高等数学英文1-1-10

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MathematicsWanYuanSchoolofScience,WHUTMymailbox:Myphone:Classmailbox:高等数学英文1-1-10SomerulesforourclassPleasetakenotesPleaseturnoffyourcell-phonesIfyouarelate,justcomeinandjoinusAskquestionsassoonaspossibleDohomeworkbyyourselfHandupyourhomeworkintime高等数学英文1-1-10IntroductionAdvancedmathematicsisaprimarycourseforcollagestudent.Inthisclass,wewillintroducesomebasicconceptsandsomeusefultoolsofmathematicsforyourfurtherstudyorresearch.PartoneTheoreticalbasisofCalculusThedifferentialCalculusanditsApplicationTheintegralCalculusanditsApplication高等数学英文1-1-10高等数学英文1-1-10I.TheIntegersandtheRationalNumbers1.Set(集合)Def:Acollectionofnumberswhichsharethesameproperty.naturalnumberrational(irrational)number(positive,negative)integer自然数（正、负）整数有(无）理数realnumber实数realline实轴origin原点complexnumber复数positivenumber正数negativenumber负数§1.1PreliminariesforCalculus高等数学英文1-1-102.TheFourArithmeticOperations（四则运算）addsumsubtractdifferencemultiplydivideproductquotient（加减乘除）（和差积商）I.TheIntegersandtheRationalNumbers§1.1PreliminariesforCalculus高等数学英文1-1-10II.InequalitiesOpenIntervalClosedIntervalInfiniteInterval1.Intervals（区间）§1.1PreliminariesforCalculus高等数学英文1-1-102.Neighborhoodofpointa(点a

的邻域）GeometricInterpretation:Thesetofpointxwhosedistancefrompointaislessthan

a

isthecenterofthisneighborhood,andistheradius.II.Inequalities§1.1PreliminariesforCalculus高等数学英文1-1-10II.Inequalities3.SolveInequalitiesSolutionThenthesolutionsetis.Example1

Solvetheinequality.§1.1PreliminariesforCalculus高等数学英文1-1-10III.AbsoluteValues（绝对值）1.AbsolutevalueSolutionExample2Letbeapositivenumber.Findapositivenumbersuchthat

Thenwechoose.§1.1PreliminariesforCalculus高等数学英文1-1-10III.AbsoluteValues2.SquareRootsprincipalrootsQuadraticFormulaaretherootsforequation§1.1PreliminariesforCalculus高等数学英文1-1-10IV.TheRectangularCoordinateSystem1.CartesianCoordinate（笛卡尔坐标系）coordinateaxes坐标轴x-axisy-axisquadrant象限x-coordinatey-coordinatey-coordinateP§1.1PreliminariesforCalculus高等数学英文1-1-10IV.TheRectangularCoordinateSystem2.Distanceformula§1.1PreliminariesforCalculus高等数学英文1-1-10IV.TheRectangularCoordinateSystem3.TheEquationofaCircleStandardformGeneralform§1.1PreliminariesforCalculus高等数学英文1-1-10V.TheStraightLine1.TheSlopeofaLine（直线的斜率）numeratordenominator分子分母§1.1PreliminariesforCalculus高等数学英文1-1-10V.TheStraightLine2.TheFo