That’s where differentiation comes in: it’s a set of tools that allows you to find the slope of a tangent line at any point on any curve. The slope of a curve isn’t as easy to calculate as the slope of a line, because the slope is different at every point of the curve (and there are technically an infinite amount of points on the curve!). Here, you’ll be studying the slope of a curve. In algebra, you found the slope of a line using the slope formula (slope = rise/run). This is illustrated in the following diagram: With integration, the opposite is true: you can find an object’s position if you know the object’s velocity or acceleration. Likewise, if you know the object’s velocity you can find that object’s acceleration. Differentiationĭifferentiation is a tool where you can find an object’s velocity and acceleration based on the formula for that object’s position. The two work hand in hand and basically do the opposite from each other (or “undo” each other), much like addition and subtraction work together in basic arithmetic. The branch that deals with differentiation is called differential calculus and the branch that deals with integration is called integral calculus. Calculus Sub CategoriesĬalculus is divided into two separate categories: differentiation and integration. Calculus gave mathematicians a set of rules to follow not tied down with long, logical justifications. Calculus found its outstanding success partly because it replaced tedious exhaustion arguments with short, routine calculations. Calculus proved suitable for finding solutions to finding areas, lengths, and volumes of curves figuring out local properties like curvature, normals, tangents, and normals-what we now recognize as problems involving differentiation and integration. Making sure that off ramp is just the right angle so that cars can safely exit.Ĭalculus emerged in the 17th century as a “shortcut” to the results obtained by the method of exhaustion.What kinds of “change”? It’s extremely useful for studying things that change rapidly (like acceleration and velocity), and it’s responsible for a myriad of modern miracles, like: Although you won’t be using small pebbles in modern calculus, you will be using tiny amounts- very tiny amounts Calculus is a system of calculation that uses infinitely small (or infinitely large) amounts to deal with change.
The word calculus comes from the Latin word for “pebble”, used for counting and calculations.
In a nutshell, it’s just what it sounds like: studying how rates (of motion, particles, vehicles…) change over time. However, if you’ve never taken calculus before, “rates of change” might not have too much meaning to you. Questions? Corrections? Post a comment! What is Calculus?Ĭalculus is the study of rates of change.
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Calculus How To has over 500 articles and videos (as of August 2020) to help you learn calculus the easy way! Looking for a specific topic? Type it into the search box at the top of the page.Ĭheck out our Practically Cheating Calculus Handbook, which gives you hundreds of easy-to-follow answers in a convenient e-book. Looking for calculus help? You’ve come to the right place.
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