Chapter 1: Real Variable Functions (PDF)

This first chapter is dedicated to basic concepts: the different kinds of numbers with the properties of real numbers and the real variable functions.

Chapter 2: Limits and Continuity (PDF)

Here we study the concepts of limits with calculation techniques and continuity, including the most important theorems. 

Chapter 3: Derivatives and their Applications (PDF)

This part studies the fundamental tool of Differential Calculus: the derivative. Important theorems are proven together with many applications.

Chapter 4: Local Study of a Function (PDF)

We focus now on the graphic representation of a function and some other applications of the derivatives, arriving at the local approximation using a Taylor polynomial.

Chapter 5: Sequences and Series of Real Numbers (PDF)
This is dedicated to the sequences of numbers with their convergence and limits and, in the second part,  to the series of numbers. What we know about functions will provide help here.

Chapter 6: Sequences and Series of Functions (PDF)
This final chapter studies the sequences and series of functions, leading to the Taylor series.

Última modificación: jueves, 6 de julio de 2023, 18:28