Ahh calculus! The subject that gave us the “derivative”, “antiderivative” and “implicit function theorem”. It involves mysterious functions like “f o f o’”, differential operators like “d/dx”, fuzzy sets, limits and continuity, series of functions and …even more! But did you know that calculus is used in our daily lives? That’s right — whether you’re eating a microwave burrito or taking a shower — there’s some calculus involved. So, let me show you five examples of how calculus can be applied to everyday life to
Calculating the Area of Your Home
To find the area of your home, you would need to measure each room and add up the area of each room. For example, if your bedroom is 10 feet by 12 feet and your kitchen is 8 feet by 15 feet, you would add 120 square feet (10 times 12) for your bedroom and 120 square feet (8 times 15) for your kitchen to get a total of 240 square feet.
Calculus can be used to determine the area of your living space as well as other aspects of real estate.
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Creating a Better Camera Lens
To make a better camera lens, it is useful to understand the process of how light enters an existing lens. In order for light to enter a lens properly, it must bend in such a way that the rays are focused on a single point at the back of the eye’s retina. This allows us to see clear images when we look through a camera or binoculars.
Using calculus, we can examine how the shape of a lens affects how we focus light rays onto our retina. Calculus helps us determine how we can change lens shapes so that they can focus light properly. In this example, it is assumed that the lens is made out of glass and has a constant thickness. If a person wants to create a better camera lens, they will need to know calculus so that they calculate how light rays are bent as they pass through different types of lenses.
Sending Satellites Into Space
One of the most far out applications of calculus is in sending satellites into space. A satellite is something (some might call it an object) that circles a planet. The path that it follows is called an orbit. Satellites are used to collect information about our weather, our land and oceans, and even distant stars and galaxies. All of this information allows us to better understand the world around us. When you look at your television screen and see the weatherman show a picture of a hurricane coming up the coast, you are seeing information sent to him by a satellite.
Satellites need very specific orbits so they can take pictures of specific places on Earth, or so they can stay in orbit for a long time without having to use much fuel (remember, there is no air in space so once a satellite uses up its fuel it cannot get more). The engineers who send satellites into orbit have to use calculus to get it right.
Determining Risk in Investments
Calculus is used to calculate the risk in various investments. You can use calculus to determine the amount of risk in a portfolio and how much you’ll need to get a certain desired return.
Risk, in investing, is the chance that an investment will lose value. When you invest in stocks, for example, there’s always a chance that the stock’s price will go down instead of up. One way to measure risk is with standard deviation, which describes how much variation there is in an investment’s return over time. The higher the standard deviation, the riskier the investment is said to be.
When you invest in a portfolio made up of several different investments, standard deviation helps describe how risky that portfolio is overall. To find it, you use calculus to find the average value of all possible variations. Then you take a look at each possible variation and figure out how far it differs from that average value. The square of that difference gives you one piece of data; once you’ve looked at every possible variation, you add up all those squares, divide by the number of values and then take the square root of that result. This final number is your standard deviation value for your portfolio.
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Forecasting Traffic Patterns
In urban planning, calculus has many uses. One of the most important is forecasting traffic patterns in cities. The average speed of a car traveling on a highway can be determined by taking the derivative of the distance with respect to time; the instantaneous rate of acceleration is calculated by taking the second derivative of distance with respect to time. Calculus also helps us determine how much fuel is used by cars and planes.