Calculus I

The course will teach you to deal with functions in one (real) variable. The syllabus includes an introduction to real numbers, sequences and series, as well as differential and integral calculus in one variable.

For my lectures I use my colleague Jose Cuesta’s Calculus book, which I find has a great balance between mathematical rigor and calculation techniques.

Based on the book, I recorded a series of lectures covering the whole text. They are hosted in my Youtube channel, and you can find a link to the lectures at the OCW UC3M page. Alternatively, you can find all the lectures under one playlist here.

Here is an example of a lecture video, where I prove that square root of 2 is irrational:

Also, in Cuesta’s book there are many exercises for each chapter, and these are solved, both in PDF and video format.

An example of problem-resolution video: