Abstract:

This work describes a Mathematic Modeling Fundamental hybrid course based on the solution of learning challenges using Differential and Integral Calculus of one variable. This course has been developed on the OpenEdx and the Canvas platforms. This course is built in order to provide engineering students with the abilities necessary to analyze and solve basic problems of Calculus.

The course consists of ten units or modules:
1) Modeling movement
2) Relationship of derivative and integral to the light of motion,
3) Using transcendent functions,
4) Using derivation rules,
5) Optimization and definite integral,
6) Geometric applications of the integral,
7) Physical applications of the definite integral,
8) Basic integration techniques,
9) Other integration techniques, and
10) The infinity and improper integrals.

On each module, the necessary theory is briefly explained through interactive videos and short notes on the topics. Besides this, the course includes: an e-Book, computational simulations using Mathematica and Matlab, an adaptive trainer for problems and exercises, a comprehensive activity about concepts and an evaluation activity. The course offers a real life situations or a mathematical challenges to be solved in a collaborative way, by example: “The hourglass”, “Roller coaster accident”, and “Covid in Mexico”.

The goal of this course is to develop the student’s abilities for mathematical modelling through differential and integral Calculus. Technology being implemented lets to give an individual following to each student. Finally, we show the results obtained recently by the students that took part in the course, and we also show several examples with their answers to the proposed problems and challenges.

Keywords:

Learning challenges, Differential Calculus, Integral Calculus