Think of it as a positive number greater than zero but less than any positive real number, or a negative number less than zero but greater than any negative real number. Newton’s and Leibniz’s formulation of differential calculus depended on the concept of an infinitesimal, or a non-zero number of negligible value. The red line is tangent to the curve y= f(x) (Graph from The Math Page) As the distance between the two points decreases, drawing closer and closer to 0, which would represent an infinitesimal change in x, then the calculated slope would, theoretically, approach the actual slope. To find slope, one divides the change in y of two points by the change in x of those same two points. the slope of a tangent line at an exact point. In Newton and Leibniz’s day, scientists could very well calculate the average slope of the curve, but did not know how to calculate the exact slope at an individual point on a curve, i.e. They, most will assert, discovered calculus. The works of Sir Issac Newton and Gottfried Leibniz, mathematicians and philosophers of the Scientific Revolution prepared the way for future analysts to formalize limits. Calculus concerns itself with the calculation and application of derivatives and integrals, which find their formal definitions in the concept of a limit. Thus, in a series of posts from now into mid-February, I want to delve into the history of calculus.Ī study of limits must precede a study of calculus. While not the epitome of all mathematics, it does, in my opinion, deserve a little time in the limelight. Typically, high school mathematics study ends at calculus.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |