пример презентации -английский -матфак ВГУ магистратура 1 курс

Presentation - 1 semester

Introduction

Good evening ladies and gentlemen. It’s a pleasure to welcome you here today.
Let me introduce myself. I'm Ivanov Petr from Voronezh State University, Russia. I'm а first student of masters section of math faculty and what I'd like to present to you today is quite short presentation which topic is history of calculus development.

The purpose of this presentation is to describe process of calculus development during time and show most important history moments and persons who considerably improved this math section.
My talk is particularly relevant to those of us who study math analysis and may be even for everybody who is here know because all we study math so we should know history of its major sections development.

In my presentation I'll focus on three major issues.

First I'll tell you what the calculus definition and also we’ll talk about the major branches of this science, then in second part of my presentation I’ll consider the calculus development history itself - it’ll be the most big part of my presentation where we’ll talk about three periods of this math section development – concretely ancient, medieval and modern period. And in the final third part I’ll give you some information about calculus applications.

It will take about 15 minutes to cover these issues – so it’s not very big, but I think that it’s should be interesting for everyone who like math history and mathematics at the whole.
I have no handouts with myself because it’s just preparing to real presentation now)

Report itsef

Part 1

So let's turn to first part of my presentation, it’ll be about calculus definition and calculus branches.

Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

It has two major branches:
1. differential calculus (concerning rates of change and slopes of curves)
2. and integral calculus (concerning accumulation of quantities and the areas under curves);
These two branches are related to each other by the fundamental theorem of calculus

I should also add that calculus is a major part of modern mathematics education and that a course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis.

That's all I wanted to say in first part of my presentation and now let's now turn to second part of presentation where we will talk about calculus development which has duration in history process.

Part 2

Ancient period

The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. Calculations of volume and area, one goal of integral calculus, can be found in the Egyptian Moscow papyrus (c. 1820 BC) – it’s one of the most important historical source of knowledge about math in Ancient Egypt.
When we talk about ancient period of math history we should mention Greek mathematics, one of them - Eudoxus used the method of exhaustion, which foreshadows the concept of the limit, to calculate areas and volumes, while Archimedes ) developed this idea further, inventing heuristics which resemble the methods of integral calculus.
The method of exhaustion was later reinvented in China in the 3rd century.
Medieval period
In this period we can mention next moments and persons like Alexander the Great's invasion of northern India brought Greek trigonometry, using the chord, to India where the sine, cosine, and tangent were conceived.
Alsod there are some results given by , Indian mathematicians in the 14th century. But they were not able to "combine many differing ideas under the two unifying themes of the derivative and the integral, show the connection between the two, and turn calculus into the great problem-solving tool we have today"
Morden period
In Europe, the foundational work was a treatise due to Bonaventura Cavalieri, who argued that volumes and areas should be computed as the sums of the volumes and areas of infinitesimally thin cross-sections. The ideas were similar to Archimedes' in The Method, but this treatise was lost until the early part of the twentieth century. Cavalieri's work was not well respected since his methods could lead to erroneous results, and the infinitesimal quantities he introduced were disreputable at first.
These ideas were arranged into a true calculus of infinitesimals by Gottfried Wilhelm Leibniz, who was originally accused of plagiarism by Newton. He is now regarded as an independent inventor of and contributor to calculus. His contribution was to provide a clear set of rules for working with infinitesimal quantities, allowing the computation of second and higher derivatives, and providing the product rule and chain rule, in their differential and integral forms. Unlike Newton, Leibniz paid a lot of attention to the formalism, often spending days determining appropriate symbols for concepts.

Leibniz and Newton are usually both credited with the invention of calculus. Newton was the first to apply calculus to general physics and Leibniz developed much of the notation used in calculus today. The basic insights that both Newton and Leibniz provided were the laws of differentiation and integration, second and higher derivatives, and the notion of an approximating polynomial series. By Newton's time, the fundamental theorem of calculus was known.
Since the time of Leibniz and Newton, many mathematicians have contributed to the continuing development of calculus. One of the first and most complete works on finite and infinitesimal analysis was written in 1748 by Maria Gaetana Agnesi
So much for point two. And let’s turn the third part of my presentation where we we’ll talk about calculus applications.
Part 3
Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired. It allows one to go from (non-constant) rates of change to the total change or vice versa, and many times in studying a problem we know one and are trying to find the other.

Maxwell's theory of electromagnetism and Einstein's theory of general relativity are also expressed in the language of differential calculus. Chemistry also uses calculus in determining reaction rates and radioactive decay. In biology, population dynamics starts with reproduction and death rates to model population changes.

Calculus can be used in conjunction with other mathematical disciplines. For example, it can be used with linear algebra to find the "best fit" linear approximation for a set of points in a domain. Or it can be used in probability theory to determine the probability of a continuous random variable from an assumed density function.

That's all I wanted to say about calculus applications – now we see that calculus give as very important methods which have practical significance.

CONCLUSION
OK. I think that’s everything I wanted to say about calculus. Just to summarize the
main points of my talk I want to said again that this presentation purpose was to describe process of calculus development during time. And know we’ve looked at calculus definition and most important branches,I also have told you about three periods of calculus development and we’ve also saw some examples of calculus applications areas.
And know And I'll be happy to answer any questions you may have. – if you have it)))
Ok – if we have no more questions - that’s all – but thanks for listening =)