## 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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### Testimonials

" 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. "

" I've enjoyed "re-learning" calculus from your site.... I never understood it in college, and out of pure curiosity to see if I could understand it now, I found your site, and found it a very valuable resource. Thank you for providing it. "

" I am studying calculus because, at 59 years old, I am in the process, out of pure enjoyment and curiosity, of finally actually learning and understanding things that previously I had only just memorized. My last exposure to Calculus was in high school in 1967 and I never had a clue as to what I was doing or why. Why at this late date have I finally discovered what it means to "understand" and to find an interest in achieving it, including the calculus? I haven't a clue to that one either... it just happened. Yours is one of several online sources that have given me a better understanding in one week of what Calculus is all about than I ever had after 1 year of it in high school. Crowell, Strang, and Silvanus Thompson's book have also been helpful. "

" I am studying calculus for personal enrichment. I have been interested in various aspects of physics, computer science, etc., that require a solid foundation in calculus. Overall, it also seems that a modern education should include such an integral aspect of human knowledge. Finally, your tutorials have made calculus seem accessible and understandable to someone like me with a shaky mathematics foundation. I thank you for introducing not only the ideological concepts, but also the philosophical framework by which to fully understand the calculus. "

" I got my PhD in Animal Nutrition (I am a Vet) studying fermentation patterns in dairy cattle using in vitro techniques. I made very nice graphs of pH and digestibility but could never produce a mathematical model out of it. First, because I didn't have the maths to understand it and do something with it; second, because of a terrible mistake of using pH data (which is a logarithmic value) and analyzing as it were a linear thing. When I finally did a conversion to linear scale I found a complete different set of patterns and I had to rewrite my thesis. By the time I finished, I had run out of money and time and had to finish up, get my stuff together and go back home. I feel I need the calculus to understand the natural world, make predictive models of events happening in different compartments (change over time) and be able to predict biological process (such as rumen pH which eventually will affect bacterial growth, digestion, milk production and animal health). I also "need" to improve my maths skills because I teach high school biology and have several "confrontations" with the math teachers, which give algebra and calculus exactly in the way you say it should not be done (exactly the way I was tought) with the obvious results you imagine. The students can differentiate and integrate but they cannot even say why they do it. When they ask me (out of pure desperation) I can only help them with my "common sense knowledge" but even so I always get an "A-HA effect", that means, they understood something... Now they know more than I do. "

" I am a student and for the first time we are being taught calculus in the school. All the students are having problem with this subject and the teacher does not help either for he has to " complete the course in the appointed time ", just as you said in your e-book, " he teaches us only number crunching ". Some of my class-mates had a chance to visit your web-site and then they inform me about it too. I found it wonderful and I think that I do not even need a teacher to learn calculus anymore, you e-book is so excellent that I cannot even tell. In the same way we are having problems with the physics, our physics teacher does not wants us to understand the concepts, he just wants us to memorize the newton's laws and many other physics equations so that we just become able to " crunch numbers ", and really, you are right, " one cannot apply theorems in the nature if he has no clue of their origin ". That is all Mr. Faraz Hussain. "

" I was a student of Biological sciences but I soon realized that I am not made for biology but mathematics, so, now I am swithcing my subjects from "biology" to "engineering". In the course of the time, I came across many problems in mathematica and physics. So far I have not found any "physics book" or "mathematics" book to be useful anywhere, not on the internet nor in the libraries. However, I did tried my best to understand the mathematical and physical concepts on my own efforts and I succeded to such a level that now I am on my way to "calculus" and "advanced physics", in my way, I found your electronic book which was free to be read and I read it. I have read its 12 chapters and I am very pleased by those. I will read them again to understand better. But still, I have not understood the basic concepts of mathematics and physics, that is why I asked you to write a book on physics too. I can tell you the problems that students mostly encounter in their studies of mathematics and physics because I am myself a student and I have many friends too. That was all. And Sir Faraz Hussain, I really want you to write an electronic book on physics and I want you to write it just like you wrote the calculus notes, "YOUR NOTES DO NOT FOLLOW THE TRADITIONAL WAYS OF TEACHING" ,That is the beauty of your notes. "

" Hi! I'm a mechanical engineer from Spain. Congratulations for your book, it shows how any human-developed knowledge is made of the same basic logical "blocks", "atoms", or however you want to call them. I wish more books like this were written! "

" I thought of you yesterday because someone was asking about squash and I told the person about your website. I also then remembered that you had a Calculus book online, which I hadn't really gone through before. So anyway, I decided to go back to the book for a glance during lunch today. Wow man, that is an amazing feat! To put all that stuff together and explained so well...damn! I'm really impressed. During my quick look, I found a few things I thought I would bring to you attention, all in the name of continuous improvement. See below this email for some comments on Section 4.4. Once again though, wow! That is some effort you put in there. You would make Miss Aaliya proud! ;) I hope to go through it in its entirety at some point. " - Masud Mahdi

" I am working my way through your online calculus and physics books. I enjoy them a lot and I find my self seeing things in a different light, courtesy of your explanations. I work as a computer technician, but my real enjoyment are the engineering classes that I take part time. So, I appreciate all the engineering explanations that you have included in your material. Thanks for taking the time to build such as fascinating online resource. "

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