Math Camp for Economists Duke

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1、MathCampforEconomistsDanielA.GrahamJuly29,2010Copyrightc2007-2008DanielA.GrahamiiContentsContentsiiiPrefacevii1LinearAlgebra11.1RealSpaces.....................................11.2CombinationsofVectors...............................51.3TheStandardLinearEq

2、uation.............................91.4SeparatingandSupportingHyperplanes........................111.5Answers......................................122MatrixAlgebra152.1LinearSpaces....................................152.2RealValuedLinearTransformationsan

3、dVectors....................162.3LinearTransformationsandMatrices.........................172.4InvertibleTransformations..............................192.5ChangeofBasisandSimilarMatrices.........................202.6SystemsofLinearEquations..............

4、...............212.7SquareMatrices...................................242.8Farkas’Lemma...................................312.9Answers......................................33iii3Topology353.1Counting......................................353.2MetricSpaces.

5、...................................393.3TopologicalSpaces.................................433.4SigmaAlgebrasandMeasureSpaces..........................453.5Answers......................................464Calculus474.1TheFirstDifferential...................

6、..............474.2QuadraticForms...................................494.3TheSecondDifferential...............................514.4ConvexandConcaveFunctions............................534.5Answers......................................565Optimization575.1Op

7、timization....................................575.2TheWellPosedProblem...............................675.3ComparativeStatics.................................706Dynamics756.1DynamicSystems..................................756.2SystemsofLinearDifferentialEq

8、uations........................816.3Liapunov’sMethod..................................88Notation91UsingMathematica93Basics.........................................93InputExpressions....................................93Sym