## Understanding Calculus

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 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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### Testimonials

" I graduated from BGSU in 1974 where I took a year in Calculus. It always bothered me that I did not fully understand the Fundamental Theorem of Calculus or more specifically the connection of the derivative and anti derivative to the theorem. As in reference to your preface, I memorized the procedures without understanding what I was doing. After 35 years it makes sense to me now. Thank you! " - Steve Wright

" Great text. Best and clearest resource I've found - especially for topics requiring geometrical interpretation. Consulted others, Stewart, Thomas, Keisler, etc. Exposition crystal clear. Others not. Many thanks. "

" Mr Faraz, I must say that your site on understanding calculus is the best resource I have seen on Calculus. I am doing a masters course in mechanical engineering in New york, and I have been gone from college for a while before continuing to my masters. I forgot a lot, but when I found your site and started reading, I understood things i never saw reason with.

I understand why calculus is used in almost all engineering courses, and I havent even gotten to half of your book. Thanks a lot. "

" I am a high school physics teacher and am trying to teach the course by having the students use as much logic as they can. I try to include as much calculus as I can without getting bogged down in the equations. I like your approach to the subject of calculus and I am looking for ways to incorporate more calculus into the curriculum. "

" I really greatly appreciate your effort to make learning calculus easier than ever. I used to do very excellent in mathematics when I was in High School. Unfortunetly I get divorced with mathematics when I joined Agricultural University where a freshmen calculus instructor used to mock us by saying mathematics has little to do with farmers, this much is enough for you (for excuses not get in to detail). That is almost 20 years ago. After that some times I feel very guilty of abandoning Mathematics and Physics which I used to like very much and which I can understand the logic behind of most seemingly complex formulas. I went to library and tried to get the simplest introductory book on calculus. But all the books I tried to read were to complicated to me and I dropped the idea of doing mathematics again. So I start to browse the internet to get some tips on learning Mathematics specially calculus. So I soon came across of this electronic book which I found very help full to regain my mathematics skill and knowledge. Thank you so much for writing this book and posting it on the internet so that every one can have access free of charge. "

" Problem with many math text I have read is they are far too concerned with correctness and proofs. This is fine once the subject has been understood on a basic level, but to first learn Calculus you need a more example driven approach like you do. I can only say I thank you for making this available. "

" I am from Greece, specifically Chania - Crete, just finished architecture in Athens, and now I started a masters in the department of Mechanics and Science of Materials in the Technical University of Crete. That includes lessons that require deep understanding of mathematics, and therefore I find your site very helpful. "

" I am a software engineer working for an investment bank. In a pursuit to understand all the risk positions and corresponding calculations, I started reading some stuff and soon came to know that I need a deep conceptual understanding of calculus and linear algebra to know the business. Actually I had learned the calculus when I was doing my bachelors in India but it was blind learning without necessarily understanding the applications in real life. I don't know whether it was my inclination to study blindly or there was something lacking in educational system which never made the subjects interesting. The way you have explained Maths as a language of science to describe the changes in situation seems so true to me after I started relating real life problems to mathematical calculations. As of now I am done with reading of first 12 chapters and already started understanding many financial risk analysis computations. "

" I think that you must assume that your visitor actually has the passion for math "or why he visits your site at all". So you should decrease the long intro. which turned into pure philosophical essay instead of an intro to the main subject. Finally , I must admit it's really a good essay about philosophy "in the wrong place" which i have really enjoyed. "

" I am a student of PUNJAB AGRICULTURAL UNIVERSITY (INDIA) and pursuing B.Tech in Agricultural Engineering. I am very much thankful to you for providing such a good material for Calculus. "

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