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Calculus, Better Explained: A Guide To Developing Lasting Intuition
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.
Frustrated With Abstract, Mechanical Lessons?
I was too. Despite years of classes, I didn't have a strong understanding of calculus concepts. Sure, I could follow mechanical steps, but I had no lasting intuition.
The classes I've seen are too long, taught in the wrong order, and without solid visualizations. Here's how this course is different:
1) It gets to the point. A typical class plods along, saving concepts like Integrals until Week 8. I want to see what calculus can offer by Minute 8. Each compact, tightly-written lesson can be read in 15 minutes.
2) Concepts are taught in their natural order. Most classes begin with the theory of limits, a technical concept discovered 150 years after calculus was invented. That's like putting a new driver into a Formula-1 racecar on day 1. We can begin with the easy-to-grasp concepts discovered 2000 years ago.
3) It has vivid analogies and visualizations. Calculus is usually defined as the "study of change"... which sounds like history or geology. Instead of an abstract definition, we'll see calculus a step-by-step viewpoint to explore patterns.
4) It's written by a human, for humans. I'm not a haughty professor or strict schoolmarm. I'm a friend who saw a fun way to internalize some difficult ideas. This course is a chat over coffee, not a keep-your-butt-in-your-seat lecture.
The goal is to help you grasp the Aha! moments behind calculus in hours, not a painful semester (or a decade, in my case).
Join Thousands Of Happy Readers
Here's a few samples of anonymous feedback as people went through the course. The material covers a variety of levels, whether you're looking for intuitive appreciation or the specifics of the rules.
"I've done all of this stuff before, and I do understand calculus intuitively, but this was the most fun I've had going through this kind of thing. The informal writing and multitude of great analogies really helps this become an enjoyable read and the rest is simple after that - you make this seem easy, but at the same time, you aren't doing it for us…This is what math education is supposed to be like :)"
"I have psychology and medicine background so I relate your ideas to my world. To me the most useful idea was what each circle production feels like. Rings are natural growth…Slices are automatable chunks and automation cheapens production… Boards in the shape on an Arch are psychologically most palatable for work (wind up, hard part, home stretch). Brilliant and kudos, from one INTP to another."
"I like how you're introducing both derivatives and integrals at the same time - it's really helps with understanding the relationship between them. Also, I appreciate how you're coming from such a different angle than is traditionally taken - it's always interesting to see where you decide to go next."
"That was breathtaking. Seriously, mail my air back please, I've grown used to it. Beautiful work, thank you. Lesson 15 was masterful. I am starting to feel calculus. "d/dx is good" (sorry, couldn't resist!)."
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.
Frustrated With Abstract, Mechanical Lessons?
I was too. Despite years of classes, I didn't have a strong understanding of calculus concepts. Sure, I could follow mechanical steps, but I had no lasting intuition.
The classes I've seen are too long, taught in the wrong order, and without solid visualizations. Here's how this course is different:
1) It gets to the point. A typical class plods along, saving concepts like Integrals until Week 8. I want to see what calculus can offer by Minute 8. Each compact, tightly-written lesson can be read in 15 minutes.
2) Concepts are taught in their natural order. Most classes begin with the theory of limits, a technical concept discovered 150 years after calculus was invented. That's like putting a new driver into a Formula-1 racecar on day 1. We can begin with the easy-to-grasp concepts discovered 2000 years ago.
3) It has vivid analogies and visualizations. Calculus is usually defined as the "study of change"... which sounds like history or geology. Instead of an abstract definition, we'll see calculus a step-by-step viewpoint to explore patterns.
4) It's written by a human, for humans. I'm not a haughty professor or strict schoolmarm. I'm a friend who saw a fun way to internalize some difficult ideas. This course is a chat over coffee, not a keep-your-butt-in-your-seat lecture.
The goal is to help you grasp the Aha! moments behind calculus in hours, not a painful semester (or a decade, in my case).
Join Thousands Of Happy Readers
Here's a few samples of anonymous feedback as people went through the course. The material covers a variety of levels, whether you're looking for intuitive appreciation or the specifics of the rules.
"I've done all of this stuff before, and I do understand calculus intuitively, but this was the most fun I've had going through this kind of thing. The informal writing and multitude of great analogies really helps this become an enjoyable read and the rest is simple after that - you make this seem easy, but at the same time, you aren't doing it for us…This is what math education is supposed to be like :)"
"I have psychology and medicine background so I relate your ideas to my world. To me the most useful idea was what each circle production feels like. Rings are natural growth…Slices are automatable chunks and automation cheapens production… Boards in the shape on an Arch are psychologically most palatable for work (wind up, hard part, home stretch). Brilliant and kudos, from one INTP to another."
"I like how you're introducing both derivatives and integrals at the same time - it's really helps with understanding the relationship between them. Also, I appreciate how you're coming from such a different angle than is traditionally taken - it's always interesting to see where you decide to go next."
"That was breathtaking. Seriously, mail my air back please, I've grown used to it. Beautiful work, thank you. Lesson 15 was masterful. I am starting to feel calculus. "d/dx is good" (sorry, couldn't resist!)."
86 pages, Paperback
Published November 14, 2015
163 people are currently reading
466 people want to read
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Displaying 1 - 18 of 18 reviews
September 19, 2023
Awesome book on Calculus (for intuitive approach)!
April 14, 2016
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.
September 6, 2021
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.
November 19, 2016
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.
June 29, 2016
Telling people what you learned from this book and seeing them get interested in calculus and saying that they "got it" is great.
September 22, 2020
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.
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.
December 22, 2019
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.
June 9, 2017
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
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
December 6, 2019
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.
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.
February 12, 2018
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.
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.
January 13, 2020
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).
September 1, 2017
This made me think about Calculus in a different way and made me appreciate its intrinsic beauty
April 20, 2018
Didn’t add anything to what i already know about Calculus, unfortunately.
February 3, 2019
Kalid is a teacher you wish you had in school
March 21, 2017
I wish someone explain me content of this book when I was in school.
very well written and explained concept on intuition level.
very well written and explained concept on intuition level.
October 1, 2022
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)
(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)
March 3, 2017
Never thought that Mathematics could be taught this way. You wish that you were taught calculus in school in the way the author does!
December 13, 2016
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.
Displaying 1 - 18 of 18 reviews