![]() ![]() I prefer starting with physical, visual examples because it’s how our minds work. That’s great, but it can be hard to relate: honestly, how often do you know the equation for velocity for an object? Less than once a week, if that. Many calculus examples are based on physics. And sometimes the little things are easier to work with. This is a recurring theme in calculus: Big things are made from little things. Calculus showed us that a disc and ring are intimately related: a disc is really just a bunch of rings. This was a quick example, but did you catch the key idea? We took a disc, split it up, and put the segments together in a different way. Yowza! The combined area of the rings = the area of the triangle = area of circle! Calculus lets us start with $\text (r) (2 \pi r) = \pi r^2$, which is the formula for area! But most of us learn these formulas independently. Don’t these formulas seem related in some way? It all fits together.Ĭalculus is similarly enlightening. You know why sugar and fat taste sweet (encourage consumption of high-calorie foods in times of scarcity). You understand why drugs lead to resistant germs (survival of the fittest). My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms of survival. Thanks to Anish.dot for the original scan.I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education.Ĭalculus relates topics in an elegant, brain-bending manner. ![]() Is appealed to it, the author will consider his mission as successfully Of the intrinsic beauty and integrity of higher mathematics or even And if in the long run the reader of the book gets a feeling Briefly, theseĭiscussions are intended to assist pupils entering a novel world ofĬalculus. Numerical sequence, limit of sequence, and function. It will lead the reader to better understanding of such concepts as I hope that this form of presentation will help a reader of theīook in learning new definitions such as those of derivative, antiderivative, definite. Inner logic of proofs, and attracting the reader’s attention to special READER to different notions, ideas, and theorems of calculus,Įmphasizing especially complicated or delicate aspects, stressing the To another the AUTHOR will lead the inquisitive and receptive The whole book is presented as a relatively free-flowingĭialogue between the AUTHOR and the READER. What better way to proofread than using 1000s of eyes? We plan to digitise all the important books with LaTeX in the near future, let me know if you want to pitch in. Please point them and I will correct them. There might be a few typos here and there or the mathematical mistakes. let me know if you are ready for volunteering for that. I have redrawn some of them like the ones above, but I would need some help with doing all of them. Some of the diagrams I have drawn using TiKz.Īt other places, I have used the existing diagrams.įor now, I have used the some of the old figures from the scan, but it would be fun to redraw them using TiKz. The result was immensely satisfying to see and is aesthetically pleasing as well.īelow are a few sample pages from the book: And the final result is a beautifully typeset book which is of the best out there for the given subject. With LaTeX the equations are typeset really beautifully. We have used XeLaTeX for typesetting the book, and friends it was fun indeed to do it. But instead, it is a completely electronic version of the book created using LaTeX! Now, many of you must be wondering why a re-post of a book? The answer is that this is not a scan of the original book. In this post, we will see the book Calculus: Basic Concepts for High Schools by Lev Tarasov. ![]()
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