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Calculus is the language of science Ever since the time of Isaac Newton and Gottfried Wilhelm von Leibniz, calculus has been our key tool for opening up and examining nature Calculus is the most powerful and versatile collection of analytical tools ever devised by mankind It is an essential part of our knowledge of the world around us, and everyone should be acquainted with its fundamental principles Calculus need not be difficult The main ideas---functions, limits, derivatives, and integrals---can all be described using everyday language The key to getting a grasp on the concepts is to work examples And that is what this book will do for you: It will work dozens of examples, and then walk you through many more It will pause to point out the pitfalls and points of confusion It will look back to assess what we have learned and then proceed ahead in measured steps The book has many learning tools to help you make your way through the subject Every new idea has features called You Try It This gives you immediate practice, at the moment of impact, with the new idea Additional features called Math Note point out interesting byways and confusing points and matters of interest Finally, the Still Struggling passages help students over difficult points Every chapter ends with a quiz to give you practice and to make sure you have mastered the material at hand The quizzes are of course open book You definitely want to refer back to the material you have read as you solve the problems And the answers are provided at the back of the book You should actually write out the solution of each problem---because this is a good skill to have, and so that you can compare your answers with those in the book By writing out the solutions you will also have an archive of your work.

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always positive and for larger and larger negative x, the function approaches the limit 1 from the negative side Go through the logic and verie the graph of Fig 2-5

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A satisfactory score on any quiz is 70% If you don t achieve that score on your first try, then do some reviewing of the trickier parts of the text and try again It is best not to proceed until you are comfortable with the chapter you are finishing There is a Final Exam at the end of the book This draws together the entire learning experience, and helps you to see everything you have learned The Final Exam is multiple choice and is practically oriented It will help you to feel good about the concrete and useful body of mathematics that you have mastered A score of 75% is a passing grade on the Final Exam A good pace for this book is one chapter per week You ought to be able to cover each section in a chapter in two or three hours You don t want to rush through the material, but you don t want to go too slowly either Set a steady pace for yourself, and endeavor to stick to it There is no substitute for strong work habits When you finish this book, it should be part of your working reference library You should refer back to it in later courses, and look things up as you need them This is an easy book to dip into We encourage you to do so Calculus is fun and exciting It is full of new ideas---and very important ones These are ideas that you will see repeatedly as you go on in engineering or physics or business or any life path where analytical thinking plays a role The key ideas of calculus are ones that make sense in many different contexts Rates of change are central to the way that we understand the world around us Aggregation and summation are incisive means of drawing information together The amazing fact about calculus is that these two key ideas are related---by the Fundamental Theorem of Calculus That is one of the main things that you will learn in this book Learn the Fundamental Theorem and you have learned what calculus is all about You should read the book with pencil in hand You will want to calculate and try things as frequently as possible Be sure to do the quizzes And take the Final Exam to be sure that you have mastered the material You will find that this book contains bibliographic references of the form [SCH1] That is an acronym that summarizes the identity of the book Using this acronym, you can easily locate the item in the Bibliography This is a seminal journey in your education, and one that you will look back on with pride and pleasure Happy hunting!.

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When the derivative of a function f exists at a point c, we denote the derivadf d f (c) = (c) In some contexts (eg, physics) the tive either by f (c) or by dx dx (c) is used In the last example, we calcuated that f (2) = 5 notation f

Critical Results Lmax = 06393 Vmax = 0019440 @ 360 deg (opening) Amax = 0000974 @ 415 deg (opening) Anose = 0000610 Area = 36020 +RCmin = 07679 @ 335 deg (opening) RCmin =(None)

As the powers of the polynomials increase, the fimctions become harder to graph In chapter 4 more complicated polynomials will be graphed with the aid of calculus

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The importance of the derivative is two-fold: it can be interpreted as rate of change and it can be interpreted as the slope Let us now consider both of these ideas

Diesel characteristic curves, (intake valve motion) Courtesy Hubbard, D, 2000

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