Overview

A weather map provides a practical example of a function of two variables. Across a wide region such as the United States, temperatures vary from one location to another. Each location can be identified by two geographic coordinates: longitude and latitude. Since a single temperature value is assigned to each coordinate pair, the situation can be represented mathematically as a function with two inputs and one output.In mathematical notation, longitude and latitude can be labeled as x and y,...

Climate refers to the prevailing weather conditions in a specific area over an extended period. As the saying goes, “Climate is what you expect. Weather is what you get.” Climate is influenced by geographic factors, such as latitude, terrain, and proximity to bodies of water.

The average temperature of Earth is the subject of much current discussion. Earth is in radiative contact with both the Sun and dark space; it receives almost all its energy from the radiation of the Sun and reflects some of it into outer space. Dark space is very cold, about 3 K, so Earth radiates energy into it. For instance, heat transfer occurs from soil and grasses, the rate of which can be so rapid that frost can occur on clear summer evenings, even in warm latitudes.
The average...

An object absorbing an electromagnetic wave would experience a force in the direction of propagation of the wave. This force occurs because electromagnetic waves contain and transport momentum. The force accounts for the wave's radiation pressure exerted on the object. Maxwell's prediction was confirmed in 1903 by Nichols and Hull by precisely measuring radiation pressures with a torsion balance. The measuring instrument had mirrors suspended from a fiber kept inside a glass container. Nichols...

The rate of heat transfer by emitted radiation is described by the Stefan-Boltzmann law of radiation: