Lectures in Calculus

This book is a collection of six years of lectures, helping high school students learn AP Calculus. The following is an excerpt from one of the lectures.Newton and Leibnitz invented calculus 350 years ago. They defined the Derivative as the change-in-f divided by a change-in-x that vanishes to zero.In the Newton-Leibnitz era, this was the way the derivative was taken. There was controversy. Paraphrasing Berkeley 300 years ago: “ If the change-in-x is zero, how can you divide by it? “Then 200 years ago, Cauchy invented Limit Theory, explaining that the change-in-x approaches zero, but never equals zero.The above excerpt shows why lectures in this book deal with Limit Theory after lectures on the Derivative and Integral. The lectures in this book cover all the topics in AP Calculus. Hence, the material is first-year college level. The book is organized so that the derivatives of all of the functions are learned in Chapter A. The integrals of all but the Log function, are learned in Chapter B. The integral of the Log function is learned in Chapter G. Notes about the examples in this book:(1) Theorems are proven by examples rather than proofs.(2) Whenever possible, cookbook methods are given to obtain solutions to problems.(3) The examples are collections from the lectures, the homework, and the quizzes.(4) The example problems are all solved. Read more