Limits: In statistics, we use limits to talk about probabilities If an experiment is redone many times, we can use the trend to determine the probability of an event. In nature, we see limits set on populations of animals. If we have a function that describes the number of deer in a population versus time, we can analyze how the population will grow with time. Because of limited resources, populations usually follow something called a logistic growth model.
Differentiation: is the process of finding the rate of change of a function: how much the y variable changes as the x variable changes by 1 unit. In physics, derivatives are very important. Position, velocity and acceleration are related by derivatives. Given an equation for the position of an object, the derivative will tell you the velocity or how fast the object is moving at any point.
Optimization: with optimization we’re able to maximize or minimize a function using derivatives.
we see calculus in medicine when examining tumors. Tumor growth is explained by derivatives. The rate of change of the tumor growth over time, lets the doctors know the severity of the disease process and can help discern if the tumor is malignant or benign. They can decide what screening and imaging is needed to monitor the tumor and ultimately guide their treatment based on these calculations.
integral : Given the derivative or rate of change, the antiderivative or integral will give you original function. It also allows you to find the area underneath the curve or the volume of a region rotated about some axis.
If a doctor or pharmacist is giving a patient a strong medication with potentially harmful side effects, they might use an integral to estimate the total concentration in the blood. This is often done when treating serious infections with the antibiotic Vancomycin.
1 of 5 : used in every day life
2 of 5: the "other way" to visualize derivatives
3 of 5: use derivatives to minimize time
4 of 5: the mathematics of tumor growth
5 of 5: math for biology
Calculus allows medical professionals to understand both the rate that the drug is released into the bloodstream and how long it takes for the drug to be metabolized into potentially harmful substrates.