Here, you find my whole video series about Real Analysis in the correct order and I also help you with some text around the videos. If you want to test your knowledge, please use the quizzes, and consult the PDF version of the video if needed. When you have any questions, you can use the comments below and ask anything. However, without further ado let’s start:
Real analysis is a video series I started for everyone who is interested in calculus with the real numbers. It is needed for a lot of other topics in mathematics and the foundation of every new career in mathematics or in fields that need mathematics as a tool:
With this you now know the topics that we will discuss in this series. Some important bullet points are limits, continuity, derivatives and integrals. In order to describe these things, we need a good understanding of the real numbers. They form the foundation of a real analysis course. Now, in the next video let us discuss sequences.
The notion of a sequence is fundamental in a lot of mathematical topics. In a real analysis course, we need sequences of real numbers, which you can visualise as an infinite list of numbers:
Now you know what a convergent sequence is. However, not all sequences are convergent. A weaker property is the notion of a bounded sequence.
At this point you know a lot about sequences, especially about convergent sequences. Since we do not want to work every time with the definition, using epsilons and so on, we prove the following limit theorems: