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The Number e as a Limit01:29

The Number e as a Limit

The number e is a fundamental constant in calculus, playing a central role in describing continuous change, particularly exponential growth. It is most naturally defined through its relationship with the natural logarithm, which is the inverse of the exponential function with base e. This relationship allows e to be characterized using basic principles of differentiation rather than as an arbitrary numerical constant.A key property of the natural logarithm function, ln x, is that its derivative...
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Adaptations that Reduce Water Loss01:57

Adaptations that Reduce Water Loss

Though evaporation from plant leaves drives transpiration, it also results in loss of water. Because water is critical for photosynthetic reactions and other cellular processes, evolutionary pressures on plants in different environments have driven the acquisition of adaptations that reduce water loss.
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VirWaTest, A Point-of-Use Method for the Detection of Viruses in Water Samples13:32

VirWaTest, A Point-of-Use Method for the Detection of Viruses in Water Samples

Here we present VirWaTest, which is a simple, affordable and portable method for the concentration and detection of viruses from water samples at the point of...
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Limiting Reactant02:27

Limiting Reactant

The relative amounts of reactants and products represented in a balanced chemical equation are often referred to as stoichiometric amounts. However, in reality, the reactants are not always present in the stoichiometric amounts indicated by the balanced equation.
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The Water Cycle01:00

The Water Cycle

The Earth’s hydrosphere includes all of the areas where the storage and movement of water occurs. Since water is the basis of all living processes, the cycling of water is extremely important to ecosystem dynamics.
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Important Public Goods01:23

Important Public Goods

Public goods are services or resources provided primarily by the government because private companies often do not have an incentive to supply them at socially efficient levels. These goods are both non-excludable, meaning that people cannot be prevented from using them, and non-rivalrous, meaning that one person's use does not reduce their availability for others.
If private firms are unable to economically prevent multiple, non-paying consumers from consuming their goods, then some...
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