1. ht= -4.9t2+ 450, where t is the time elapsed in seconds and h is the height in metres.…
Follow-Up: Suppose you are the owner of Saucy Soup Company. You need to present an argument to your board of directors as to what shape soup can your company should sell. Some things to keep in mind:…
Isaac Newton, an English man and a Protestant, used only his mind to describe the laws of gravity. He used the scientific method and was the first person to use calculus.…
The article, “Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus” by Dr. Judith V. Grabiner talks about the beginning of rigorous Calculus and how and why it was developed. Dr.Grabiner starts out by discussing the origins of Calculus and shows how Calculus did not need rigor during its inception in the 18th century. The founders of Calculus, Leibniz and Newton, and other mathematicians in their era seemingly did not care for rigor since they only thought Calculus as a tool to solve many problems. Since Calculus worked in their favor, they had no reason to worry about its foundation. The author also mentions the counterintuitiveness of Cauchy’s works on rigorous Calculus but acknowledges his brilliance in giving Calculus more…
While much of his time was dedicated to mathematics and optics during these years, he also examined circular motion, analyzed the moon and the planets, and laid the foundations for his laws of gravity. Newton studied Descartes La Géometrie among other mathematical works and discovered the binomial theorem. He also discovered the method of fluxions, which was his realization that “the integration of a function is merely the inverse procedure of differentiating it.” (CONNOR/ ROBERTSON, 2000:3) Using his new discovery of fluxions, Newton wrote On Analysis by Infinite Series (1669) and On the Methods of Series and Fluxions (1671) and invented new methods to find areas, tangents, minimum and maximum points on graphs, and the length of curves.…
When we went to the library to find a book for English class, the first book I checked out was entitled The Last Nazi. It was a book about the last known nazi that lived through the holocaust. It was interesting at first but then it was really hard for me to continue to read, because not only was it a historical non-fiction, it also included a large variety of words above my reading level. The second book I chose was, Calculus The Easy Way, one of the reasons I chose that book was because I thought it was going to help me in math, but It was not a good choice for my essay. The third book I chose was from the library, out of all those books I couldn’t find a good one. When I was ready to leave, a book on the checkout counter caught my eyes. The book title is Need. It's about teens living in Nottawa, Wisconsin who join the newest, hottest, networking site. It's a site that allows people to request anything that they NEED. However, access to this site is only by invitation only. Anything at all can be asked and your request will be fulfilled only if you accomplish a certain task that will be assigned by the site itself. It's a fast paced book, it takes social media stalking and bullying to a whole new level.…
The derivative of the function f with respect to the variable x is the function f ′ whose…
Lastly, Newton has many contributions to modern day life. One of his big ones that I already said was the Three Laws Of Motion. He also did work on the idea of Gravity. He helped in math also, he created a new form of math called calculus. Calculus is the study of how things change.…
His discoveries in mathematics were just as important. He came up with the Binomial Theorem and was one of the two creators of calculus. These discoveries represented a quantum leap in the fields of math and science allowing for calculations that more accurately modeled the behavior of the universe than ever before. Without these advances in math, scientists could not design vehicles to carry us and other machines into space and also plot the best and safest course. Calculus gave scientist the tools to set…
When calculus was invented, has always been a question in Math. The first signs of calculus were done by Greek mathematicians. Zeno of Elea of about 450 B.C. gave a number of problems which were based on the infinite. His argument was that motion is impossible. Other Greek mathematicians that contributed to the method of exhaustion are Leucippus, Democritus and Antiphon. The method of exhaustion is so called because one thinks of the areas measured expanding so that they account for more and more of the required area. Archimedes made one of the greatest contributions of the Greek. One advancement he made was to show that the area of a segment of a parabola is 4/3 the area of a triangle with the same base and vertex and 2/3 of the area of the circumscribed parallelogram. Archimedes also “invented” the volume and surface area of a sphere, the volume and area of a cone, the surface area of an ellipse, and the volume of any segment of a parabolic. No progress or advancements were made in calculus until the 17th century. One great mathematician that was born in Barsa, Persia is Abu Ali-Hasan ibn al-Haytham. He integrated a fourth-degree polynomial. In the 3rd century AD Liu Hui of China used the method of exhaustion in order to fin the area of a circle. In the 5th century AD Zu Chongzhi also used it to find the volume of a sphere. In the 12th century Bhaskara II of India developed an early derivative representing infinitesimal change and described an early form of “Rolle’s theorem”. Seki Kowa expanded the method of exhaustion in the early 17th century in Japan. In AD 1668 James Gregory provided a special case of the second fundamental theorem of calculus.…
Having a Calculus background doesn’t mean I excel in it. It is not a good idea to ignore what the teacher says and do other things because of “over confidence” (32). Sometimes I…
A piece of paper stained with salted tears, a mechanical pencil shaking frantically in a clenched fist, eraser shavings forming unidentifiable constellations on the sleek wooden desk - the devil in disguise, root of all evil: this was advanced placement calculus.…
As I walked into the class for the Advanced Placement Calculus (AP Calculus) course, I immediately took my seat. As I entered the room the teacher was solving a quite difficult equation. I took out my paper and pencil and began to write. The calculus teacher asked the class to solve the equations using a graphing calculator. I was not too sure about my answers but I continued to do the work. “All done?”, my math teacher asked to the class. “What did you get for number 1?” As the class confidently blurted their answers, I remained quiet after realizing that I had gotten every answer wrong. I did not expect that almost every day of being in AP Calculus would give me that same feeling of disappointment as I experienced on the first day. I tried…
Probability refers to the likelihood or relative frequency for something to happen. Blaise Pascal is referred to as the father of probability. Pascal contributed to the branch of mathematics known as probability in 1653. Through his work in probability, Pascal invented the binomial coefficients which are now known as Pascal’s Triangle. Pascal’s major input to the philosophy of mathematics came with his “Of the Geometric Spirit””.1 Blaise Pascal was also a major contributor to the founding of Statistics.…
He studied calculus for a large portion of his life. Newton realized the slope of a curve was constantly changing, and there was no effective equation to calculate the tangent line to the curve at any given point. A slope at a particular point had to be approximated by taking the average slope of smaller segments of the curve. Newton, with the help of Gottfried Leibniz, calculated a derivative function f ‘(x). This gives the slope at any point of a function f(x). It was a much quicker method than the one previously being used. This process of calculating the slope or derivative of a curve or function is called differential calculus. Newton tended to call it the “method of fluxions” and the instantaneous rate of change at a point on a curve the "fluxion", and the changing values of x and y are the “fluents". Having established the derivative function for a particular curve, it is then an easy matter to calculate the slope at any particular point on that curve, just by inserting a value for x. In the case of a time-distance graph, for example, this slope represents the speed of the object at a particular…