What exactly is calculas?

Question

Like what does diff and int mean eaxactly can anyone explain nin simple language.

Answer 1

Calculus is the study of the infinite. One of the first things you do in a Calculus course is learn how to take a "limit," which describes the behavior of a function as its independent variable (often represented by x) approaches a certain value. When you take the limit of a function that describes the change in value of a function as the change in value of the independent variable approaches zero, you get the derivative. That is, f'(x)= lim h --> 0 (f(x + h) - f(x)) / h, where f'(x) is the derivative of the function f(x), x is a variable, and h represents some change in the value of the independent variable. Typically, a derivative is obtained through a simpler process using the following equations: f(x)=a*x^n and f'(x)=a*n*x^(n-1), where x is a variable and a and n represent constants. A derivative is just the rate of change of a function at a given point. You can visualize a derivative geometrically as the slope of a line that is tangent to a graph of a function at x. You can also think about a derivative physically. Suppose you have a function that describes the velocity of a car. Then, the derivative of that function will describe the rate of change of the car's velocity, or the acceleration. To integrate a function, one takes the "anti-derivative." Which can be thought of as taking a derivative in reverse. So, int(f'(x))=f(x). Integrals have many applications, one of the simplest of which can be seen by returning to our car example. For instance, if you know the acceleration and initial velocity of a car, you can integrate to find the cars current velocity.

Answer 2

In computer science, lambda calculus is a formal system designed to investigate function definition, function application, and recursion. It was introduced by Alonzo Church and Stephen Cole Kleene in the 1930s; Church used lambda calculus in 1936 to give a negative answer to the Entscheidungsproblem. Lambda calculus can be used to cleanly define what a computable function is. The question of whether two lambda calculus expressions are equivalent cannot be solved by a general algorithm, and this was the first question, even before the halting problem, for which undecidability could be proved. Lambda calculus has greatly influenced functional programming languages, such as Lisp, ML and Haskell.

Lambda calculus can be called the smallest universal programming language. It consists of a single transformation rule (variable substitution) and a single function definition scheme. Lambda calculus is universal in the sense that any computable function can be expressed and evaluated using this formalism. It is thus equivalent to the Turing machine formalism. However, lambda calculus emphasizes the use of transformation rules, and does not care about the actual machine implementing them. It is an approach more related to software than to hardware.

This article deals with the "untyped lambda calculus" as originally conceived by Church. Since then, some typed lambda calculi have been developed.

Answer 3

To understand the meaningfulness of calculus, let's do a review of what we've learned beforehand.

In the past, you've probably had to calculate areas/volumes of a square, circle, or n-gon. You may have had to calculate lengths of straight lines drawn from A to B. You may also have had to calculate slopes for lines on a graph.

Calculus takes into account all of these things, especially for irregular cases where you don't just have a circle or a square. You might want to find the area of a puddle, calculate the length of a squiggly line. Calculus allows you to do that.

Differentiation is the process of finding the rate of change of something. Put more simply, differentiation helps you find how fast something is changing, whether that is the slope of a line or the speed at which water flows out of an irregular box.

Integration is just the opposite, finding the sum of something -- the area, length, volumes of a particular function.

Answer 4

Calculus as it was explained to me is simply the math involving real world functions and rates relating to them.

Differentiating is basically finding the slope of a given function.

Integrating comes in two forms: definite and indefinite.
Integrating is also called antidifferentiating because it is the opposite function of differentiating.
Definite can be seen as finding the area under a curve with relation to an axis.
Indefinite can be seen as taking the function and using those values as the slopes of a new function.

Answer 5

Differentiation is a means of determining the rate of change of one thing with another. In simple terms this is like the speed of your car as you drive. If you are going 60 miles per hour, that means that your position, as measured from the place you started, is going to change at a rate of 60 miles in one hour.
Integration is the total change. So if you went 60 miles per hour for 3 hours, you integrate the speed with respect to time to find out how far you went, in this case 180 miles.

Answer 6

There are actually two types of Calculus. There is differential, which is what diff stands for, and there is intergral, which is what int stands for. Differential involves the study of the various slopes of lines and integral involves what goes on underneath curves.

Answer 7

Calculus is the study of change and motion. It is used to work out numerical valuesthat are inconstant and variable, such as a speed of a car, which may be said to be traveling at a steady of 50 mph (80kmp), but whose speed is in fact varying, although only slightly, from moment to moment. Calculus is also used to find areas and volumes of irregularly shaped figures and the lengths of curves. It is a very important tool in modern physics.

In computer science, lambda calculus is a formal system designed to investigate function definition, functionapplication, and recursion. It was introduced by Alonzo Church and Stephen Cole Kleene somewhere in the 1930s; Church used lambda calculus in 1936 to give a negative answer to the Entscheidungsproblem. Lambda calculus can be used to cleanly define what a computable function is. The question of whether two lambda calculus expressions are equivalent cannot be solved by a general algorithm, and this was the first question, even before the halting problem, for whic undecidability could be proved. Lambda calculus has greatly influence functional programming languages, such as Lisp, ML and Haskell.

Lambda calculus can be called the smallest universal programming language. It consists of a single transformation rule (variable substiotution) and a single fuction definition scheme. Lambda calculus is universal in the sense that any computable function can be expressed and evaluated using this formalism. It is thus equivalentto the Turing machine formalism. However, lambda calculus emphasizes the use of transformation rules, and does not care about the actual machine implementing them. It is an approach more related to software than to hardware.

This article deals with the "untyped lambda calculus" as originally conceived by Church. Since then, some typed lambda calculi have been developed.

To understand the meaningfulness of calculus, let's do a review of what we learned beforehand.

In the past, you've probably had to calculate areas/volumes of a square, circle, or n-gon. You may have had to calculate lengths of straight lines drawn from A to B. You may also have had to calculate slopes for lines on a graph.
Calculus into account all of thesse things, especially for irregular cases where you don't just have a circle or a square, You might find the area of the puddle, calculate the length of a squiggly line. Calculus allows you to do that.

Differentiation is the process of finding the rate of change of something. Put more simply, differentiation helps you find how fast how something is changing, whether that is a slope of a line or the speed at which water flows out of an irregular box.

Intergation is just the opposite, finding the sum of something-the are, length, volumes of a particular function.

Calculus is a central branch of mathematics, developed from algebra and geometry. It is built on two major complementary ideas, both of which rely critically on the concept of limits. The first is differential calculus, which is concerned with the instantaneous rate of change of quantities of respect to other quantities, or more precisely, the local behaviour of functions. This can be illustrated by the slope of a function's graph. The second is intergal calculus, which studies the accumulation of quantities, such aas areas under a curve, linear distance traveled, or volume displaced. This two processes act inversely to each other, a fact delivered concluively by the fundamental theorem of calculus.

Examples of typical differential problems include:

finding the acceleration and velocity of a free-falling body at a particular moment.
finding the optimal number of units a company should produce to maximize their profit.

Examples of intergal calculus problems include:

finding areas and volumes.
finding the amount of water pumped by a pump with a se power input but varying conditions of pumping loses and pressure.
finding the amount of parkinglot plowed by a snowplow of given power with varying rates of snowfall.

Today, calculus is used in every of the physichal sciences, on computer science, in statistics, and in engineering; in economics, business, and medicine: and as a genneral method whenever the goal is an optimal solution to a problem that can be given in a mathematical form.

Differential calculus:

The derivative measures the sensitivity of one variable to small changes in another variable.

Consider the formula:

Speed= (Distance) / (Time)

for an object moving at constant speed. The speed of a car, as measured by the speedometer, is the derivative of the car's distance traveled, as measured by the odometer, as a function of time. Calculus is a mathematical tool for dealing with this complex but natural and familiar situation.

Differential calculus can be used to determine the instantaneous speed at any given instant while the formula "speed=distance/ time" only gives the average speed, and cannot be applied to an instant in time becauseit then gives an undefined quotient zero/zero. Calculus avoids division by zero using the limit, roughly speaking, is a method of controlling an otherwise unconrollable output, such as division by zero or multiplication by infinity. More formally, differential calculus defines the instantaneous rate of change (the derivative) of a mathematical fucntion's value, with respect

Answer 8

Calculus has to deal with differentiation and integration of many equations. This can be used to determine the gradient of a specific curve by differentiating its equation, or to obtain the area between the curve and the x-axis, by integrating the equation.

Answer 9

Calculus is a field of mathematics which deals with infinitesimal limits and the normal or partial differentiation and integration of functions of one or more variables.

Answer 10

Damn difficult --that's what calculas is---exactly--and if you don't believe me--take a course in it for yourself--and in less than three weeks you'll be agreeing with me charlie brown---damn difficult math---