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The main differences between differential calculus and integral calculus lie in their distinct objectives. Differential calculus is primarily concerned with the study of rates at which quantities change, while integral calculus focuses on the accumulation of quantities, such as areas under a curve.
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. [1] It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. [2]
Basic calculus explains about the two different types of calculus called “Differential Calculus” and “Integral Calculus”. Differential Calculus helps to find the rate of change of a quantity, whereas integral calculus helps to find the quantity when the rate of change is known.
dx (when Δx approaches zero) gives the actual derivative and integral*. *Note: this is a computer model and actually uses a very small Δx to simulate dx, and can make erors. For true derivatives refer to Derivative Rules, and for integrals refer to Introduction to Integration.
First published in 1991 by Wellesley-Cambridge Press, this updated 3rd edition of the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.
In differential calculus, we try to understand how functions change — a powerful tool for solving practical problems such as maximizing profit or minimizing costs. In integral calculus, we study the accumulation of functions which allow us to compute values such as volumes and medical dosages.
Differential equations are equations that include both a function and its derivative (or higher-order derivatives). For example, y=y' is a differential equation. Learn how to find and represent solutions of basic differential equations.