AP Calculus Review

AP Calculus review flashcards covering math language, limits, differentiation, integration, differential equations, applications, parametric equations, sequences, series, and more.

∃

There exists…

∀

For all…

⇒

Implies…

≪

Much less than…

∈

Be an element of…

y’

First derivative

Limit

The value of a function as it approaches some value from one or both sides.

Continuity

A region of a function with no abrupt changes or jumps.

L’Hôpital’s rule

Take the derivative of both the numerator and denominator independently, put them together, and evaluate the limit again.

Derivative

The rate of change of a function.

Differentiable

A function must be smooth and continuous with no cusps

Composite Differentiation

A fancy way of describing taking a derivative of a function in a function

Inverse Differentiation

Taking the derivative of an inverse function

Implicit Differentiation

Taking the derivative with variables on both sides of the equation, leading to derivatives on both sides of the equation.

Optimization

Try to set up an equation with what you’re solving for on one side, and an expression with just one variable on the other

Newton’s Method

An antiquated method for approximating a function’s x intercept by picking a random value and using the function’s derivative to get closer and closer to the zero

Intermediate Value Theorem

If the function f(x) is continuous on the interval [a,b], then for any number c between f(a) and f(b), there exists a value d in the open interval (a,b) such that f(d) = c.

Differential

A method of estimating a function without the function itself.

Integral

An integral is the antiderivative of a function

Bounded Integral

The area under the curve between the specified values

Improper Integral

A bounded integral where either or both bounds are infinite, or the graph is undefined somewhere between its bounds: [a,b]

U Substitution

By substituting u for some kind of algebraic expression, we can simplify the problem, we just need to make sure that the entire integral is in terms of a single variable

Integration by Parts

uv ­ ∫v du = ∫u dv

Trigonometric Substitution

Integration using sine, cosine, tangent

Partial Fractions

Integrals using A, B, and C constants

Differential Equation

Equation with a derivative in it

Area Underneath a Curve

Area underneath the function R(x) on the interval [a,b]

Parametric Equations

A set of equations which relate to an independent variable

Polar Coordinate

A method of describing a location using an angle and a radius from the pole

Power Series

A method of modeling a non-polynomial function with a polynomial