Luis Bernal González - Böcker

Real Analysis: An Undergraduate Problem Book for Mathematicians, Applied Scientists, and Engineers is a classical Real Analysis/Calculus problem book. This topic has been a compulsory subject for every undergraduate studying mathematics or engineering for a very long time. This volume contains a huge number of engaging problems and solutions, as well as detailed explanations of how to achieve these solutions. This latter quality is something that many problem books lack, and it is hoped that this feature will be useful to students and instructors alike. FeaturesHundreds of problems and solutionsCan be used as a stand-alone problem book, or in conjunction with the author’s textbook, Real Analysis: An Undergraduate Textbook for Mathematicians, Applied Scientists, and Engineers, ISBN 9781032481487Perfect resource for undergraduate students studying a first course in Calculus or Real AnalysisContains explanatory figures, detailed techniques, tricks, hints, and “recipes” on how to proceed once we have a calculus problem in front of us.

Real Analysis: An Undergraduate Problem Book for Mathematicians, Applied Scientists, and Engineers is a classical Real Analysis/Calculus problem book. This topic has been a compulsory subject for every undergraduate studying mathematics or engineering for a very long time. This volume contains a huge number of engaging problems and solutions, as well as detailed explanations of how to achieve these solutions. This latter quality is something that many problem books lack, and it is hoped that this feature will be useful to students and instructors alike. FeaturesHundreds of problems and solutionsCan be used as a stand-alone problem book, or in conjunction with the author’s textbook, Real Analysis: An Undergraduate Textbook for Mathematicians, Applied Scientists, and Engineers, ISBN 9781032481487Perfect resource for undergraduate students studying a first course in Calculus or Real AnalysisContains explanatory figures, detailed techniques, tricks, hints, and “recipes” on how to proceed once we have a calculus problem in front of us.

Renewed interest in vector spaces and linear algebras has spurred the search for large algebraic structures composed of mathematical objects with special properties. Bringing together research that was otherwise scattered throughout the literature, Lineability: The Search for Linearity in Mathematics collects the main results on the conditions for the existence of large algebraic substructures. It investigates lineability issues in a variety of areas, including real and complex analysis.After presenting basic concepts about the existence of linear structures, the book discusses lineability properties of families of functions defined on a subset of the real line as well as the lineability of special families of holomorphic (or analytic) functions defined on some domain of the complex plane. It next focuses on spaces of sequences and spaces of integrable functions before covering the phenomenon of universality from an algebraic point of view. The authors then describe the linear structure of the set of zeros of a polynomial defined on a real or complex Banach space and explore specialized topics, such as the lineability of various families of vectors. The book concludes with an account of general techniques for discovering lineability in its diverse degrees.