Calculus Essays

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Calculus


"One of the greatest contributions to modern mathematics, science, and
engineering was the invention of calculus near the end of the 17th century,"
says The New Book of Popular Science. Without the invention of calculus, many
technological accomplishments, such as the landing on the moon, would have been
difficult.
The word "calculus" originated from the Latin word meaning pebble. This is
probably because people many years ago used pebbles to count and do arithmetic
problems.
The two people with an enormous contribution to the discovery of the
theorems of calculus were Sir Isaac Newton of England and Baron Gottfried
Wilhelm of Germany. They discovered these theorems during the 17th century
within a few years of each other.
Isaac Newton was considered one of the great physicists all time. He
applied calculus to his theories of motion and gravitational pull. He was able
to discover a function and describe mathematically the motion of all objects in
the universe.
Calculus was invented to help solve problems dealing with "changing or
varying" quantities. Calculus is considered "mathematics of change." There are
some basic or general parts of calculus. Some of these are functions,
derivative, antiderivatives, sequences, integral functions, and multivariate
calculus.
Some believe that calculus is too hard or impossible to learn without much
memorization but if you think that calculus is all memorizing then you will not
get the object of learning calculus. People say that calculus is just the
revision or expansion of old or basic equations and I believe that also.
In economics and business there are some uses for calculus. One important
application of integral calculus in business is the evaluation of the area under
a function. This can be used in a probability model. Probability is another
uses in integral calculus for business because you could find how often
something will appear in a certain range in a certain time. A function used for
probability in uniform distribution. The function is f(x) = 1 (b - a) for a <
x >= b. Some economics uses is figuring marginal and total cost. The function
is TC = {MC = TVC + FC. Another is the demand on a sales product. ex. Demand on
Beer that brings in different variables to see how the consumption of beer is.
The function is a multivariate function f(m, p, r, s) = (1.058)(m^.136)(p^-
.727)(r^.914)(s^.816) where m = aggregate real income : p = average
retail price of beer r = average retail price level of all other consumer goods
s = measure of strength of beer (how consumers like it) as you can see if
everything but r stays constant then the demand will go up.
Some terms used in calculus frequently used to learn you need to know what
they are. Derivative is the fundamental concept of calculus that is how things
change. (ex. instantaneous velocity) Functions are always used in all
applications. A function is an equation with one or more variables where only
one x value will produce only one y value is a function. Also you will need to
learn and memorize some theorems and identities to be able to expand and
breakdown equations.

THE NEW BOOK OF POPULAR SCIENCE

Calculus p.431 - 433 Brief Calculus and its Applications

Larry J. Goldstein / David C. Lay / David L. Schneider McGraw Hill Encyclopedia
of Science and Technology #3 ed. 7

A First Course in Calculus Lang, Serge Addison-Wesley Publishing Company

Calculus for Business and Economics Childress, Robert L. Prentice Hall inc.
Englewood Cliffs, New Jersey



 

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What Is Calculus

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What is Calculus?

A definition found of calculus in a dictionary was this; a method of computation or calculation in a special notation (as of logic or symbolic logic). The historical perspective of calculus is that people had a problem in finding areas and finding tangent lines. The thing that was discovered to figure these problems out was calculus. Some influential people in the development of calculus were Isaac Newton (1642-1727), and Gottfried Wilhelm Leibniz (1646-1716). Isaac Newton is considered on of the most influential men in the development of calculus. Newton at first kept all his discoveries to himself. He feared that people would not accept his work and disagree with them. He wrote one of the most important scientific books of all time, Philosophiae Naturalis Principia Mathematica. It took the work of another man to finally convince him to publish his work on calculus, Gottfried Wilhelm Leibniz. Leibniz is another influential man in the history of calculus. He taught himself mathematics. Leibniz accomplished what Newton did, but was not recognized for his work as much as Newton was.
     Calculus is important in my major of Biomedical engineering because there are many machines that are made possible for humans benefit. MRI (magnetic resonance imaging) is made possible for looking at internal tissues of the human body. Another example would be controlling chaotic behavior in the human heart. I think that calculus will be very helpful in my major, so it is important for me to understand it as best as I can.
     I think that the class is going at a fast pace. I have to study a lot to keep up. It seems that lately I understand it, but on the last exam I made stupid mistakes. I need to get more practice done. I like the way you make us read the up coming sections. I get a better feel of what is being covered in class.
     I find limits to be interesting to me. I sort of understood them, but I still have some problems in grasping the idea.

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Continuity is also interesting. In calculus I found that limits and continuity take more thought than actual algebraic work. I like how it makes me think differently. I still have to work on this part.
     I am frustrated with how hard I try but right now my grade is not showing the effort I am putting into this class. I want to do well in calculus and I am going to have to try harder to do well.



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