calculus document

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A Calculus Refresherv1. March 2003This work is licensed under the Creative CommonsAttribution-Noncommercial-Share Alike 3.0 Unported License.To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/or send a letter to Creative Commons, 171 Second Street, Suite 300,San Francisco, California, 94105, USA.www.mathcentre.ac.ukc mathcentre 2003Contents1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.Foreword2Preliminary work2How to use this booklet2Reminders3Tables of derivatives and integrals4Derivatives of basic functionsLinearity in differentiationHigher derivativesThe product rule for differentiationThe quotient rule for differentiationThe chain rule for differentiationDifferentiation of functions defined implicitlyDifferentiation of functions defined parametricallyMiscellaneous differentiation exercisesIntegrals of basic functionsLinearity in integrationEvaluating definite integralsIntegration by partsIntegration by substitutionIntegration using partial fractionsIntegration using trigonometrical identitiesMiscellaneous integration exercisesAnswersAcknowledgementswww.mathcentre.ac.uk157910111315161720212324262933353946c mathcentre 2003This work is licensed under the Creative CommonsAttribution-Noncommercial-Share Alike 3.0 Unported License.To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/or send a letter to Creati

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