Category: Calculus
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The Ultimate Guide of Integration
One of the first signs that you have mastered calculus (and much of advanced mathematics and physics) is that you can look at expressions involving integrals and immediately understand what they are saying. We wrote The Guide to Integrals so that you can learn exactly how to do that. You first need to build strong…
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The 7 Deadly Sins of Calculus
You have probably seen expressions like these: These are actually warning signs telling us that two quantities are competing and that direct substitution is not enough. Understanding them is essential because they appear everywhere in limits, and limits are the foundation of all calculus. I created a visual guide explaining where all 7 forms come…
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How Trigonometry Turns Triangles into Waves
If you have an analytical mind, you probably noticed that waves appear everywhere around us. But the secret to describe them is by studying triangles. So, the question is: How do you get from a triangle to a wave in a natural way, just by following the math? After you understand this connection between them,…
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The Most Important Concept in Calculus
I’ve been teaching calculus for about 9 years now, but when I was learning it for the very first time I remember that I couldn’t understand the relation between limits, derivatives, integrals, sequences and series. They seemed completely unrelated to each other. Now I know that the problem is that I was missing the big…
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The Language of Calculus
Take a look at this equation: 1+sinx+1−sinx=3\sqrt{1+\sin x} + \sqrt{1-\sin x}=\sqrt{3} Now, think to yourself: “How would you go about solving it?” You don’t need to know Calculus to do it, but you do need a very strong foundation in the Language of Calculus. This is actually the main reason people struggle so much with…
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The Roadmap to Master Calculus
The PDF is accompanied by this video. We’d like to keep our videos free of interruptions and sponsors, so that the sole focus is the subject at hand. If you find value in our videos and would like to support our work further, and get very useful info that is unavailable anywhere else, consider purchasing…