In these four modules (module 1, module 2, module 3, module 4), you will use your coding skills to understand the fundamental concepts of precalculus and calculus. More specifically, you will use the R programming language and its powerful graphical tools to visually explore the concepts like function, limit, continuity, differentiation and integration.
Many high-schooler find calculus difficult, because its concepts appear too abstract. Although various resources are available to help students pass exams, a "drilling approach" for calculus does not help in the long run. A solid foundation is needed to excel in college engineering and science classes.
Calculus can be better understood, when accompanied by visual presentation of the ideas. All concepts like limit, continuity, differentiation and integration have geometric meaning. Moreover, visual presentation is easier to grasp than algebraic manipulation of symbols. However, visual study of calculus had been challenging in the past, because drawing each function on graph papers got rather tiring.
This module covers limits and derivatives. The concept of derivative will be presented both as an operation and as visual analysis. We will follow the book "Calculus Made Easy" written anonymously by British mathematician Silvanus Thompson. This hundred year old book is still popular and it never went out of print.
|week 1 (Dec 2)||Derivative as an operation on functions, practice|
|week 2 (Dec 9)||Understanding slpes of functions, and derivatives|
|week 3 (Dec 16)||Concept of limit, dy/dx --> linking algebra and geometry|
|week 4 (Jan 6)||Uses of derivatives, Maxima and minima using visualization|