Real Analysis

Prerequisites

Order	Page	Concepts	Notes
1	Functions	What is a function? Domain, codomain, image, inverse image.
2	Injections, Surjections and Bijections	Injective, surjective and bijective functions. Inverse functions. Involutions.
3	Functions	Function composition.

Analysis of Real Functions

Order	Page	Concepts	Notes
1	[[Functions of the Real Numbers#real-valued-functions	Real functions]]	Real-valued and real functions.
2	Boundedness of Real Functions	Bounded functions.
3	[[Periodicity	Periodicity of Real Functions]]	Periodicity and antiperiodicity of real functions.
4	[[Monotony	Monotony of Real Functions]]	Increasing and decreasing functions.
5	Real Sequences	Real sequences, both finite and infinite.
6	Real Sequences	Convergence and limits of real sequences.
7	Real Sequences	Monotony of real sequences.
8	Limits of Real Functions	One-sided limits, two-sided limits, infinite limits, limits at infinity.
9	Limits of Real Functions	Linearity of limits, arithmetic with limits.	Ignore L’Hôpital’s rule for now.
10	Limits of Real Functions	Asymptotes and how to find them.
11	Continuity of Real Functions	Continuity of real functions, properties of continuous functions.	Ignore properties related to integration for now.
12	Differentiation of Real Functions	Differentiability and derivatives of real functions, differentiation rules, common derivatives.
13	Extrema	Minima and maxima of real functions, using derivatives to find extrema.
14	[[Monotony#criteria	Monotony Criteria]]	Testing a function for monotony via derivatives.