# Calculus for Beginners and Artists: Prof. Daniel Kleitman, MIT

Professor Daniel Kleitman, Emeritus Professor of Applied Mathematics at MIT

Calculus for Beginners and Artists

From Chapter 1 What is Calculus and Why do we Study it? “Calculus is the study of how things change. It provides a framework for modeling systems in which there is change, and a way to deduce the predictions of such models…It provides a way for us to construct relatively simple quantitative models of change, and to deduce their consequences.”

# MIT: Big Picture of Calculus

MIT Open Courseware

Big Picture of Calculus

“Calculus is about change. One function tells how quickly another function is changing. Professor Strang of MIT shows how calculus applies to ordinary life situations.”

Calculus is required to find any properties of an orbit, for example where an object will be at a given time, or how fast it is travelling at a given position.

# NASA Scientific Visualization Studio

NASA Scientific Visualization Studio

A wonderful resource of visualizations to help understand celestial phenomena.

The SVS makes use of images from e.g. the Lunar Reconnaissance Orbiter and the Deep Space Climate Observatory to create visualizations of phenomena like eclipses of the Moon.

Examples:

Moon Phase and Libration, 2017

“The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 24 seconds, as it is in this animation, our changing view of the Moon makes it look like it’s wobbling. This wobble is called libration.”

2017 Eclipse and the Moon’s Orbit

Shows how the orbital plane of the Moon creates the potential for an eclipse only when the intersection with the ecliptic plane is oriented towards the Sun.

From a Million Miles Away, NASA Camera Shows Moon Crossing Face of Earth

“A NASA camera aboard the Deep Space Climate Observatory (DSCOVR) satellite captured a unique view of the moon as it moved in front of the sunlit side of Earth last month. The series of test images shows the fully illuminated “dark side” of the moon that is never visible from Earth.”