![]() (PS: A kind reader has created an animated powerpoint slideshow that helps present this idea more visually (best viewed in PowerPoint, due to the animations). Let’s fingerpaint a bit, and get into the chemistry along the way. The natural log can be seen as an integral, or the time needed to grow. Case in point: e is technically defined by a limit, but the intuition of growth is how it was discovered. Would it be so bad if everyone understood calculus to the “non-rigorous” level that Newton did? That it changed how they saw the world, as it did for him?Ī premature focus on rigor dissuades students and makes math hard to learn. I don’t want to (and can’t) teach an analysis course or train researchers. We’re looking at the sweetness of sugar from the level of brain-chemistry, instead of recognizing it as Nature’s way of saying “This has lots of energy. We’ve created complex mechanical constructs to “rigorously” prove calculus, but have lost our intuition in the process. Just a few words on “rigor”.ĭid you know we don’t learn calculus the way Newton and Leibniz discovered it? They used intuitive ideas of “fluxions” and “infinitesimals” which were replaced with limits because “Sure, it works in practice. I can feel the math pedants firing up their keyboards. That’s just not happening with your velocity equation. That ring/circle thing we made? You could build it out of several pipe cleaners, separate them, and straighten them into a crude triangle to see if the math really works. 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. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there.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. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Stop fearing calculus, and learn to embrace the challenge. Features things to remember, things to forget, and things you can't get away with.Instructs you how to approximate area with integration.Explores sequences, series, and graphing common functions.Includes foundations in algebra, trigonometry, and pre-calculus concepts.It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win. Breaking that barrier down means recognizing calculus for what it is-simply a tool for studying the ways in which variables interact. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be.Ĭalculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. Slay the calculus monster with this user-friendly guideĬalculus For Dummies, 2nd Edition makes calculus manageable-even if you're one of the many students who sweat at the thought of it. Science Fiction
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