Types of Functions > Contents: Function of One Variable Ordinary Derivative Function of Two Variables What is a Function of One Variable? A function of one variable calculates one output value for one input value. For example, f(x) = 2x…

Calculus Definitions > Contents: Extreme Values of a Polynomial Extreme Value Theorem Extreme Values of a Polynomial Extreme values of a polynomial are the peaks and valleys of the polynomial—the points where direction changes. The peaks and valleys are called…

Calculus Definitions > Contents: What is Fourier Analysis? Fourier Series What is Fourier Analysis? Fourier Analysis is an extension of the Fourier theorem, which tells us that every function can be represented by a sum of sines and cosines from…

Sequence and Series > Contents: Harmonic Series Alternating Harmonic Series Harmonic Series The harmonic series is defined as: Each term of the series, except the first, is the harmonic mean of its neighbors. The harmonic series is widely used in…

Types of Functions > What is an Entire Function? What is the Exponential Integral Function? What is an Entire Function? An entire function (also called an integral function) is analytic on the entire complex plane. It’s called an “entire” function…

Types of Functions > Contents (Click to skip to that section): Bounded Function Definition Upper Bound Least Upper Bound (LUB) Bounded Sequence 1. What is a Bounded Function? Bounded functions have some kind of boundaries or constraints placed upon them.…

Types of Functions > Contents: Affine Function Affine Transformation Affine Function An affine function is a linear function plus a translation or offset (Chen, 2010; Sloughter, 2001). Differential calculus works by approximation with affine functions. A function f is only…

Derivatives > Contents: Polar Coordinates Definition Cylindrical Coordinates What is a Polar Function? Polar Derivatives Polar Coordinates Definition Polar coordinates are very similar to the “usual” rectangular coordinates: both systems are two dimensional, they locate a point in space, and…

Sequence and Series > Contents: Binomial Series Binomial Function Hypergeometric Function Binomial Series The binomial series is a type of Maclaurin series for the power function f(x) = (1 + x)m. You can find the series expansion with a formula:…

Calculus Definitions > A horizontal tangent line is parallel to the x-axis and shows where a function has a slope of zero. You can find these lines either by looking at a graph (which usually gives an approximation) or by…