Titlebook: A Short Book on Long Sums; Infinite Series for Fernando Q. Gouvêa Textbook 2023 The Editor(s) (if applicable) and The Author(s), under exc

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Textbook 2023izes understanding the fundamental ideas. Power series—and infinite series in general—are? a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural.?.Calculus is about functions, so the book turns

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A Short Book on Long Sums978-3-031-37557-6Series ISSN 0172-6056 Series E-ISSN 2197-5604

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978-3-031-37559-0The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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https://doi.org/10.1007/978-3-030-97895-2We look into the distance and outline some of the ways the theory can be extended. We consider functions of a complex variable, more general series and the issue of uniform convergence, Fourier series, and finally take a quick look at Dirichlet series.