Mathematics

Fundamental Theorem of Calculus, Part 2 (Explaining Calculus #17)

We have now discussed an extremely important tenet in the development of calculus, which is called the first part of the Fundamental Theorem of Calculus. We briefly recall what we deduced in the last post: Fundamental Theorem of Calculus, Part 1: If is a function that tells us the area underneath the graph of fromContinue reading “Fundamental Theorem of Calculus, Part 2 (Explaining Calculus #17)”

Why Prove a Theorem Twice?

I have written before on the problem and solution of the problem of “Pythagorean Triples”. The problem, based on the Pythagorean theorem for right triangles, asks for all possible solutions to this equation which have all of whole numbers. Not just any right triangle works – for instance if then , which is definitely notContinue reading “Why Prove a Theorem Twice?”

Fundamental Theorem of Calculus, Part 1 (Explaining Calculus #16)

We have recently talked about two concepts that appear rather disparate. We have discussed antiderivatives – which is the idea of reversing all the rules for taking derivatives, and Riemann sums, which are used to calculate the areas underneath complicated shapes. What do these have to do with each other? It does not look likeContinue reading “Fundamental Theorem of Calculus, Part 1 (Explaining Calculus #16)”

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About Me

Hi, I’m Will. I’m studying as a graduate student in math, and am also interested in theology, education, philosophy, science, and mental health. My goal here is to write defending the views I have on these subjects and to help interested readers learn more about these subjects.

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