## Understanding Calculus

#### e-Book for \$4

 Preface 1. Why Study   Calculus 2. Numbers 3. Functions 4. The Derivative 5. Differentiation 6. Applications 7. Free Falling   Motion 8. Understanding  Derivative 9. Derivative  Approximations 10. Integration   Theory 11. Understanding   Integration 12. Differentials

 Inverse Functions Exponents Exponential  Functions Applications of   Exponential  Functions Sine and Cosine   Function Sine Function Sine Function -   Differentiation and   Integration Oscillatory Motion Mean Value   Theorem Taylor Series More Taylor Series Integration   Techniques

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### Understanding Calculus

Understanding Calculus is a complete online introductory book that focuses on concepts. Integrated throughout the e-book are many engineering applications aimed at developing the student's scientific approach towards problem solving.

The book has as much to do with calculus as with philosophy. My motivation in writing it was to prove to myself that I could understand a complex subject like calculus by applying simple rules of logic and reason. As Henry Ford said, " Nothing is particularly hard if you divide it into small jobs ". Too much of the world is complicated by layers of evolution. If you understand how each layer is put down then you can begin to understand the complex systems that govern our world. Charles Darwin wrote in 1859 in his On The Origin of Species,

" When we no longer look at an organic being as a savage looks at a ship, as at something wholly beyond his comprehension; when we regard every production of nature as one which had a history; when we contemplate every complex structure and instinct as the summing up of many contrivances, each useful to the possessor, nearly in the same as when we look at any great mechanical invention as the summing of the labour, the experience, the reason, and even the blunders of numerous workmen; when we thus view each organic being, how far more interesting, I speak from experience, will the study of natural history become! "

Darwin's words are equally applicable to art as well as science. Every artist's performance requires a great deal of craft. Even stand-up comedy is not a question of going on stage and saying funny things. There is an enormous amount of work, practice and thought that would have to go into it.

My advice to students is to find something that fascinates you. As Physics Nobel Laureate Richard Feynman said, " Study hard what interests you the most in the most undisciplined and original manner possible." The price for seeking understanding is that one must be willing to tolerate ambiguities and accept one's own ignorance. Feynman said, " I can live with doubt and uncertainty. I think it is much more interesting to live not knowing than to have answers which might be wrong."

I hope you find the book enlightening as the goal is to learn by understanding, not by memorizing. I am currently writing another book called, Understanding Physics. Please do not hesitate to contact me with your feedback and questions.

Faraz Hussain - Author

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