Calculus, Better Explained: A Guide To Developing Lasting Intuition

by Kalid Azad

Calculus, Better Explained is the calculus primer you wish you had in school. Learn the essential concepts using concrete analogies and vivid diagrams, not mechanical definitions. Calculus isn't a set of rules, it's a specific, practical viewpoint we can apply to everyday thinking.

Genres: Mathematics, Science, Nonfiction, Calculus, Technical

86 pages, Paperback

Published November 14, 2015

Reviews

[Reet · Rating 4 out of 5]

Awesome book on Calculus (for intuitive approach)!

[Nick · Rating 4 out of 5]

I liked this book a lot. The explanations were very digestible and the equations have me mental meat to chew on. I feel like I would need to sit down and read a little bit every day to full understand it (versus the quick read through I just did), but it definitely did help me to understand what Calculus fundamentally is and why it is important.

[Yura Gavrilovich · Rating 3 out of 5]

I like that the book is short, has a lot of visualizations and tries to explain calculus in a straightforward way. But for some reason most analogies from this book didn't "click" for me.

[Roberto Rigolin F Lopes · Rating 4 out of 5]

About 2200 years ago, Archimedes figured out the formulas for area and volume of a sphere. The man was genius but this challenge probably took quite a bit of his brainpower. Nowadays anyone can replicate his "Aha!" moments using Calculus + computers. This book is a guide through Archimedes brilliant reasoning showing off Calculus as a useful and intuitive tool. Kalid shares ingenious analogies to explain differentiation/integration refreshing your view of Calculus. The whole thing is an exciting show that may ignite further studies.

[Alex · Rating 5 out of 5]

Telling people what you learned from this book and seeing them get interested in calculus and saying that they "got it" is great.

[Art Thomas · Rating 5 out of 5]

I read this here and there over the last month and a half. It had been a while since I took a true calculus class and figured why not start with the basics to get my mind in the right place?

My relationship with calculus is somewhat complicated. I took it in high school and never really got the mechanics behind it. My teacher was just OK, and really made it more about memorization and shortcuts. Fine for high school I guess but it took away a lot of the magic of math.

I then took it again in college and it was fine but also just seemed very rigorous. I changed majors (not because of calc, it was just a byproduct) and didn't really take it again until I was prepping for graduate school. That's when it really took off. I took calc 1, 2 and 3 at my local community college. Taught by a retired professor it was math the way it should be, taking calculus from the ground up and really visualizing what everything meant. My appreciation for the beauty of the math was finally there.

This book is very reminiscent of those classes for me. It's basic but moves away from memorization and formulas to what integrals and derivatives really are. I'd recommend it for anyone starting to learn calculus or anyone returning for a primer.

[Micyukcha · Rating 4 out of 5]

Geometry as a way to calculus! Azad uses visualizations, intuition and normal language over formulas, rote memorization and jargon. Integrals and derivatives actually make sense now. Reminds me of flatland, which probably helped me build that narrative intuition for the rules and theory of calculus. It also reminds me of how we take data as reality (as opposed to representation), in the sense that the dimensions we see and can’t see form our concept of truth and in math are represented by formulas as opposed to the formulas representing reality. Once that sequence is agreed upon, there is a small inkling or sensation that there is a reality past the reality as sensed by our default normal daily interactions.

[Loren · Rating 4 out of 5]

Explains the why behind the math. It will be particularly helpful if u at least have a rudimentary understanding of calculus and tend to be a more visual type of

Explains the why behind the math. It will be particularly helpful if you are at least rudimentarily conversant with calculus already and are a visual person

[Venkatesh-Prasad · Rating 4 out of 5]

Good supplement to understand basics of calculus

While few parts of the book seemed a bit hurried, overall the book was similar to the author's earlier book on math -- helps to build the intuition about calculus with lots of diagrams and step by step unfolding of derivations with explanation.

[Timeo Williams · Rating 4 out of 5]

Well done Kalid

A wonderful intuitive display of Calculus. With great day to day examples and images. Much appreciated Kalid. I recommend this book for those looking to understand this topic in a very simplified manner.

[Paweł Cisło · Rating 4 out of 5]

Author intuitively explains steps into calculus that took the brightest minds of our planet 2000 years of thought to discover. After the lecture, you should understand that most of the idea works around X-Ray and Time-Lapse Vision (splitting things apart and glueing together).

[Kevin · Rating 5 out of 5]

This made me think about Calculus in a different way and made me appreciate its intrinsic beauty

[- · Rating 2 out of 5]

Didn’t add anything to what i already know about Calculus, unfortunately.

[Kaustubh Sule · Rating 5 out of 5]

Kalid is a teacher you wish you had in school

[Chetan Dhembre · Rating 5 out of 5]

I wish someone explain me content of this book when I was in school.
very well written and explained concept on intuition level.

[Craine · Rating 5 out of 5]

Just a phenomenal entry book to working with the intuitions behind calculus. A must read for anyone remotely interested in mathematics, with emphasis on entry level university or the keen high school student. I should mention that this book however, should not be treated as a textbook. There are hardly any exercises and as title emphasizes its all about developing intuitions behind the most central themes in calculus. His formulation of treating the derivative as x-raying an object
(splitting a shape into sections as we move along a path) and integration as "gluing together" sections and measuring the result is especially ingenious

My only objection is that I wish the book was longer, but that is I'm sure a general sentiment shared by all readers of this marvelous book.

(Note I don't like the star rating and as such I only rate books based upon one star or five stars corresponding to the in my opinion preferable rating system of thumbs up/down. This later rating system encourages in my opinion the degree to which the reader is likely to engage with a review instead of merely glancing at the number of stars)

[Prashant Ghabak · Rating 4 out of 5]

Never thought that Mathematics could be taught this way. You wish that you were taught calculus in school in the way the author does!

[Ben Gutierrez · Rating 4 out of 5]

This is not a substitute for a course in calculus. It's meant to provide some different ways of thinking about calculus, which has been notoriously difficult for students to think about. It's not the best math writing out there, and it's certainly not the most rigorous, but it gets the job done. I will recommend this little book to anyone trying to understand calculus better.