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When you read the first page of the new review book by Henry Gu, THE CALCULUS HANDBOOK, CONCEPTS AND SKILLS, the following words will greet you:"Calculus is the
subject. Function is the object. Infinity is the concept. Limit is the result", you are then welcomed into the beautiful and complex world of Calculus by someone who knows it so well and understands how difficult it is for so many to learn. In the Preface, Mr.Gu says:"Calculus can not be made easy, but it can be made simple. This book is concise, but the scope of the contents is not". With these words, any high school student about to start AP Calculus, either AB or BC,or any first year college student starting Calculus 1 and then 2 for the first time, will be gently ushered into a world of greater understanding of a subject where each topic is made clearer in every way. It's as though Mr.Gu, knowing full well the difficulties students have with the subject, having taught it for many years, has read the minds of college and high school students and is offering his own tutorial as the topics proceed from Functions, their graphs, then Limits and Continuity all the way to the final chapter, Infinite Series. One of the most difficult topics for many students is Related Rates, and on page 24 of the book, there is a wonderful and simple explanation of what a formula is, having two or more variables, and when they change with time, how "taking the derivative of the equation with respect to time will relate rates of change of variables". Mr Gu then offers examples of these problems in a very clear and understandable way as he does throughout the book. The diagrams in the book are very easy to comprehend. Chapter X, page 62, offers a wonderful explanation of The Mean Value Theorem and a subsequent problem involving instantaneous rate of change. The book offers much more than just Calculus! The Appendix A1 cover Basic Formulas in Algebra, Geometry and Trigonometry. The appendix A2 covers Calculus Formulas from Rules of Differentiation, Integration, Definite Integration to Infinite Series. Appendix A3will instruct students in the use of the Graphing Calculator! This review book is a wonderful reference for both students and teachers and Mr. Gu, as he did with his previous review books,"TEACHER'S CHOICE MATH REGENTS REVIEW and STUDENTS CHOICE REGENTS REVIEW of each year of high school math, has done an amazing job.
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