Functions and Analysis

    

Calculus and Applications

Authors: Teo Banica

This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:mathbb Rtomathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and of the integral $int_a^bf(x)dx$. Then we investigate the case of the complex functions $f:mathbb Ctomathbb C$, and notably the holomorphic functions, and harmonic functions. Then, we discuss the multivariable functions, $f:mathbb R^Ntomathbb R^M$ or $f:mathbb R^Ntomathbb C^M$ or $f:mathbb C^Ntomathbb C^M$, with general theory, integration results, maximization questions, and basic applications to physics.

Comments: 400 Pages.

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Submission history

[v1] 2024-01-02 03:38:09
[v2] 2026-01-01 00:42:27

Unique-IP document downloads: 362 times

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