## 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 am living in Germany and work at Nokia R&D. I wanted to use my time to work on things which I scored well but never understood correctly. Things like calculus, functional programming, Knuth books, Kernel programming were somethings which I wanted to touch back...and now its time! I liked the chapter 1 of yours. Rarely I find such philosophy from science journals or books. I see that you are from the Indian subcontinent. Thats the secret maybe, I think I can learn a lot from you. "

" Appreciate the book you have written. Your work is a solid piece of mathematical art. You know the psychology of the reader & have chosen the correct sequence of ideas & words to explain concepts which we cannot touch or see! You are the man !!! "

" I am studying Calculus because I never fully understood the full logic of integration, even though I took a year of Calculus as an undergrad at UCLA, where I got an A in every class. I always understood derivatives very well, but never fully understood integration or the Fundamental Theorem of Calculus. I love your website, and other than chapter 11.1 being hard for me to follow, your website has really helped me understand this at a greater level. Thank you so much. By the way, I am 38 years old and live in Los Angeles, where I work in Real Estate. "

" Many errors I notice seem to be in repeated wording, missing diction and misuse of plurals. Probably due to thinking faster then you can type and running through spell checkers. However, for some instances this may be intentional on your part to convey an idea. I applaud your approach to identify and remedy a fundamental failure of most education in mathematics. Something I have been observing for 45 years. I can only assume why you undertook this noble deed. It is commendable. Don't let it fall into the class of so many well meaning, poorly written texts written by professors for professors to praise each other all the way to the bank. "

" I am one of those engineers you mentioned in your prelude. I have a vast background in mechanical application and technical discipline and long to master the mathematical expression of my ideas. I spent some time reading the history of mathematics in an attempt to grasp what the problems were that spawned new tools. I never had the capacity to merely memorize. I learn by knowing with intimacy instead. Currently I am in aspects of aerospace and start-up entrepreneurial business with nothing requiring mathematics at this time. "

" I have taught AP Calculus for 20 years and this is by far the most eloquent explanation of Taylor's theorem I have seen. Bravo! "

" First of all congratulations for your amazing work and thank you so much. I am an Arab young student and a big fan of science especially physics. The problem is that I have always struggled with physics and maths in school and never understood them. So I used to tell myself that I did not have an adequate brain for science and am not intelligent enough. But the interest for science was always there in my mind. After reading your book I descovered that my only problem is having the wrong educational system in my country and wrong teachers, they are really good at making students hate science! Anyway thanks for the chance you give to students to understand. "

" I just downloaded your book. My formal education is very limited and I intend to try and broaden my view of the world in which I live. I have been busy working most of my life and now that I am retired I am trying to give myself a liberal education at the age of 69. I am doing this at home. I am disabled and this learning adventure along with my hobbies keeps me busy. I think that you are doing all of us a great service by sharing your knowledge with us. I just hope that I am up to the challenge! Be well and thank you again. "

" I would think it necessary to spend more time on discussing limits, including their existence depending on agreement between left and right sided limits. It is not discussed in sufficient detail, in my opinion, nor is it mentioned that functions are only differentiable where they are continuous. "

" It is such a pity that universities (or at least the one I'm at in Brisbane) do not teach you what is going on, they just give you equations and expect you to use them and not really ask questions. I am studying electrical engineering and have been told that if I would like to understand the maths then either I learn it my self or I join the dual degree of maths and electrical. That is just crazy to me, they expect that every one is going to work for some big company and not pay attention to the details of what they do. "

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