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 ...
Read More
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.
Read Less
Add this copy of A Short Book on Long Sums to cart. $54.47, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2023 by Springer.
Add this copy of A Short Book on Long Sums: Infinite Series for Calculus to cart. $55.81, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2023 by Springer.
Add this copy of A Short Book on Long Sums to cart. $61.75, new condition, Sold by Books2anywhere rated 5.0 out of 5 stars, ships from Fairford, GLOUCESTERSHIRE, UNITED KINGDOM, published 2023 by Springer International Publishing AG.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Add this copy of A Short Book on Long Sums: Infinite Series for Calculus to cart. $54.45, new condition, Sold by GreatBookPricesUK5 rated 4.0 out of 5 stars, ships from Castle Donington, DERBYSHIRE, UNITED KINGDOM, published 2023 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Sewn binding. Cloth over boards. 145 p. Contains: Illustrations, black & white, Illustrations, color. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
