I have text-books about Taylor series but they do not mention Taylor series applications. Can anyone please suggest a few references to learn the same?
2026-04-01 00:25:32.1775003132
Can someone recommend for me a text-book about applications of Taylor series?
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I don't know of any textbook that focuses on applications of Taylor series.
However, here is a list (in French) of theorems that can be proved as applications of Taylor's formula. The proofs are not given in the document, but reference is made to books where the proofs can be found. The material would be roughly at the upper undergraduate level (years 3 and 4 of university) in the U.S.
https://agreg-maths.fr/uploads/versions/596/218.pdf
Here are other similar documents.
https://www.imo.universite-paris-saclay.fr/~perrin/CAPES/analyse/fonctions/formulesdetaylor%2807%29.pdf
http://perso.eleves.ens-rennes.fr/people/emeline.luirard/Lecons/218.pdf
For simple applications to computing approximate values of functions that could be understood by a first-year student, have a look at Chapter 14 of A First Course in Calculus, 3rd ed. by Serge Lang.