Part: Real Analysis of Multiple Variables

In this part of BookofProofs we will be dealing with the real analysis of multiple variables. In particular, we will treat topics like the continuity, differentiability and integrability of real-valued functions with multiple variables.

It is the continuation of the study of real analysis of one variable, which in some sense is a prerequisite to this part. In particular, readers familiar with the concepts of real analysis of one variable $x\in\mathbb R$ will recognize that many of these concepts can be generalized for higher dimensions, where $x$ is a vector of a $n$-dimensional Euclidean vector space $x\in\mathbb R^n$, $n > 1$.

Theoretical minimum (in a nutshell)

With respect to this, before you dive deeper into the material to follow, you might find it helpful to make sure that you are acquainted with some basic facts treated elsewhere in BookofProofs. Ideally, you should be already acquainted with:

Concepts you will learn in this part of BookofProofs

  1. Chapter: Differentiability
  2. Chapter: Integrability
  3. Chapter: Fixed Point Theory
  4. Definition: Curves In the Multidimensional Space \(\mathbb R^n\)
  5. Definition: Generalized Polynomial Function
  6. Proposition: Definition of the Metric Space \(\mathbb R^n\), Euclidean Norm

Parts: 1 2

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