Overview

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.

Throughout its ~4.5 billion year history, the Earth has experienced periods of warming and cooling. However, the current drastic increase in global temperatures is well outside of the Earth’s cyclic norms, and evidence for human-caused global climate change is compelling. Paleoclimatology, the study of ancient climate conditions, provides ample evidence for human-caused global climate change by comparing recent conditions with those in the past.

Change in atmospheric pressure with height is particularly interesting. The decrease in atmospheric pressure with increasing altitude is due to the decreasing gravitational force per unit area as we move away from the surface of the earth.
Assuming the air temperature is constant at a given altitude and that the ideal gas law of thermodynamics describes the atmosphere to a good approximation, one can find the variation of atmospheric pressure with height.
Let p(y) be the atmospheric pressure at...

Body temperature reflects the equilibrium between heat production and heat loss within the body. Most heat is generated by metabolically active tissues, particularly the liver, heart, brain, kidneys, and endocrine organs. At rest, skeletal muscles contribute 20–30% of total heat production, but during vigorous exercise, this can increase up to 30–40 times.
The average body temperature is approximately 37°C (98.6°F) and typically ranges from 36.1–37.2°C (97–99°F), remaining relatively stable...

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,...