How2Day: Problems of Differential & Integral Calculus

Calculus involves many types of problems. calculatrice image by photlook from Fotolia.com
Calculus is a branch of mathematics, most basically described as the study of constantly-changing quantities. Calculus was invented in the 17th Century by Isaac Newton and G.W. Leibniz. It plays a key role in applications beyond mathematics, stretching to physics and engineering. The two most basic tools of calculus are differentiation and integration. Understanding some of the basic problems of these two aspects of calculus can help people learn more about it.

Differential calculus is essentially gaining an understanding of a particular function's rate of change (sometimes expressed as the "slope," suggesting a line of a graph as it rises or falls). However, the most common term for this concept is the derivative. Problems in differential calculus work to either find the derivative or calculate the derivative's effect on other variables. Often, this will involve one variable getting steadily smaller, and examining how that changes another variable. Other differential calculus problems involve how one dependent variable, usually expressed by the letter f, changes in terms of another independent variable, usually expressed by the letter x.

Implicit differential calculus problems come up when you do not know the solution for the dependent variable in the problem.

Logarithmic differential calculus problems deal with extending the Product Rule--one of the most basic formulas in differential calculus--to more than two functions.

Integral calculus problems deal with the limit of possible sums of a group of elements under a certain condition. That condition occurs when the number of total elements increases while the size of the individual elements decreases. Integral calculus problems always involve finding the highest possible sum of all of these pieces. Integrals are often also referred to as anti-derivatives.

Integration by parts problems constitutes one of the major techniques of integral calculus. This technique comes into play when you already have the product of two different functions and know the integral of one and the derivative of the other, but not for both.

Synthetic division is another technique used with many integral calculus problems. You will use synthetic division when the degree of the polynomial on the top is greater than or equal to the degree on the polynomial on the bottom.

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