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Analytical topology --- Functional analysis --- Afbeeldingen (Wiskunde) --- Applications (Mathematiques) --- Fonctions continues --- Functies [Doorlopende ] --- Functions [Continuous ] --- Mappings (Mathematics) --- Maps (Mathematics) --- Functions, Continuous. --- Applications (Mathématiques) --- 515.126 --- Functions, Continuous --- Functions --- Topology --- Transformations (Mathematics) --- Continuous functions --- Continuous mappings --- 515.126 Continuous mappings --- Applications (Mathématiques)
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515.142.2 --- General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- Differential forms. --- Homology theory. --- 515.142.2 General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories
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512.58 --- 515.142.2 --- Categories (Mathematics) --- -Topological algebras --- -Algebraic topology --- -Topology --- Algebras, Topological --- Functional analysis --- Linear topological spaces --- Rings (Algebra) --- Categories. Category theory --- General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- Congresses --- Algebraic topology --- Topological algebras --- Congresses. --- -Categories. Category theory --- 515.142.2 General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- 512.58 Categories. Category theory --- -515.142.2 General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories
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Algebraic topology --- Topological transformation groups. --- 515.14 --- 515.142.2 --- Homology theory --- Topological transformation groups --- Manifolds (Mathematics) --- Transformation groups --- Cohomology theory --- Contrahomology theory --- General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- 515.142.2 General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- 515.14 Algebraic topology
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Ordinary differential equations --- Topology --- 515.126 --- 512.541.5 --- 512.76 --- Continuous mappings --- Mappings of a group into itself and into other groups. Automorphisms. Endomorphisms. Characteristic subgroups. Homomorphic images of a group. Equivalent Abelian groups. Quasi-isomorphisms --- Birational geometry. Mappings etc. --- Functions of real variables. --- Mappings (Mathematics) --- Topological dynamics. --- Mappings (Mathematics). --- 512.76 Birational geometry. Mappings etc. --- 512.541.5 Mappings of a group into itself and into other groups. Automorphisms. Endomorphisms. Characteristic subgroups. Homomorphic images of a group. Equivalent Abelian groups. Quasi-isomorphisms --- 515.126 Continuous mappings
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515.1 --- 512.58 --- 515.142.2 --- Topology --- Categories. Category theory --- General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- 515.142.2 General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- 512.58 Categories. Category theory --- 515.1 Topology --- Categories (Mathematics) --- Congresses. --- Topologie --- Catégories (mathématiques)
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Topology --- Fixed point theory. --- Mappings (Mathematics) --- 515.126.4 --- 515.142.22 --- 512.813 --- Fixed point theory --- Homotopy theory --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Transformations (Mathematics) --- Deformations, Continuous --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics) --- Fixed points and coincidences --- Study of topological spaces and continuous mappings by homological methods. Homological dimension theory. Homological theory of fixed points and coincidence points --- Special classes of Lie groups. Compact, semisimple, solvable, nilpotent Lie groups --- Homotopy theory. --- Mappings (Mathematics). --- 512.813 Special classes of Lie groups. Compact, semisimple, solvable, nilpotent Lie groups --- 515.142.22 Study of topological spaces and continuous mappings by homological methods. Homological dimension theory. Homological theory of fixed points and coincidence points --- 515.126.4 Fixed points and coincidences
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Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms. Some praise for the previous edition: "The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often, the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of particular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, a discussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches like this are not isolated cases; the book includes a large number of notes on people and ideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities." --Physics Today "Very well written (i.e., extremely readable), very well targeted (mainly to an average student of physics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's with applications and with all their necessary pedagogically-mathematical background)...The main merits of the text are its clarity (achieved via returns and innovations of the context), balance (building the subject step by step) and originality (recollect: the existence of the complex numbers is only admitted far in the second half of the text!). Last but not least, the student reader is impressed by the graphical quality of the text (figures first of all, but also boxes with the essentials, summarizing comments in the left column etc.)...Summarizing: Well done." --Zentralblatt MATH.
Mathematical physics -- Problems, exercises, etc. --- Mathematical physics -- Study and teaching. --- Mathematical physics. --- Mathematical physics --- Applied Physics --- Physics - General --- Physics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Study and teaching. --- Physical mathematics --- Mathematics --- Fréchet spaces. --- Fréchet spaces --- Espaces nucléaires (Analyse fonctionnelle) --- 515.142.2 --- General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- 515.142.2 General topological categories. Categories whose objects are topological spaces subject to various general restrictions, and whose morphisms are either continuous mappings or homotopy classes of such mappings. Other closely related categories --- Physics. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Mathematical Methods in Physics. --- Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 512.58 --- 512.58 Categories. Category theory --- Categories. Category theory --- Analytical spaces --- Algebraic topology --- Categories (Mathematics) --- Topology --- Congresses. --- Linear operators. --- Nuclear spaces (Functional analysis). --- Nuclear spaces (Functional analysis) --- Linear operators --- Opérateurs linéaires --- Global analysis (Mathematics). --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Fréchet, Espaces de. --- Fréchet spaces. --- Topologie --- Catégories (mathématiques) --- 517.1 Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Espaces nucléaires (analyse fonctionnelle) --- Fréchet, Espaces de. --- Espaces nucléaires (analyse fonctionnelle) --- Topology. --- Catégories (mathématiques) --- Topologie generale --- Analyse fonctionnelle --- Espaces particuliers --- Espaces de suites
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