Functions and Analysis

    

The Study of Functions

Authors: Teo Banica

This is an introduction to the study of real functions, $f:mathbb Rtomathbb R$. We first discuss motivations and examples, ways of representing functions, and with a detailed look into the basic functions, namely polynomials, and $sin,cos,exp,log$. Then we discuss continuity, with the standard results on the subject, and notably with the Weierstrass approximation theorem. We then discuss derivatives, again with the standard results on the subject, notably with the Taylor formula and its applications. Finally, we discuss integrals, with what can be done with Riemann sums, the relation with the derivatives, and with a look into more advanced functional analysis, and several variables too.

Comments: 400 Pages.

Download: PDF

Submission history

[v1] 2025-12-21 23:29:17

Unique-IP document downloads: 300 times

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