In the 'real world', the purpose of a course of study in pre-calculus is to prepare the student for a course of study in Calculus.
hopefully never...
Depends on the work you do. For example, say you work at a supermarket, either at a cash register or arranging stuff in the shelves, you would probably not use calculus in your daily work; if you are an economist consultant that has to try to optimize profit for the same supermarket, it is quite possible that you do use calculus.
Analysis is a broader term for Calculus and the theorems behind it. It is studied both with real and complex numbers as real and complex analysis. Usually calculus just deals with the basic problems of differential calculus and integral calculus.
It is certainly used in calculus, just as calculus can be used in trigonometry.
Physicists, chemists, engineers, and many other scientific and technical specialists use calculus constantly in their work. It is a technique of fundamental importance.
Mainly Leibniz's and Newton's version is used in Calculus Textbooks.
Robert A. Adams has written: 'Calculus' 'Calculus - a Complete Course' 'Calculus of several variables' -- subject(s): Calculus, Functions of several real variables, Vector analysis 'Single Variable Calculus Edition' 'Calculus of Several Variables' 'Calculus Complete Course'
Calculus has been helpful to create exquisite designs
Isaac Newton developed a complete system of calculus that makes complex calculations of rates and relationships much simpler than they would otherwise be. Calculus is used extensively in engineering.
I am assuming you understand the distinction between single-variable calculus (calculus of one variable) and multivariable calculus (calculus of several variables). Well, if you know the former, that is highly beneficial because the same techniques are used in the latter -- they are generalized to apply to calculus of n-variables. This is ultimately the goal of single-variable calculus. Why? Well, if you think about it, single-variable is not really applicable. Not many real world phenomena involve one variable. For example, in macroeconomics, GDP = Y is a function of many variables: Consumption (a function of net taxes and income), Investment (a function of real interest rates), Government Spending, and Net Exports. That is, Y=f(C(Y,T), I(r), G, NX). To perform many of the tools of calculus (e.g. finding how Y changes as G increases) to this function, one must know and apply multivariable calculus.
Calculus is a branch of mathematics which came from the thoughts of many different individuals. For example, the Greek scholar Archimedes (287-212 B.C.) calculated the areas and volumes of complex shapes. Isaac Newton further developed the notion of calculus. There are two branches of calculus which are: differential calculus and integral calculus. The former seeks to describe the magnitude of the instantaneous rate of change of a graph, this is called the derivative. For example: the derivative of a position vs. time graph is a velocity vs. time graph, this is because the rate of change of position is velocity. The latter seeks to describe the area covered by a graph and is called the integral. For example: the integral of a velocity vs. time graph is the total displacement. Calculus is useful because the world is rarely static; it is a dynamic and complex place. Calculus is used to model real-world situations, or to extrapolate the change of variables.