A short book on long sums : infinite series for calculus students / Fernando Q. Gouvêa.
2023
QA295
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Details
Title
A short book on long sums : infinite series for calculus students / Fernando Q. Gouvêa.
ISBN
9783031375576 (electronic bk.)
3031375572 (electronic bk.)
3031375564
9783031375569
3031375572 (electronic bk.)
3031375564
9783031375569
Publication Details
Cham : Springer, 2023.
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-031-37557-6 doi
Call Number
QA295
Dewey Decimal Classification
515/.2432
Summary
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 seriesand infinite series in generalare 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 instructors 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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed December 18, 2023).
Series
Undergraduate texts in mathematics. Readings in mathematics.
Available in Other Form
Print version: 9783031375569
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Table of Contents
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.
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.