Cartesian Coordinates: An Introduction to Vectors and Basic Vector Functions (The New Mathematics for the Millions Book 20)

The measurements that are taken in the physical sciences involve different types of quantities. Some are just measurement of magnitude, things that are called scalars. Some measurements involve both magnitude and direction, things that are called vectors and some even more intricate measurements involve higher order things called tensors.

This book is an introduction to vectors written for students at a high school or first year university level. The books is written for students sho have never worked with vectors before and is also good for students who want to review or improve on their understanding of vectors.

There are also thirty two worked through examples as well as book questions designed to help you learn about vectors.

The first two types of measurements – measurements of magnitudes and measurements with both magnitude and direction – are the subject of this book. Tensors will not be touched upon in this book but will be a topic for another The New Mathematics for the Millions books.

One of the oldest discoveries, a discovery that dates back to ancient times, is that all natural phenomena can be characterized in terms of measurements of their physical characteristics.

It was in fact an article of faith of the Pythagoreans that order in the universe can be characterized in terms of numbers. The past twenty centuries have added substance to the pursuit of scientific knowledge. Modern day science and mathematics, and our belief in measurement as a foundation in the pursuit of “Cause and Effect” relationships – what we call phenomena – make us modern day Pythagoreans.

Measurement of mere magnitudes, measurements involving scalars, is taught through middle school. When high school students come across Vectors for the first time – measurements involving both a magnitude and direction – they more times than nought become anxious. This sometimes also happens when they come across Calculus.

While “Calculus is just applied algebra with a few new ideas thrown in,” vectors are less difficult than even the algebra that we are taught in middle school. If you mastered algebra, then you will master both Calculus and Vectors. For those of you who are interested, there are several books in the The New Mathematics for the Millions series that touch on different aspects of Calculus.

If this is your first introduction to Vectors, don’t fret. If this is a refresher or you are working at mastering vectors, might I paraphrase what the Nobel Prize winning physicist Richard Feynman once said when asked by a journalist how he learned his physics:

“If I didn’t understand something the first time, I would read it a second time. If I didn’t understand it the second time, I read it a third time. If I did not understand it the third time, I tossed the thing aside and went onto something else.”

At which the journalist quipped “surely you must be Joking Dr. Feynman.” Richard Feynman merely shook his head.