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 would like to thank you again and to tell you that with the help of your book, I managed to get a very good score in mathematical analysis exam. Which I am very happy about and I really feel I have gained a lot of knowledge from your book and it completely changed the way I understand things. "

" The one thing I hated about calculus was that they never explained what anything was. Up until now, I never even understood what calculus was even a study of, except finding whatever a derivative is and how y of something looked on a graph. I just read only 3 chapters of your book and I have been doing calc for close to 9 hours now. I am totally enthralled by calculus now. I never thought i would say it is my favorite subject. Excellent work! Thank you so so much. "

" My name is Rafael Roquetto, I am a computer science graduation student in Brazil, and work as a computer programmer for Citigroup IT Center. I have always been trying to understand calculus. I had already managed to understand it "graphically", geometrically, but I was never able to get the true calculus philosophy: THE RATE OF CHANGE OF A FUNCTION, DEPENDENT AND INDEPENDENT DIMENSIONS and whatsoever. Therefore, I would like to thank you for writing this wonderful tutorial, book, or whatever you call it. Your work really helped opening my mind, and I feel really enlightened now. Thank you very much. "

" Wow, this is absolutely amazing, you give background information then you connect that with calculus without all of the number crunching. This made me think, which I love to do, and I thank you for that. "

" I am on a quest for knowledge, or more precisely, questions, and then answers to those questions. I discovered Atheism then, Philosophy, Psychology and re discovered Physics (after an A-Level of memorisation and no answers) and am on a journey of actually learning what the world is about, rather than having to try and remember what I am told it is about. I believe Maths is a big part of the journey. From a little searching, I found your book and with such a great start, how could I not read on. I have no practical reason for learning any of this, other than for my own pleasure, as I am currently in a year of limbo before I go to University to do a BA in Video (or documentary). But I am currently loving learning, and your book is finally giving me an understanding of things I before had just been told to take for granted. "

" For many days I had been seeking for such a comprehensive guide on calculus. I also agree that nothing is impossible to learn and feel when you split it into fragments of logical components. This book makes us believe the same. Thank you very much for writing and providing such a good book. I teach Mathematics and English literature and I believe Mathematics can be interesting and romantic as literature too, when there will be writer like you. "

" I love your book... so far I'm on Chapter 6, and I love it so much that I start reading it any chance I can get. Thank you so much for Understanding Calculus. What a great gift you've given so many people. "

" I love the way you are presenting the course. I am a 52 year old businessman, decided to go back to school to enhance my knowledge and improve my skills. Currently I am taking some post graduate courses in Finance. Since I forgot all math (algebra and Calculus), I search on the net and I am very lucky to find your fantastic book. I just started today. In fact, I had a plan to jump right away to derivatives and integration, but the way you are presenting the course impressed me a lot, and decided to read it all word by word. "

" I think you have articulated Calculus where the average person not versed in it - can understand it, and apply it to problems. I also feel you have defined Calculus and its concepts very well, especially how it lends to a more scientific approach to life.. critical thinking, broading one's scope of the things. I want to thank you for offering this. " - Beatrice Lewis

" Wow! Your section on why study calculus actually made me want to study this stuff and I was just browsing. Calculus seems almost philosphical when you explain it in you intro. You made it sound interesting! A feat in of itself! Well done sir! "

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