vector calculus

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1、MathematicalTripos:IAVectorCalculusContents0Introductioni0.1Schedule..................................................i0.2Lectures..................................................i0.3PrintedNotes...............................................ii0.4ExamplesSheets..

2、...........................................iii0.5PreviousComments,CommentsonCommentsandStyleofLectures.................iii0.6Books...................................................iv0.7Revision..................................................iv0.7.1Vectors......

3、........................................iv30.7.2Cylindricalpolarco-ordinates(ρ,φ,z)inR..........................vi30.7.3Sphericalpolarco-ordinates(r,θ,φ)inR............................vi0.7.4Determinants............................................vi1PartialDifferen

4、tiation11.1ScalarFunctionsofOneVariable....................................11.1.1Limits...............................................11.1.2Continuity.............................................11.1.3Differentiability..........................................11.1.

5、4Taylor’sTheorem.........................................21.2FunctionsofSeveralVariables......................................21.2.1Limits...............................................31.2.2Continuity.............................................31.3DerivativesofV

6、ectorFunctionsofOneVariable............................41.3.1Example..............................................41.4PartialDerivatives............................................41.4.1Definition.............................................51.4.2Examples..........

7、...................................51.4.3DirectionalDerivatives......................................71.5Differentiability..............................................71.5.1ScalarFunctionsofTwoVariables...............................71.5.2FunctionsofSeveralVariabl

8、es..................................81.5.3PropertiesofDifferentiableFunctions.............................91.6TheChainRuleandChangeofVariables...........