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Real Analysis of One Variable

This part of BookofProofs deals with the analysis of real-valued functions with one variable, i.e. the functions of the form $f:\mathbb R\mapsto \mathbb R, x\mapsto f(x)$. Using the axiomatic method, it systematically derives some basic concepts like sequences and limits, real series, continuous real functions, differentiable functions, the Riemann integral, Taylor Series, and Fourier series.

Using the axiomatic method, almost all of these concepts follow from the defining properties of real numbers.

| | | | Contributors: bookofproofs

1.Basics of Real Analysis of One Variable

2.Ordering of Real Numbers and Modulus

3.Proposition: Defining Properties of the Field of Real Numbers

4.Sequences and Limits

5.Real Infinite Series

6.Types of Real Functions

7.Properties of Real Functions

8.Taylor Series

9.Power Series

10.Fourier Series

11.Definition: Real Intervals


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