Transcription of Understanding Basic Calculus
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Understanding Basic Calculus
UnderstandingBasic ChungDedicated to all the people who have helped me in my book is a revised and expanded version of the lecture notes forBasic Calculusand other similar coursesoffered by the Department of Mathematics, University of Hong Kong, from the first semester of the academicyear 1998-1999 through the second semester of 2006-2007. It can be used as a textbook or a reference bookfor an introductory course on one variable this book, much emphasis is put on explanations of concepts and solutions to examples. By readingthe book carefully, students should be able to understand the concepts introduced and know how to answerquestions with justification. At the end of each section (except the last few), there is an exercise. Studentsare advised to do as many questions as possible. Most of the exercises are simple drills.
Chapter 0 Revision 0.1 Exponents Definition (1) Let n be a positive integer and let a be a real number. We define an to be the real number given by an = a| a{z}a n factors (2) Let n be a negative integer n, that is, n = k where k is a positive integer, and let a be a real number di erent from 0. We define ak to be the real number given by ak = 1 ak (3) (i) Let a be a real number di erent ...
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