It accounts for why the Earth has active volcanoes, but the Moon does not, why the human brain has numerous folds, why deciduous trees lose their leaves every Fall, and why nanoparticles of gold melt at surprisingly low temperatures. It is a phenomenon well known to every scientist, but this book is the first comprehensive treatment of this effect.

Engineering mathematics. --- Engineering—Data processing. --- Planetary science. --- Engineering geology. --- Mathematical and Computational Engineering Applications. --- Planetary Science. --- Geoengineering. --- Engineering --- Civil engineering --- Geology, Economic --- Planetary sciences --- Planetology --- Engineering analysis --- Mathematical analysis --- Geology --- Mathematics --- Surfaces --- Areas and volumes. --- Surface area --- Superfícies (Matemàtica)

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Càlcul --- Càlcul infinitesimal --- Límits (Matemàtica) --- Aritmètica --- Anàlisi harmònica --- Anàlisi p-àdica --- Càlcul diferencial --- Càlcul fraccional --- Càlcul mental --- Corbes --- Curvatura --- Equacions diferencials --- Sèries de Fourier --- Superfícies (Matemàtica) --- Teories no lineals --- Anàlisi matemàtica --- Concepte de nombre --- Funcions --- Geometria infinitesimal --- Mètode ABN --- Numeració --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal

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Functional analysis --- Mathematical analysis --- Numerical methods of optimisation --- Operational research. Game theory --- Mathematics --- Applied physical engineering --- analyse (wiskunde) --- economie --- wiskunde --- kansrekening --- optimalisatie --- Calculus --- Càlcul --- Càlcul infinitesimal --- Límits (Matemàtica) --- Aritmètica --- Anàlisi harmònica --- Anàlisi p-àdica --- Càlcul diferencial --- Càlcul fraccional --- Càlcul mental --- Corbes --- Curvatura --- Equacions diferencials --- Sèries de Fourier --- Superfícies (Matemàtica) --- Teories no lineals --- Anàlisi matemàtica --- Concepte de nombre --- Funcions --- Geometria infinitesimal --- Mètode ABN --- Numeració

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Engineering mathematics. --- Geometry, Differential. --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Differential geometry --- Engineering --- Engineering analysis --- Mathematics --- Matemàtica per a enginyers --- Geometria diferencial --- Càlcul --- Càlcul infinitesimal --- Límits (Matemàtica) --- Aritmètica --- Anàlisi harmònica --- Anàlisi p-àdica --- Càlcul diferencial --- Càlcul fraccional --- Càlcul mental --- Corbes --- Curvatura --- Equacions diferencials --- Sèries de Fourier --- Superfícies (Matemàtica) --- Teories no lineals --- Anàlisi matemàtica --- Concepte de nombre --- Funcions --- Geometria infinitesimal --- Mètode ABN --- Numeració --- Geometria --- Càlcul de tensors --- Connexions (Matemàtica) --- Coordenades --- Cossos convexos --- Dominis convexos --- Espais de curvatura constant --- Espais simètrics --- Estructures hermitianes --- Formes diferencials --- G-estructures --- Geodèsiques (Matemàtica) --- Geometria de Riemann --- Geometria diferencial global --- Geometria integral --- Geometria simplèctica --- Hiperespai --- Subvarietats (Matemàtica) --- Topologia diferencial --- Varietats (Matemàtica) --- Varietats de Kähler --- Matemàtica en l'electrònica --- Mecànica aplicada --- Anàlisi dimensional