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Mastering Technical Mathematics, Third Edition, 3rd Edition

by Stan Gibilisco, Norman H. Crowhurst

October 2007

Beginner

627 pages

15h 41m

English

McGraw-Hill Education TAB

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Numbers and NumeralsCounting in Tens and DozensWriting Numerals Greater Than 10Why Zero Is Used in CountingBy Tens and Hundreds to ThousandsDon’t Forget the ZerosMillions and MoreWhat About Infinity?Addition Is Counting onAdding Three or More NumbersAdding Larger NumbersCarryingChecking AnswersWeightsUsing the Grocer’s BalanceQuestions and Problems
Taking AwayChecking Subtraction by AdditionBorrowingSubtracting with Larger NumbersWorking with MoneyMaking ChangeSubtracting WeightsSubtracting Liquid MeasuresQuestions and Problems

It’s a ShortcutMaking a TablePatterns in Multiplication TablesHow Calculators MultiplyCarrying in MultiplicationUsing Your Calculator to Verify This ProcessPut Those Zeros to Work!Using Subtraction to MultiplyMultiplying by FactorsMultiplying in Nondecimal SystemsQuestions and Problems
Let’s Think Like a CalculatorDivision “Undoes” MultiplicationAlternative NotationDividing into Longer NumbersMultiplication Checks DivisionMore About How a Calculator Does ItDividing by Larger Numbers (The People Way)Division by FactorsWhen a Remainder Is LeftHow a Calculator Handles FractionsDecimal Equivalents of FractionsMore Difficult FractionsWhere Groups of Digits RepeatConverting Recurring Decimals to FractionsQuestions and Problems
Slicing up a PieFactors Help Simplify FractionsSpotting the FactorsPrime NumbersFactoring into PrimesPrime Factors of 139Prime Factors of 493Prime Factors of 546Adding and Subtracting FractionsFinding the Common DenominatorSignificant FiguresApproximate Division and MultiplicationApproximate Addition and SubtractionQuestions and Problems
Length Times Length Is AreaWhat Is a Square?Different Shapes with the Same AreaSquare Measure Vs. Linear MeasureRight TrianglesParallelogramsArea of a ParallelogramArea of an Acute TriangleArea of an Obtuse TriangleMetric MeasureArea ProblemsQuestions and Problems
Time as a DimensionTime and SpeedAverage SpeedMaking up for Lost TimeFractional GrowthPercentagesPercentages with MoneyPercentages up and downThe Bar GraphOther GraphsInterpolationGraphs Can Help You Evaluate Data and Find ErrorsQuestions and Problems
Shortcuts for Long ProblemsGraphs Help You Find Errors and SolutionsManipulating EquationsWriting It as AlgebraItalics—or Not?Grouping SymbolsSolving Problems with Grouping SymbolsPutting a Problem into AlgebraMagic by AlgebraA Boat-in-the-River ProblemNumber ProblemsQuestions and Problems
Orderly Writing in AlgebraShowing “Place” in AlgebraDimension in AlgebraEquations and InequalitiesA Consecutive-Number ProblemSimultaneous EquationsA Fraction ProblemA Little More PracticeSolving by SubstitutionSolving for ReciprocalsLong Division and FactoringQuestions and Problems
A Quadratic ExampleLinear Vs. Quadratic FormsA Quadratic Graph Is SymmetricSolving a Quadratic EquationFactors of a QuadraticFinding FactorsCompleting the SquareWhat the Answers MeanThe Quadratic FormulaA Quadratic ProblemQuestions and Problems
Sum and Difference in GeometryDifference of Squares Finds FactorsFinding Square RootsSigns in Successive RootsReal Vs. Imaginary NumbersComplex NumbersComplex Numbers Find New RootsA Problem Using Simultaneous EquationsQuestions and Problems
What Is Force?Units of ForceAcceleration, Speed, and DistanceForce and WorkWork and EnergyEnergy and PowerGravity as a Source of EnergyWeight as ForceGravitational Measure of WorkEnergy for Constant AccelerationPotential and Kinetic EnergyKinetic Energy and SpeedAcceleration at Constant PowerHow a Spring Stores EnergyHow a Spring Transfers EnergyResonance CycleTravel and Speed in Resonant SystemQuestions and Problems
Fractions, Projections, Extremes, and MeansProportions in PracticeShape and SizeAbout Angles in TrianglesUse of Right TrianglesAngles Identified by RatiosTheorem of PythagorasNames for Angle RatiosSpotting the TriangleDegree Measure of AnglesThree Applications of TrigonometryQuestions and Problems
Ratios for Sum AnglesFinding Tan (A + B)An Example: Ratios for 75°Ratios for Angles Greater Than 90°Ratios for Difference AnglesRatios Through the Four QuadrantsPythagoras in TrigonometryDouble AnglesHigher Multiple AnglesProperties of the Isosceles TriangleAngles in a CircleAngles in a SemicircleDefinitionsQuestions and Problems
Mechanical CountersDuodecimal NumbersConversion from Decimal to DuodecimalConversion from Duodecimal to DecimalOctal NumbersHexadecimal numbersBinary NumbersComparing the ValuesConverting Decimal to BinaryBinary MultiplicationBinary DivisionIndicesNegative and Fractional ExponentsSurdsQuestions and Problems
Arithmetic ProgressionGeometric ProgressionHarmonic ProgressionArithmetic SeriesGeometric SeriesConvergenceRate of ConvergencePermutationsCombinationsPowers of a BinomialAlternative Notation for Multiplying NumbersQuestions and Problems
Rates of ChangeInfinitesimal ChangesSuccessive DifferentiationDifferentiating a PolynomialSuccessive Differentiation of MovementCircular Measure of AnglesDerivatives of Sine and CosineSuccessive Derivatives of SineQuestions and Problems
Frequency and Period of a Sine WaveSinusoidal MotionHarmonic MotionLinear and Nonlinear RelationshipsMultiples and PowersFunctionsDerivative of ConstantDerivative of Sum of Two FunctionsDerivative of Difference of Two FunctionsDerivative of Function Multiplied by a ConstantDerivative of Product of Two FunctionsDerivative of Product of Three FunctionsDerivative of Quotient of Two FunctionsReciprocal DerivativesDerivative of Function Raised to a PowerChain RuleQuestions and Problems
Adding up the PiecesThe AntiderivativePatterns in CalculationsThe Constant of IntegrationDefinite IntegralsFinding Area by IntegrationArea of a CircleCurved Areas of Cylinders and ConesSurface Area of a SphereVolumes of Wedges and PyramidsVolumes of Cones and SpheresQuestions and Problems
Local Maximum and MinimumPoint of InflectionMaximum and Minimum SlopeMaximum Area with Constant PerimeterBox with Minimum Surface AreaCylinder with Minimum Surface AreaCone with Minimum Surface AreaEquations for Circles, Ellipses, and ParabolasDirectrix, Focus, and EccentricityThe Ellipse and the CircleRelationships Between Focus, Directrix, and EccentricityFocus Property of ParabolaFocus Property of EllipseHyperbola: Eccentricity Greater Than 1Geometry of Conic SectionsQuestions and Problems
Mathematician’s Polar CoordinatesSome ExamplesCompressed Polar CoordinatesMathematician’s Polar vs. Cartesian CoordinatesNavigator’s Polar CoordinatesMathematician’s Vs. Navigator’s Polar CoordinatesNavigator’s Polar Vs. Cartesian CoordinatesLatitude and LongitudeCelestial CoordinatesCartesian Three-SpaceCylindrical CoordinatesSpherical CoordinatesQuestions and Problems
Imaginary QuantitiesThe Complex Number PlaneMultiplying Complex QuantitiesThree Cube Root ExamplesReciprocal of a Complex QuantityDivision of Complex QuantitiesRationalizationChecking ResultsOperation SummaryUse of a Complex PlaneRoots by Complex QuantitiesQuestions and Problems
ParallaxThe Base-lineAccuracyDistance to an ObjectStadimetryInterstellar Distance MeasurementDistance Vs. ParallaxA Point of ConfusionRadarLaws of Sines and CosinesUse of RadarHow to Hunt a “Fox”The Fox Finds ItselfPosition of a ShipQuestions and Problems
The Logarithm BaseCommon LogarithmsNatural LogarithmsBasic Properties of LogarithmsConversion of Log FunctionsLogarithm ComparisonsThe Exponential BaseCommon ExponentialsNatural ExponentialsAlternative ExpressionsLogarithms Vs. ExponentialsBasic Properties of ExponentialsExponential ComparisonsNumerical Orders of MagnitudeQuestions and Problems
Standard FormAlternative FormThe “Times” SignPlain-Text ExponentsOrders of MagnitudeWhen to Use Scientific NotationPrefix MultipliersMultiplicationDivisionRaising to a PowerTaking a RootAdditionSubtractionSignificant FiguresHow Accurate Are You?What About 0?What About Exact Values?More About Addition and SubtractionQuestions and Problems
Magnitude and DirectionSum of Two VectorsMultiplication of a Vector by a ScalarDot Product of Two VectorsMagnitude and Direction in the Polar PlaneSum of Two Vectors in the Polar PlaneMultiplication of a Vector by a Scalar in the Polar PlaneDot Product of Two Vectors in Polar PlaneMagnitude in XYZ SpaceDirection in XYZ SpaceSum of two Vectors in XYZ SpaceMultiplication of a Vector by a Scalar in XYZ SpaceDot Product of Two Vectors in XYZ SpaceCross Product of Two VectorsNegative Vector MagnitudesQuestions and Problems
SentencesNegation (Not)Conjunction (And)Disjunction (Or)Implication (If/Then)Logical Equivalence (Iff)Truth TablesTables for Basic Logic FunctionsThe Equals SignQ.E.D.PrecedenceContradiction and Double NegationCommutative LawsAssociative LawsLaw of Implication ReversalDe Morgan’s LawsDistributive LawTruth Table ProofsProofs Without TablesQuestions and Problems
Imagine That!Time-SpacePosition and MotionTime as DisplacementUniversal SpeedThe Four-CubeThe Rectangular Four-PrismImpossible PathsGeneral Time-Space HypervolumeCartesian N-SpaceDistance FormulasVertices of a TesseractHypervolume of a Four-PrismEuclid’s AxiomsThe Parallel PostulateGeodesicsModified Parallel PostulateNo Parallel GeodesicsMore Than One Parallel GeodesicCurved SpaceThe “Hyperfunnel”Questions and Problems
ExperimentVariablePopulationSample, Event, and CensusRandom VariableFrequencyParameterStatisticDistributionFrequency DistributionCumulative Frequency DataMeanMedianModeQuestions and Problems
Sets and Set NotationEvent Vs. OutcomeSample SpaceMathematical ProbabilityEmpirical ProbabilityLaw of Large NumbersIndependent OutcomesMutually Exclusive OutcomesComplementary OutcomesNondisjoint OutcomesMultiple OutcomesThe Density FunctionExpressing the PatternArea under the CurveUniform DistributionNormal DistributionThe Empirical RuleQuestions and Problems
1. Solutions to End-of-Chapter Questions and Problems

Content preview from Mastering Technical Mathematics, Third Edition, 3rd Edition

29	A Statistics Primer

Statistics is the analysis of data, which is information expressed as measurable or observable quantities. Statistical data is usually obtained by looking at the real world or universe, although it can also be generated by computers in virtual worlds.

EXPERIMENT

In statistics, an experiment is an act of collecting data with the intent of learning or discovering something. For example, you might conduct an experiment to determine the most popular channels for frequency-modulation (FM) radio broadcast stations whose transmitters are located in U.S. towns having fewer than 5,000 people. Or you might conduct an experiment to determine the lowest barometric pressures inside the eyes of all the Atlantic hurricanes that ...

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ISBN: 9780071595421

Mastering Technical Mathematics, Third Edition, 3rd Edition

by Stan Gibilisco, Norman H. Crowhurst

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and much more.