Calculus

Stressing an intuitive rather than rigorous/formal approach to calculus, this student-oriented text covers all of the standard topics. Integration of chapter-end computer exercises and calculator exercises throughout the text and a graphing calculator appendix recognise the impact of technology on calculus. An abundance of interesting applications from engineering, physics, biology, chemistry, economics, astronomy, medicine and pure mathematics shows the far-reaching relevance of calculus. An algebra review is provided in Chapter 10. Numerous examples throughout the text contain all the algebraic steps, with key steps highlighted in colour, needed to complete the solution. The examples are complimented by more than 7,000 section and chapter exercises featuring drill, application, calculator, ''show/prove/disprove'', and challenge problems. Each problem set begins with ''Self-quiz'' questions to help students evaluate their understanding of basic ideas in the section. The development of calculus is outlined in extensive historical notes. Biographical sketches impart information on renowned mathematicians Content: Front Matter, Page i Dedication, Page ii Copyright, Page ii PREFACE, Pages iii-vii TO THE INSTRUCTOR, Pages ix-xi ONE - PRELIMINARIES, Pages 1-52 TWO - LIMITS AND DERIVATIVES, Pages 53-133 THREE - MORE ABOUT DERIVATIVES, Pages 134-183 FOUR - APPLICATIONS OF THE DERIVATIVE, Pages 184-249 FIVE - THE INTEGRAL, Pages 250-323 SIX - EXPONENTIALS AND LOGARITHMS, Pages 324-383 SEVEN - THE TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS, Pages 384-425 EIGHT - TECHNIQUES OF INTEGRATION, Pages 426-481 NINE - FURTHER APPLICATIONS OF THE DEFINITE INTEGRAL, Pages 482-525 TEN - TOPICS IN ANALYTIC GEOMETRY, Pages 526-549 ELEVEN - POLAR COORDINATES, Pages 550-575 TWELVE - INDETERMINATE FORMS AND IMPROPER INTEGRALS, Pages 576-598 THIRTEEN - TAYLOR POLYNOMIALS AND APPROXIMATION, Pages 599-613 FOURTEEN - SEQUENCES AND SERIES, Pages 614-667 FIFTEEN - VECTORS IN THE PLANE, Pages 668-688 SIXTEEN - VECTOR FUNCTIONS, VECTOR DIFFERENTIATION, AND PARAMETRIC EQUATIONS, Pages 689-738 SEVENTEEN - VECTORS IN SPACE, Pages 739-792 EIGHTEEN - DIFFERENTIATION OF FUNCTIONS OF TWO AND THREE VARIABLES, Pages 793-876 NINETEEN - MULTIPLE INTEGRATION, Pages 877-927 TWENTY - INTRODUCTION TO VECTOR ANALYSIS, Pages 928-989 TWENTY-ONE - ORDINARY DIFFERENTIAL EQUATIONS, Pages 990-1020 APPENDIX 1 - REVIEW OF TRIGONOMETRY, Pages A1-A14 APPENDIX 2 - MATHEMATICAL INDUCTION, Pages A15-A18 APPENDIX 3 - DETERMINANTS, Pages A19-A28 APPENDIX 4 - THE BINOMIAL THEOREM, Pages A29-A31 APPENDIX 5 - THE PROOFS OF SOME THEOREMS ON LIMITS, CONTINUITY, AND DIFFERENTIATION, Pages A32-A38 APPENDIX 6 - COMPLEX NUMBERS, Pages A39-A45 TABLE A.1 - Exponential Functions, Page A46 TABLE A.2 - Natural Logarithms, Page A47 TABLE A.3 - Common Logarithms, Pages A48-A49 TABLE A.4 - Trigonometric Functions, Page A50 TABLE A.5 - Hyperbolic Functions, Page A51 TABLE A.6 - Integrals, Pages A52-A60 ANSWERS TO ODD-NUMBERED PROBLEMS AND REVIEW EXERCISES, Pages A61-A129 INDEX, Pages A131-A138