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“I can’t wait to learn some new spells!” Twilight Sparkle said cheerfully as she pulled out a book from the shelf of her library and looked at the title in confusion.
“Calculus? Wonder what that is.” She opened it up to find a series of strange looking spells. “What the heck are these spells? Lim something as x goes to sideways 8? F apostrophe of some spell which is also sometimes written as that spell preceded by dy on top of dx? What the heck is that long S thing beside some of the spells that for some reason end in dx? Or am I reading too far too soon and should just start on page 1?”
Calculus is a crack fic of earlier math, so this means any author of a Calculus textbook is a crack fic author much like myself, and probably took a higher dose of crack when writing said books than I do when writing my fanfics.
“Hi Twilight! Whatcha doin?” Pinkie Pie wondered.
“My latest book of advanced magic, which for some reason is called Calculus and I’m practicing my magic.”
Twilight used her magic to manipulate a quill to write on some papyrus and wrote down one of the problems.
“That looks more like solving pen and paper puzzles than practicing magic. Boooring!” Pinkie Pie commented.
“It was in the magic section of the library, therefore it’s a magic book and therefore I am practicing magic.” Twilight insisted. She turned her attention back to her problem. “Oh okay. So the beginning of the book is a refresher for anyone who doesn’t know basic elementary school math and even beyond. So these f parentheses x things are functions and these lims above horizontal arrows are limits and the sideways 8 is actually infinity. And then a bunch of trig stuff too. Hmm, lim of 1 over x as x approaches 0. Oh that’s sideways 8. Yay I did my first spell.”
She completed more “spells” from her Calculus book. Rather than firing a cantrip from her horn like she was used to doing, she wrote down f prime of a function over another function. “Since it’s in a fractional form like this, I gotta use the quotient rule.” And so she completed her magic spell by computing f prime times g minus g prime times f all over g squared. Now that she thought of it, since 1 over x to the power of anything was actually x to the negative of that power, this meant that the derivative of 1/x squared could be solved by either the power rule, chain rule, or quotient rule. She didn’t remember having this much flexibility with the previous magic that she learned.
Just for shits and giggles, she tried using the trig substitution method of integration on x squared plus 6.
“The integral of cosine to the 5th of x times sine to the 8th of x dx from the interval 69 to 420.” Twilight giggled at the bounds of integration.
Rainbowdash flew as fast as she could through the library front door and was panting heavily, and she looked gravely concerned about something.
“Hey Twilight, we could use your assistance. Tirek has come back and he doesn’t look very happy.”
“Whew. Thanks for telling me Rainbowdash. Perhaps now I can actually apply my magic for a practical purpose.”
“There you are, Twilight.” Tirek angrily said to her. Twilight pulled out an inkwell and feather and began writing down the indefinite integral of 1 over x^5+1 dx.
“Try this on for size!” Twilight yelled as she wrote down the convoluted series of steps to compute the novel-length antiderivative.
“What are you doing Twilight? Blast him into next millennium!” Rainbowdash yelled.
“I AM DOING MAGIC!” Twilight insisted. “And now we have a final result of all of that and cannot forget to add +C to the end.”
“Ha ha ha ha, how cute. Are you blasting me with your magic? Cuz I don’t feel very blasted by magic.”
Fluttershy channeled her inner “YOU’RE GOING TO LOVE ME!” and hit Tirek over the head with a baseball bat, knocking him out. Twilight looked up from her notes and saw that Tirek was down for the count.
“Woo hoo, my magic worked!” Twilight did a happy dance. “Imma have to write a thank you letter to the authors of this book of magic titled Calculus since it can be used to defeat arc villains.”
Once she reached the double and triple integrals, partial derivatives, and vector fields, it felt like a crack fic of Calculus itself. “Hmm, so double integrals represent a volume underneath a curved surface. Alright, sounds straightforward.” As far as she knew she still thought she was learning more magic. Multivariable chain rule, divergence and curl, functions that output vectors instead of single numbers were all on the table.
“Ya know what? Since I know that my Calculus magic works because it was able to defeat the likes of Lord Tirek, I’ve got an idea. I’m gonna hogtie myself up inside a barrel, go down Neighagra falls in it, and use the magic that I learned from my Calculus book to free myself.”
Despite the sheer amount of effort her friends spent trying to talk her out of her stunt that she was confident about being able to complete, they all accepted that they might not ever see her again.
“Goodbye Twilight. We’ll miss you.”
"We love you."
“Quit being over-dramatic. I’ll be fine. You’ll see me again,” Twilight insisted.
While Twilight was going toward Neighagra Falls hogtied in a barrel, she was working on a triple integral problem. “The triple integral of the function e to the z times sin of y cubed over the square root of x times cos of y to the e to the x to the pi power with 67 and 45, 34 and 12, and 34 and pi over e as the bounds of integration.” There wasn’t much time to do her escape so she had to think fast. “These are basically double integrals with some extra steps. Pick a variable and integrate with respect to it while treating all other variables as constants, solve the resulting integral, and then plug the answer into the variable you just integrated with respect to, rinse and repeat. Easy peasy.”
She was heading swiftly towards the waterfall, but she was still busy manipulating multi-variables, about to save herself with her magic as far as she knew.
"A ha, done!" She exclaimed as she got the final answer of her triple integral problem. But she was still tied up in her barrel.
"Oh crap, did I do something wrong? My magic worked before. How come it's not working now?”
She was surprised and increasingly terrified at the barrel apparently not somehow magically saving itself from the waterfall, and no matter how much she looked over the integral problem she couldn't find where she might have made a mistake. And then she found it. “A ha. Sign error. Those are all too common even for the best math students. This 5 should be a -5.” and then she recomputed from there and got a different final answer. But still no mysterious saving of her life. In fact there was no time to look it over again (just for the record she got everything correct this time) and standout relationships of her life flashed before her eyes.
Twilight Sparkle’s funeral was attended by the now Mane 5, Celestia, Spike, and even Discord, who were all sobbing uncontrollably.
“By executive action I hereby ban every single math book in the entirety of Equestria so that never again will anyone ever mistake it for magic and get themselves killed as a result.” Celestia declared. She gathered every single math textbook in existence into a huge pile and Spike did the honors by setting it alight with his fiery breath, making this the largest book burning in Equestrian history.
The massive increase in ponies having no idea what 2+2 is or what the Pythagorean Theorem is or the amount of structures made with a shoddy build quality was a small price to pay for no pony else hurtling themselves over Neighagra Falls while hogtied and stuffed inside a barrel while making a feeble effort to escape just by solving an iterated integral.