Screen LibraryIntroduction to mathematical analysis
The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, theLebesgue integral, vector calculus and differential equations. After having created a solid foundation of topology...
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| Literature type: | Electronic eBook |
| Language: | English |
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| Online Access: |
http://dx.doi.org/10.1007/978-3-0348-0636-7 |
| Summary: |
The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, theLebesgue integral, vector calculus and differential equations. After having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today. |
| Carrier Form: | 1 online resource (510 p.) |
| Bibliography: | Includes bibliographical references and indexes. |
| ISBN: |
9783034806367 (electronic bk.) 3034806361 (electronic bk.) |
| Index Number: | QA300 |
| CLC: | O17 |
| Contents: |
A Rigorous Approach to Advanced Calculus. Preliminaries -- Metric and Topological Spaces I -- Multivariable Differential Calculus -- Integration I: Multivariable Riemann Integral and Basic Ideas Toward the Lebesgue Integral -- Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration -- Systems of Ordinary Differential Equations -- Systems of Linear Differential Equations -- Line Integrals and Green's Theorem -- Analysis and Geometry. Metric and Topological Spaces II -- Complex Analysis I: Basic Concepts -- Multilinear Algebra -- Smooth Manifolds, Differential Forms and Stokes' Theorem -- Complex Analysis II: Further Topics -- Calculus of Variations and the Geodesic Equation -- Tensor Calculus and Riemannian Geometry -- Banach and Hilbert Spaces: Elements of Functional Analysis -- A Few Applications of Hilbert Spaces. |