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Calculus
Calculus rests on a small stock of derivatives, antiderivatives and differentiation rules you must know without hesitating. Lumi has you recite them at spaced intervals so your effort goes into the reasoning.
How to turn this subject into cards
Make one set of standard derivatives, one of antiderivatives, one of rules (product, quotient, chain) and one of methods for curve sketching, extrema or optimisation problems. The trap is applying a rule in class with the model in front of you, then slipping alone, for example forgetting the derivative of the inside function in a chain rule. Lumi quizzes you on both the rule and the trap. Spaced revision helps these reflexes last (Cepeda et al., 2008). It helps you remember formulas, rules and method steps.
Example card
Try it, Lumi turns it into fill in the blank questions in your browser.
Calculus · teach this card to Lumi
The power rule says the derivative of x to the n is n times x to the n minus 1. The chain rule says the derivative of f of g of x is f prime of g of x times g prime of x. The derivative of sin x is cos x. The integral of 1 over x is the natural log of the absolute value of x plus C. The Fundamental Theorem of Calculus says the derivative of the integral of f from a to x is f of x.
Lumi’s question
The _____ says the derivative of x to the n is n times x to the n minus 1.
Pick the missing word
Answer right to light Lumi up
Its lamp fades when a fact slips away.
Levels where Lumi offers this subject
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Teach this to Lumi
Give Lumi your calculus notes, it gives them back as questions at the right moment.