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Complex analysis --- Functions of complex variables --- Mathematical analysis --- Functions of complex variables. --- 517.53 --- complexe functies --- möbiustransformaties --- machtreeksen --- residu --- vectorvelden --- stelling van cauchy --- green --- Advanced calculus --- Analysis (Mathematics) --- Algebra --- Complex variables --- Elliptic functions --- Functions of real variables --- Functions of a complex variable --- 517.1 Mathematical analysis --- 517.53 Functions of a complex variable --- 517.1. --- Mathematical analysis. --- 517.1
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517.53 --- Functions of complex variables --- Mathematical analysis --- 517.1 Mathematical analysis --- Complex variables --- 517.53 Functions of a complex variable --- Functions of a complex variable --- Elliptic functions --- Functions of real variables --- 517.1. --- Functions of complex variables. --- Mathematical analysis. --- Fonctions d'une variable complexe --- Analyse mathématique --- Analyse mathématique --- Fonctions d'une variable complexe. --- Analyse mathématique. --- 517.1
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An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner.Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book.Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
Differential forms. --- Geometry, Differential. --- MATHEMATICS / Geometry / Differential. --- A Geometric Approach to Differential Forms. --- A Visual Introduction to Differential Forms and Calculus on Manifolds. --- Cartan. --- David Bachman. --- Einstein. --- Faraday. --- Generalized Stokes Theorem. --- Generalized Stokes’ Theorem. --- Generalized Stokes’s Theorem. --- Jon Pierre Fortney. --- Maxwell. --- Newton. --- Penrose. --- Principia. --- Pseudo-Riemannian Geometry. --- Riemann Tensor. --- Riemannian Geometry. --- curvature. --- curved surfaces. --- electromagnetism. --- general relativity. --- geometric. --- gravitation. --- manifolds. --- moving frames. --- relativity theory. --- space-time. --- spacetime. --- special relativity. --- visual. --- Differential geometry --- Forms, Differential --- Continuous groups --- Geometry, Differential --- Mathematics. --- Math --- Science --- Generalized Stokes' Theorem. --- Generalized Stokes's Theorem. --- Geometry, differential.
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"Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton's geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss's famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein's field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell's equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan's method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book"--Publisher's description
Differential forms. --- Differential forms. --- Formes différentielles. --- Geometry, Differential. --- Geometry, Differential. --- Géométrie différentielle.
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