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Intro To Learning Calculus. I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education. Calculus relates topics in an elegant, brain-bending manner. My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms of survival. You understand why drugs lead to resistant germs (survival of the fittest). You know why sugar and fat taste sweet (encourage consumption of high-calorie foods in times of scarcity). It all fits together. Calculus is similarly enlightening. They are. Unfortunately, calculus can epitomize what’s wrong with math education. It really shouldn’t be this way. Math, art, and ideas I’ve learned something from school: Math isn’t the hard part of math; motivation is. Teachers focused more on publishing/perishing than teachingSelf-fulfilling prophecies that math is difficult, boring, unpopular or “not your subject”Textbooks and curriculums more concerned with profits and test results than insight Poetry is similar.

Free Mathematics Books Download | Ebooks Online Textbooks. Wolfram Alpha: Computation. Derivatives of Trig Functions. Trigonometric functions are useful in our practical lives in diverse areas such as astronomy, physics, surveying, carpentry etc. How can we find the derivatives of the trigonometric functions? Our starting point is the following limit: Using the derivative language, this limit means that .

This limit may also be used to give a related one which is of equal importance: To see why, it is enough to rewrite the expression involving the cosine as But , so we have This limit equals and thus In fact, we may use these limits to find the derivative of and at any point x=a. So which implies So we have proved that exists and Similarly, we obtain that exists and that Since , and are all quotients of the functions , we can compute their derivatives with the help of the quotient rule: It is quite interesting to see the close relationship between (and also between From the above results we get These two results are very useful in solving some differential equations. Example 1. . So using the product rule, we get Exercise 1. Calculus Video Tutorials. Pi is Wrong: Tau. Table of Trigonometric Identities. [Geometry][Algebra][Differential Equations] [Calculus][Complex Variables][Matrix Algebra] S.O.S MATHematics home page Do you need more help?