INTRODUCTION OF CALCULUS
Calculus is concerned with the comparing quantities which differ in a non-linear way. It's used extensively in engineering and science since many of things we are studying do not behave in the simple linear fashion. If the quantities are continually changing we need the calculus to study what is going on.
Calculus was developed very independently by Englishman Sir Isaac Newton and by German, Gottfried Leibniz. They were both working on the problems of motion towards end of the 17th century. There was bitter dispute between men over who developed the calculus first. Development of an accurate clock in 17th century led to the significant developments in mathematics and science amongst greatest of these was calculus.
WHAT IS CALCULUS?
Calculus is the broad area of mathematics dealing with the topics as the instantaneous rates of change, the areas under curves and sequences or series. Underlying all of these topics is concept of the limit. This consists of analyzing the behavior of function at point's ever closer to particular point but without ever actually reaching that point. As typical application of the methods of the calculus,
Calculus is mathematical study of the change, in the same way that geometry is study of the shape and algebra is the study of the operations and their application to solving the equations.
HISTORY OF CALCULUS
Main duty of historian of the mathematics as well as his fondest privilege is to explain humanity of the mathematics to illustrate its beauty, greatness, and dignity, and to describe how the incessant efforts and accumulated genius of the many generations have to built up that magnificent the monument the object of the our most legitimate pride as men and of humility, wonder, and thankfulness as individuals.
Discovery of calculus is the often attributed to two men, the one of Isaac Newton and Gottfried Leibniz who is independently developed its foundations. Although they both are instrumental in creation they thought of fundamental concepts in the very different ways. While Newton considered the variables changing with the time, Leibniz thought of variables x and y as the raging over sequences of the infinitely close values. He introduced d x or d y as differences between successive principles of these sequences.
APPLICATIONS OF CALCULUS
Calculus has two basic applications they are:
Differential calculus; Simplest introduction to the differential calculus involves an explicit series of the numbers. Given series (42, 43, 3, 18, 34), the differential of the series would be (1, -40, 15, 16). And the new series is the derived from difference of the successive numbers which gives rise to the name differential. Differentials used on the explicit series of the numbers as done here.
Integral calculus: Differential calculus can also be introduced by series of the numbers. Original series can almost be derived the solely from differential. Instead of taking difference however integration involves the taking sum. Given first number of original series 42, the rest of the original series can be derived by the adding each successive number in differential (42+1, 43-40, 3+15, 18+16).
WHY LEARN CALCULUS
Calculus is the essential for many areas of the science and engineering. Calculus is also necessary to the study motion of the gases and particles the interaction of the forces and the transfer of the energy. It is also useful in the business whenever the rates are involved. For example, the equations involving supply or interest and demand curves are grounded in language of the calculus. The Calculus also provides important tools in the understanding functions and has led to development of the new areas of the mathematics including the real and complex topology, analysis, and non-Euclidean geometry.
WHAT IS INVOLVED IN CALCULUS
The Learning calculus like much of the mathematics includes the two parts:
Understanding the concepts: Explain what it the means when you take the derivative rather than simply apply the formulas for the finding a derivative.
Symbolic manipulation: Like other branches of the mathematics, calculus is written in the symbols that represent the concepts.
WHAT IS THE PURPOSE OF CALCULUS
Goals and purpose of the calculus we both expressed the desire to the introduce students to the mathematics different from the calculus that is the more modern and in many ways more important. Calculus is the one of the great intellectual achievements of the humankind and it explains behavior of the moving and changing the quantities in physical world. It is worth time to the learn even if sometimes it seems like we spend too much of time on the calculus and its type.
Calculus is the useful in the engineering and construction. If you are not involved in one of that field, you may not use it commonly. Calculus is the great training for mind. Calculus opens up the avenues of study that would not be available otherwise.
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