*This book tells of adventures that took place in the land of Carmorra. The story is told here because, by following these adventures, you can learn differential and integral calculus.*— The Introduction to Calculus the Easy Way

- The King: His name is never actually mentioned.
- Marcus Recordis: The Royal Keeper of Records. Often gets into arguments or competitions with the next two characters.
- Professor Stanislavsky: The kingdom's premier pure scientist.
- Alexanderman Trigonometeris: Introduced in
*Trigonometry the Easy Way*, he specializes in triangles and the trigonometric functions. - Gerard Macinius Builder: The head craftsman for the kingdom.
- The Gremlin: The Big Bad, who claims that the heroes' inability to master mathematics will allow him to conquer Carmorra.

- Alphabet Soup Cans: A rare example in non-interactive media. About half of the math developed is in response to challenges by The Gremlin.
- Baseball Episode: A few of these in
*Algebra*, used to provide examples for word problems. - Black and Nerdy: Trigonometeris is illustrated as a man with African facial features and hair, although he's not given a physical description.
- Card-Carrying Villain: The Gremlin fits the character type, and in
*Algebra,*reveals that he also fulfills this literally. - Formulaic Magic: Played with in Recordis's illustration. Despite not having any magical power, Recordis has the trademark symbol-covered robe and pointy hat of a wizard. Of course, the symbols on Recordis's robe are numbers and mathematical symbols.
- Gentle Giant: Pal
- Geographic Flexibility: The kingdom of Carmorra adds geographical features as needed for various word problem examples.
- Mood Whiplash: Most of The Gremlin's challenges have no specific penalties for failing; few even have a time limit. Then in Chapter 8 of
*Calculus the Easy Way*, the heroes have three hours to derive the Fundamental Theorem of Integral Calculus; if they fail, the entire country will be destroyed in a fire or flood. - Robe and Wizard Hat: Recordis is depicted wearing robes and a pointy hat covered with mathematical symbols. Oddly enough, these symbols include variables, despite having been designed before the discovery of algebra.
- Welcome Episode: The first chapter of
*Calculus*introduces the narrator to the characters. - What Could Possibly Go Wrong?: Chapter 9 of
*Calculus*starts with Recordis boasting, "Now we can do just about anything!" Shortly thereafter, he tries to impress a count by integrating the function*t*(*x*)=*x*^{-1}. However, they had not yet discovered the exception to the power rule for integration, which leads to an embarrassing problem.