Author: DiBeo’s
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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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Top 23 Differential Equations in Mathematical Physics
Hi it’s Luca, Here is a list of the TOP 23 differential equations in mathematical physics, together with the areas they belong to: Classical Mechanics (1) Newtons Second Law (2) Simple Harmonic Oscillator (3) Euler–Lagrange Equation (4) Hamilton Equations (5) Hamilton–Jacobi Equation Basic ODE Models (6) Radioactive Decay Law (7) Logistic Growth Equation Diffusion and…
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Why Proving 1+1=2 Turned Out to Be So Hard
Why did it take 362 pages before it could be proven that 1 + 1 = 2 ? It sounds absurd at first, and incredibly obvious. But in the early 1900s, Alfred North Whitehead and Bertrand Russell were trying to do something much more ambitious. They wanted to show that all of mathematics could be…
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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 Linear Algebra
Imagine we have 3 vectors in space. At first, they seem to be completely unrelated to each other, but look closely. When we define them with these specific coordinates, then (technically) we can observe a hidden structure. Can you tell which? Your answer, here, will show whether or not you have the necessary intuition to…
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This Simple Problem Helps You Think Like Gauss
Here’s a classic question that you probably heard of before. It’s simple, but we will look at it from a completely different perspective that will show whether you really know how to think about mathematics: What is 1 + 2 + 3 + … + 200 ? Now, stop right there. How long do you…
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How To Solve Differential Equations
Look at this differential equation: My challenge for you is to decide which one is the best method to solve it, based on its structure. It has a very common structure, but only a person with trained eyes can recognize the pattern and can tell what the method is! In this video, we will see…