Basic calculus Introduction

Introduction

 

While arithmetic deals with sums, differences, products, and quotients, calculus deals with derivatives and integrals. The derivative andintegral can be
Described in everyday language in terms of anautomobile trip. an automobile instrument panel has a speedometermarked off in miles per hour with a needle indicating the speed. theinstrument Panel also has an odometer which tallies up the distancetravelled in
Miles (the mileage ).

 

Boththe speedometer reading and the odometer reading change with time; that is, they are both "Functions of time," the speed shown onthe speedometer is the rate
Of change, or derivative, of thedistance. speed is found by taking a very small interval of time andforming the ratio of the change in distance to the change in time. the distance shown on the odometer is the integral of the speed fromtime zero to the present.
Distance is found by adding up the distancetravelled from the first use of the car to the present.

 

Thecalculus has a great variety of applications in the natural andsocial sciences. Some of the possibilities are stored strated in theproblems. However, future
Applications are hard to predict, and sothe student shocould be able to apply the calculus himself in newsituations. for this reason it is important to learn why the calculusworks as well as what it can do. to explain why the calculus works, we present a large
Number of example, And we develop the mathematicaltheory with great care.