User:Fiona
Fiona Ma - Second year, Faculty of Arts.
Calculus is used in many fields of study, which is why teachers always tell you to continue math past the point where it becomes mandatory because 83 different fields of work require math 12 and beyond. Calculus focuses on limits, functions, derivatives etc. and is the study of change, or the rate of change. Economics is a field that relies most heavily on calculus besides math, because economics focuses on functional relationships such as different variables, income, elasticities etc. Calculus especially is mostly used to determine marginal revenues and costs which helps to calculate how profit will increase in response to each input of production given.
Example: Microeconomics focuses on firm production, and firms produce its output so that marginal cost=marginal revenue. To calculate profit which equals to revenue-cost, we want to take the derivative and set it to zero to maximize profits. Therefore, marginal profit=marginal revenue-marginal cost and profit will be maximized when marginal revenue = marginal cost
http://www.youtube.com/watch?v=LmftTXTE3Fw
Also, similar to the example we did in class previously on elasticites, we can see that calculus is also used. To calculate the elasticity, we just have to find the percentage change : Elasticity - (percentage change in X) / (percentage change in Y) = (dX/dY) times (Y/X), where dX/dY is the derivative of X with respect to Y, therefore allowing us to calculate elasticity with calculus.
The Pythagorean theorem is used to calculate the hypotenuse of a right angle triangle. This theorem has been around for centuries and researchers found that it was apparent in many historical references. For example, the Egyptians used this theorem to build their pyramids. Although this theorem wasn’t put into a mathematical formula, the Egyptians had their own measuring system using a rope with 12 knots of equal distance showing their understanding of the 3,4, and 5 right angle triangle. To this day, we still use this theorem/method not only in math classes, but to design and build modern-day structures just like the Egyptians used it to build their pyramids. The Pythagorean theorem is defined as: a²+b²=c² (with c as the length of the hypotenuse). An example of this question would be: Matthew loves to zip line across buildings, he wants to zip line across two identical buildings that are 30 meters apart and he wants to zip line from the 10th floor to the 6th floor of the other building. Matthew knows that each floor is 10 meters high. How long should his zip line rope be? We can deduct that side A is 30m, and side B is 40m (10(10-6)). Using the Pythagorean theorem, we can solve for side C, which is the length of his zip line. A²+B² = C²
30²+40² = C²
900+1600 = C²
C = √ (900+1600)
C = √ (2500)
C = 50m
Using the Pythagorean theorem, we can conclude that Matthew’s zip line needs to be 50m long.
References :
http://ejad.best.vwh.net/java/pythagoras/history.html http://en.wikipedia.org/wiki/Pythagorean_theorem