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MATH 237 (3)
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Department
Mathematics
Course
MATH 237
Professor
Richard Ennis
Semester
Fall

Description
Calculus3CourseNotesforMATH237Edition421JWainwrightandDWolczukDepartmentofAppliedMathematicsCopyrightJWainwrightAugust19912ndEditionJuly1995DWolczuk3rdEditionApril2008DWolczuk4thEditionSeptember2009updatedOctober2010ContentsPrefaceiiTotheStudentReaderiiiAcknowledgementsv1GraphsofScalarFunctions211ScalarFunctions212GeometricInterpretationofzfxy42Limits921DenitionofaLimit922LimitTheorems1023ProvingaLimitDoesNotExist1124ProvingaLimitExists143ContinuousFunctions2031DenitionofaContinuousFunction2032TheContinuityTheorems2233Limitsrevisited284TheLinearApproximation2941PartialDerivatives2942SecondPartialDerivatives3243TheTangentPlane3544LinearApproximationforzfxy3645LinearApproximationinHigherDimensions395DierentiableFunctions4251DenitionofDierentiability4252DierentiabilityandContinuity47CONTENTSCONTENTS53ContinuousPartialDerivativesandDierentiability4954TheLinearApproximationRevisited526TheChainRule5561BasicChainRuleinTwoDimensions5562ExtensionsoftheBasicChainRule6263TheChainRuleforSecondPartialDerivatives677DirectionalDerivativesandtheGradientVector7271DirectionalDerivatives7272TheGradientVectorinTwoDimensions7673TheGradientVectorinThreeDimensions808TaylorPolynomialsandTaylorsTheorem8281TheTaylorPolynomialofDegree28282TaylorsFormulawithSecondDegreeRemainder8583Generalizations899CriticalPoints9191LocalExtremaandCriticalPoints9192TheSecondDerivativeTest9593ProofoftheSecondPartialDerivativeTest10610OptimizationProblems109101ExtremeValueTheorem109102AlgorithmforExtremeValues112103OptimizationwithConstraints11511CoordinateSystems124111PolarCoordinates124112CylindricalCoordinates131113SphericalCoordinates1332212MappingsofRintoR137121TheGeometryofMappings138122TheLinearApproximationofaMapping142123CompositeMappingsandtheChainRule145
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