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A short book on long sumsinfinite series for calculus students /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A short book on long sumsby Fernando Q. Gouvêa.
其他題名:	infinite series for calculus students /
作者:	Gouvea, Fernando Q.
出版者:	Cham :Springer Nature Switzerland :2023.
面頁冊數:	xi, 145 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Power series.
電子資源:	https://doi.org/10.1007/978-3-031-37557-6
ISBN:	9783031375576$q(electronic bk.)

A short book on long sumsinfinite series for calculus students /
Gouvea, Fernando Q.

A short book on long sumsinfinite series for calculus students /[electronic resource] :by Fernando Q. Gouvêa. - Cham :Springer Nature Switzerland :2023. - xi, 145 p. :ill., digital ;24 cm. - Readings in mathematics,2945-5847. - Readings in mathematics..

- To the reader -- Getting close with lines -- Getting closer with polynomials -- Going all the way: Convergence -- Power series -- Distant mountains -- Appendix A: SageMath: A (very) short introduction -- Appendix B: Why I do it this way -- Bibliography.

This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes 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 on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions. The derivative is reinterpreted in terms of linear approximations, which then leads to Taylor polynomials and the question of convergence. Enough of the theory of convergence is developed to allow a more complete understanding of power series and their applications. A final chapter looks at the distant horizon and discusses other kinds of series representations. SageMath, a free open-source mathematics software system, is used throughout to do computations, provide examples, and create many graphs. While most problems do not require SageMath, students are encouraged to use it where appropriate. An instructor's guide with solutions to all the problems is available. The book is intended as a supplementary textbook for calculus courses; lecturers and instructors will find innovative and engaging ways to teach this topic. The informal and conversational tone make the book useful to any student seeking to understand this essential aspect of analysis.

ISBN: 9783031375576$q(electronic bk.)

Standard No.: 10.1007/978-3-031-37557-6doiSubjects--Topical Terms:

468018
Power series.

LC Class. No.: QA295

Dewey Class. No.: 515.2432

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520 $a This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes 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 on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions. The derivative is reinterpreted in terms of linear approximations, which then leads to Taylor polynomials and the question of convergence. Enough of the theory of convergence is developed to allow a more complete understanding of power series and their applications. A final chapter looks at the distant horizon and discusses other kinds of series representations. SageMath, a free open-source mathematics software system, is used throughout to do computations, provide examples, and create many graphs. While most problems do not require SageMath, students are encouraged to use it where appropriate. An instructor's guide with solutions to all the problems is available. The book is intended as a supplementary textbook for calculus courses; lecturers and instructors will find innovative and engaging ways to teach this topic. The informal and conversational tone make the book useful to any student seeking to understand this essential aspect of analysis.
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