Understanding Basic Calculus

  • From the preface This book is a revised and expanded version of the lecture notes for Basic Calculus and other similar courses offered by the Department of Mathematics, University of Hong Kong, from the first semester of the academic year 1998-1999 through the second semester of 2006-2007...... Accompanying the pdf file of this book is a set of Mathematica notebook files (with extension .nb, one for each chapter) which give the answers to most of the questions in the exercises.
  • BasicCalculus.pdf
  • calculus_mathematica_nb_files.zip
  • The pdf file is designed to be printed on both sides of A4 paper without page scaling. Blank pages are generated, where necessary, so that chapters always start on odd pages.

  • calculus_source_files.zip The zip file contains the source files (tex, eps and other files) that are used to produce the book.

  • Files for lectures The following files (pdf, xls, zip for html plus gif, etc.) were used by the author to teach the course Basic Calculus in 2006-2007 Semester 2. The pdf files are better read in full screen mode (download and save them first, press Ctrl+L if they are not opened properly). The html files illustrate some concepts using animations. To open the html files, unzip the corresponding zip files.

  • Lecture_01.pdf     video1.wmv (download from HKU Math Dept)
  • Lecture_02.pdf
  • Lecture_03.pdf
  • Lecture_04.pdf
  • Lecture_05.pdf
  • Lecture_06.pdf
  • Lecture_07.pdf
  • Lecture_08.pdf     velocity.xls
  • Lecture_09.pdf     area.zip     area.xls     sequence_limit.zip     function_limit.zip
  • Lecture_10.pdf
  • Limit_Mistake.pdf     Limit_Summary.pdf     Lecture_11.pdf     e.xls
  • russell_paradox.pdf     paradox.pdf     Lecture_12.pdf     slope.zip     slope1.zip     secant_slope.xls
  • Lecture_13.pdf     no_slope.zip
  • Lecture_14.pdf
  • Lecture_15.pdf
  • Lecture_16.pdf
  • Lecture_17.pdf
  • Lecture_18.pdf
  • Lecture_19.pdf
  • Lecture_20.pdf     angle.zip     angle60.zip     angle-300.zip     angle420.zip
  • Lecture_21.pdf     sine_cont.zip     sine_x.xls
  • Lecture_22.pdf     limit_e.xls     interest.xls
  • Lecture_23.pdf
  • Lecture_24.pdf
  • Lecture_25.pdf
  • Lecture_26.pdf
  • Lecture_27.pdf
  • Lecture_28.pdf
  • Lecture_29.pdf
  • Lecture_30.pdf     MATH0802_introduction.pdf
  • Note Since the book is a revised version of the lecture notes, some definitions and terminologies used in the book are different from that given in the lectures. The following gives a few of such differences.

    1. In the lectures, functions are assumed to be differentiable. Thus critical point of a function f means a number where the derivative of f is 0.
    2. In the book, the term critical number is used instead of critical point and there are new terminologies like local maximizer/minimizer.
    3. The definite for definite integral in the book is different from that in the lectures.
    4. In the lectures, primitive and antiderivative have the same meaning whereas in the book, they have different definitions.