Some ideas on how we learn mathematics.
Short story of the concept of derivative.
Reals as infinite decimal sequences.
Motivations of the reals.
Models associated to elementary functions.
Diffculties associated to the concept of limit.
Defining the derivative without limits.
A continuos nowhere differentiable function.
A critical analysis of the Riemann and Darboux integrals.
How to teach the integral.
Material collected from various sources, indicated at http://web.math.unifi.it/users/bianchi/programma_corso_didattica_calcolo_in_linea.html
Learning Objectives
Think about the didactical aspects of the main concepts of calculus
Prerequisites
Advanced Calculus
Teaching Methods
Lectures
Type of Assessment
Give a lecture and pass an oral exam
Course program
Some ideas on how we learn mathematics
Short story of the concepts of derivative
Reals as infinite decimal sequences
Motivation of the reals
Models associated to elementary functions
Diffculties associated to the limit
Defining the derivative without limits
A continuos nowhere differentiable function
A critical analysis of the Riemann and Darboux integrals
How to teach the integrals