The product rule is applied to functions that are the product of two terms, which both depend on x, for example, y = (x - 3)(2x 2 - 1). The most straightforward approach would be to multiply out the ...

What is the Calculus of Variations? Many problems involve finding a function that maximizes or minimizes an integral expression. One example is finding the curve giving the shortest distance between ...

Functions with Corners: 2.1: Some examples of graphs with corners which I talked about in lecture. The tangent line to a graph does not exist at a corner. Algebraic Simplification: 2.3: When computing ...

We can also use calculus to solve problems involving work, energy, and power. In IB Math, students learn how to apply calculus to solve various physics problems, including those involving motion, ...

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space. The points could be an infinite collection of electrons ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

It revealed that mathematics is full of monsters: impossible-seeming functions, strange objects (it’s one of the earliest examples of a fractal), wild behaviors. “There’s a whole universe of ...

ABSTRACT: In this work, a new class of analytic and univalent functions , , with respect to other points that include symmetrical and conjugats in the unit disk are studied. The estimated coefficients ...