2006-11-26 21:18:16 · 14 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Differentiation and integration are mathematical operations applied to polynomial functions.
The first is differential calculus, which is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behavior of functions. This can be illustrated by the slope of a function's graph. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance travelled, or volume displaced. These two processes act inversely to each other, as shown by the fundamental theorem of calculus.
These operations are frequently used solve complex scientific problems, for instance, in the physics area. fundamental advances in calculus during the 17th and 18th century had a deep impact on the ensuing development of physics. Today, calculus is used in every branch of the physical sciences, in computer science, in statistics, and in engineering; in economics, business, and medicine; and as a general method whenever the goal is an optimal solution to a problem that can be given in mathematical form.
2006-11-26 21:30:06 · answer #1 · answered by vijaya l 4 · 0⤊ 0⤋
Differentiation Helps you to find the basic block of any problem with which it is built..
Similarly Integrationm is used for finding the net result of a small criteria when it gets joined.
These r the physical meanings of Differentiation And Integration.
2006-11-26 21:29:53 · answer #2 · answered by Aswin Velu 1 · 1⤊ 0⤋
Differentiation and integration are very important to explain various physical relations .For example differentiation gives an expression for velocity as dy/dt where y is displacement and t is the time associated with the displacement . so the value of the velocity at any instant between the start and the end point of motion of any object is clearly seen. Similarly if value of any fn is obtained at one instant then whole expression for the function is got using integration. Not just for primitive purposes but also for high level applications diff. and integ. are very important
2006-11-26 23:28:17 · answer #3 · answered by vignesh w 1 · 0⤊ 0⤋
Differentiation and Integration are the backbone of mathematics
Called calculus and almost all of engineering and many other science is based on this branch.We use differentiation to analyse several types of curves (line, circle, parabola, ellipse, etc) maximum value and minimum value of functions, and in finding approximate values eg Sin(45.25) deg , value of sq root (256.95) etc. Also differential equation, equation of motion , Simple harmonic and other types can be analysed and understood.It is a very vast subject.
Similarly Integration which is an opposite or differentiation is also used in finding areas under curve. For eg can you find area of a circle by conventional ways ? We can find it by integration.Integration also replaces summation (sigma) at a very senior level.Like differentiation Integration has several higher level applications.
In physics Gauss theorem and many other such theorems can be aptly described accurately by integration.
Do learn calculus - it is interesting
2006-11-26 22:57:44 · answer #4 · answered by Mathematishan 5 · 0⤊ 0⤋
The development and use of calculus has had wide reaching effects on all areas of modern living. It underlies nearly all of the sciences, especially physics. Virtually all modern developments such as building techniques, aviation, and other technologies make fundamental use of calculus. Many algebraic formulas now used for ballistics, heating and cooling, and other practical sciences were worked out through the use of calculus. In a handbook, an algebraic formula based on calculus methods may be applied without knowing its origins. The success of calculus has been extended over time to differential equations, vector calculus, calculus of variations, complex analysis, and differential topology.
But the trick is to understand how to do it instead of learning it by heart.
2006-11-27 01:37:53 · answer #5 · answered by cv 3 · 0⤊ 0⤋
What Is Differentiation In Mathematics
2016-12-11 17:35:33 · answer #6 · answered by ? 4 · 0⤊ 0⤋
Integration and differentiation use two important factors in mathematics
Integration is summing up of lot of items..differentiation is to calculate rate of change
2016-09-27 19:59:20 · answer #7 · answered by Greeshma 1 · 0⤊ 0⤋
Differentiation Helps you to find the basic block of any problem with which it is built..
Similarly Integrationm is used for finding the net result of a small criteria when it gets joined.
2006-11-27 16:23:16 · answer #8 · answered by arpita 5 · 0⤊ 0⤋
Solving some mathematical questions.
2006-11-26 21:44:10 · answer #9 · answered by vinisha v 2 · 0⤊ 0⤋
They are used to solve many mechancal problems, civil construction calculas and many more like this.
2006-11-28 21:56:36 · answer #10 · answered by Ketan 2 · 0⤊ 0⤋