كتاب Handbook of Industrial Engineering Equations,Formulas and Calculations
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 كتاب Handbook of Industrial Engineering Equations,Formulas and Calculations

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عدد المساهمات : 14261
التقييم : 22948
تاريخ التسجيل : 01/07/2009
العمر : 28
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية

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Handbook of Industrial Engineering Equations,Formulas and Calculations


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Prefacexxix
Authorsxxxi
1 Computational Foundations of Industrial Engineering
Efficacy of Mathematical Modeling1-1
Industrial Engineering and Computations1-1
Definition and Applications1-5
Orientation to STEM1-6
IE Catchphrases1-6
Span and Utility of IE1-6
Heritage from Industrial Revolution1-7
Historical Accounts1-8
Chronology of Applications1-10
Importance of IE Calculations1-14
Importance of Calculations Guide1-16
Basic Queuing Equations1-17
Queuing Birth–Death Processes1-21
Laws of Motion of Queuing Birth and Death1-21
Queuing Birth–Death Law 11-21
Queuing Birth–Death Law 21-21
Queuing Birth–Death Law 31-21
Data Types for Computational Analysis1-22
Nominal Scale1-22
Ordinal Scale1-22
Interval Scale1-22
Ration Scale1-23
Cardinal Scale1-23
References1-23
ix
x Contents
2 Basic Mathematical Calculations
Quadratic Equation2-1
Overall Mean2-2
Chebyshev’s Theorem2-2
Permutations2-2
Combinations2-2
Failure2-3
Probability Distribution2-3
Probability2-3
Distribution Function2-3
Expected Value2-4
Variance2-5
Binomial Distribution2-5
Poisson Distribution2-5
Mean of a Binomial Distribution2-6
Normal Distribution2-6
Cumulative Distribution Function2-6
Population Mean2-6
Standard Error of the Mean2-6
t-Distribution2-7
Chi-Squared Distribution2-7
Definition of Set and Notation2-7
Set Terms and Symbols2-8
Venn Diagrams2-8
Operations on Sets2-9
De Morgan’s Laws2-9
Counting the Elements in a Set2-10
Permutations2-10
Combinations2-11
ProbabilityTerminology2-11
Basic Probability Principles2-11
Random Variable2-12
Mean Valueˆ xor Expected Valueμ2-12
Series Expansions2-12
Mathematical Signs and Symbols2-15
Greek Alphabets2-16
Algebra2-17
Laws of Algebraic Operations2-17
Special Products and Factors2-17
Powers and Roots2-19
Proportion2-19
Sum of Arithmetic Progression tonTerms2-20
Sum of Geometric Progression tonTerms2-20
Contents xi
Arithmetic Mean ofnQuantities,A2-20
Geometric Mean ofnQuantities,G2-20
Harmonic Mean ofnQuantities,H2-20
Generalized Mean2-20
Solution of Quadratic Equations2-21
Solution of Cubic Equations2-21
Trigonometric Solution of the Cubic Equation2-22
Solution of Quadratic Equations2-23
Partial Fractions2-23
Nonrepeated Linear Factors2-23
Repeated Linear Factors2-24
General terms2-24
Repeated Linear Factors2-25
Factors of Higher Degree2-25
Geometry2-25
Triangles2-25
Right Triangle2-26
Equilateral Triangle2-26
General Triangle2-26
Menelaus’ Theorem2-27
Ceva’s Theorem2-27
Quadrilaterals2-27
Rectangle2-27
Parallelogram2-27
Rhombus2-28
Trapezoid2-28
GeneralQuadrilateral2-28
Theorem2-28
Regular Polygon ofnSides Each of Lengthb2-28
Circle of radiusr2-28
Regular Polygon ofnsides Inscribed in a Circle of Radiusr2-29
Regular Polygon ofnSides Circumscribing a Circle of Radiusr2-29
Cyclic Quadrilateral2-29
Prolemy’s Theorem2-29
Cyclic-Inscriptable Quadrilateral2-30
Sector of Circle of Radiusr2-30
Radius of a Circle Inscribed in a Triangle of Sidesa,b, andc2-30
Radius of a Circle Circumscribing a Triangle of Sidesa,b, andc2-30
Segment of a Circle of Radiusr2-30
Ellipse of Semimajor Axisaand Semiminor Axisb2-31
Segment of a Parabola2-31
Planar Areas by Approximation2-31
Solids Bounded By Planes2-31
Cube2-32
xii Contents
Rectangular Parallelepiped (or Box)2-32
Prism2-32
Truncated Triangular Prism2-32
Pyramid2-32
Frustum of a Pyramid2-33
Prismatoid2-33
Regular Polyhedra2-33
Sphere of Radiusr2-34
Right Circular Cylinder of Radiusrand Heighth2-34
Circular Cylinder of Radiusrand Slant Height2-35
Cylinder of Cross-Sectional AreaAand Slant Height2-35
Right Circular Cone of Radiusrand Heighth2-35
Spherical Cap of Radiusrand Heighth2-35
Frustum of a Right Circular Cone of Radiiaandband Heighth2-35
Zone and Segment of Two Bases2-35
Lune2-36
Spherical Sector2-36
Spherical Triangle and Polygon2-36
Spheroids2-36
Ellipsoid2-36
Oblate Spheroid2-36
Prolate Spheroid2-37
Circular Torus2-37
Formulas from Plane Analytic Geometry2-37
Distancedbetween Two Points2-37
Slopemof Line Joining Two Points2-37
Equation of a Line Joining Two Points2-37
Equation of a Line in Terms ofx-intercepta= 0 andy-interceptb= 0 2-38
Normal Form for Equation of a Line2-38
General Equation of a Line2-38
DistanceFrom a Point (x1,y1) to the LineAx+By+C=02-38
Angleψbetween Two Lines Having Slopesm1andm22-38
Area of a Triangle with Vertices2-39
Transformation of Coordinates Involving Pure Translation2-39
Transformation of Coordinates Involving Pure Rotation2-39
Transformation of Coordinates Involving Translation and Rotation2-39
Polar Coordinates (r,θ) 2-40
Plane Curves2-40
Catenary, Hyperbolic Cosine2-40
Cardioid2-40
Circle2-40
Cassinian Curves2-41
Cotangent Curve2-41
Cubical Parabola2-41
Contents xiii
Cosecant Curve2-41
Cosine Curve2-41
Ellipse2-41
Gamma Function2-41
Hyperbolic Functions2-41
Inverse Cosine Curve2-42
Inverse Sine Curve2-42
Inverse Tangent Curve2-42
Logarithmic Curve2-42
Parabola2-42
Cubical Parabola2-42
Tangent Curve2-42
Distancedbetween Two Points2-43
Logarithmic Identities2-46
Series Expansions2-47
Limiting Values2-47
Inequalities2-47
Polynomial Approximations2-48
Exponential Function Series Expansion2-49
Fundamental Properties2-49
Definition of General Powers2-49
Logarithmic and Exponential Functions2-50
Periodic Property2-50
Polynomial Approximations2-50
Slopes2-53
Trigonometricratios2-53
Sine Law2-55
Cosine Law2-56
Algebra2-56
Expanding2-56
Factoring2-57
Roots of a Quadratic Equation2-57
Law of exponents2-57
Logarithms2-58
3 Statistical Distributions, Methods, and Applications
Discrete Distributions3-1
Bernoulli Distribution3-1
Beta Binomial Distribution3-1
Beta Pascal Distribution3-3
Binomial Distribution3-3
Discrete Weibull Distribution3-3
Geometric Distribution3-3
xiv Contents
Hypergeometric Distribution3-3
Negative Binomial Distribution3-4
Poisson Distribution3-4
Rectangular (Discrete Uniform) Distribution3-4
Continuous Distributions3-4
Arcsin Distribution3-4
Beta Distribution3-5
Cauchy Distribution3-5
Chi Distribution3-5
Chi-Square Distribution3-5
Erlang Distribution3-5
Exponential Distribution3-6
Extreme-Value Distribution3-6
FDistribution3-6
Gamma Distribution3-7
Half-Normal Distribution3-7
Laplace (Double Exponential) Distribution3-7
Logistic Distribution3-7
Lognormal Distribution3-7
Noncentral Chi-Square Distribution3-8
NoncentralFDistribution3-8
Noncentralt-Distribution3-8
Normal Distribution3-9
Pareto Distribution3-9
Rayleigh Distribution3-9
t-Distribution3-9
TriangularDistribution3-10
Uniform Distribution3-10
Weibull Distribution3-10
Distribution Parameters3-10
Average3-10
Variance3-11
Standard Deviation3-11
Standard Error3-11
Skewness3-11
Standardized Skewness3-11
Kurtosis3-11
Standardized Kurtosis3-11
Weighted Average3-11
Estimation and Testing3-11
100(1−α)% Confidence Interval for Mean3-11
100(1−α)% Confidence Interval for Variance3-11
100(1−α)% Confidence Interval for Difference in Means3-12
100(1−α)% Confidence Interval for Ratio of Variances3-12
Contents xv
Normal Probability Plot3-12
Comparison of Poisson Rates3-13
Distribution Functions—Parameter Estimation3-13
Bernoulli3-13
Binomial3-13
Discrete Uniform3-13
Geometric3-13
Negative Binomial3-13
Poisson3-13
Beta3-14
Chi-Square3-14
Erlang3-14
Exponential3-14
FDistribution3-14
Gamma3-14
Log–Normal3-15
Normal3-15
Student’st3-15
Triangular3-15
Uniform3-15
Weibull3-16
Chi-Square Test for Distribution Fitting3-16
Kolmogorov–Smirnov Test3-16
ANOVA3-16
Notation3-16
StandardError (Internal)3-17
Standard Error (Pooled)3-17
Interval Estimates3-17
Tukey Interval3-17
Scheffe Interval3-17
CochranC-Test3-17
Bartlett Test3-18
Hartley’s Test3-18
Kruskal–Wallis Test3-18
Adjustment for Ties3-18
Freidman Test3-18
Regression3-19
Notation3-19
Regression Statistics3-19
Predictions3-20
Nonlinear Regression3-21
Ridge Regression3-21
Quality Control3-22
For All Quality Control Formulas3-22
xvi Contents
Subgroup Statistics3-22
X Bar Charts3-22
Capability Ratios3-23
R Charts3-24
S Charts3-24
C Charts3-24
U Charts3-24
P Charts3-24
NP Charts3-25
CuSum Chart for the Mean3-25
Multivariate Control Charts3-25
Time-Series Analysis3-25
Notation3-25
Autocorrelation at Lagk3-26
Partial Autocorrelation at Lagk3-26
Cross-Correlation at Lagk3-26
Box-Cox3-26
Periodogram (computed using Fast Fourier Transform)3-27
Categorical Analysis3-27
Notation3-27
Totals3-27
Chi-Square3-27
Fisher’s Exact Test3-28
Lambda3-28
Uncertainty Coefficient3-28
Somer’sD3-29
Eta 3-29
Contingency Coefficient3-30
Cramer’sV3-30
Conditional Gamma3-30
Pearson’sR3-30
Kendall’s Taub3-30
TauC3-30
Probability Terminology3-30
Basic Probability Principles3-31
Random Variable3-31
Mean Valueˆ xor Expected Valueμ3-31
Discrete Distribution Formulas3-32
Bernoulli Distribution3-32
Beta Binomial Distribution3-32
Beta Pascal Distribution3-32
Binomial Distribution3-32
Discrete Weibull Distribution3-32
Geometric Distribution3-33
Contents xvii
Hypergeometric Distribution3-33
Negative Binomial Distribution3-33
Poisson Distribution3-34
Rectangular (Discrete Uniform) Distribution3-34
Continuous Distribution Formulas3-34
Arcsin Distribution3-34
Beta Distribution3-35
Cauchy Distribution3-35
Chi Distribution3-35
Chi-Square Distribution3-35
Erlang Distribution3-35
Exponential Distribution3-35
Extreme-Value Distribution3-36
FDistribution3-36
Gamma Distribution3-36
Half-Normal Distribution3-36
Laplace (Double Exponential) Distribution3-37
Logistic Distribution3-37
Lognormal Distribution3-37
Noncentral Chi-Square Distribution3-37
NoncentralFDistribution3-38
Noncentralt-Distribution3-38
Normal Distribution3-38
Pareto Distribution3-38
Rayleigh Distribution3-39
t-Distribution3-39
TriangularDistribution3-39
Uniform Distribution3-39
Weibull Distribution3-40
Variate Generation Techniques3-40
Notation3-40
Variate Generation Algorithms3-40
References3-42
4Computations with Descriptive Statistics
Sample Average4-1
Application Areas4-1
Sample calculations4-1
Sample Variance4-1
Application Areas4-1
Sample Calculations4-2
Sample Standard Deviation4-2
Application Areas4-2
Sample Standard Error of the Mean4-3
xviii Contents
Application Areas4-3
Skewness4-3
Standardized Skewness4-3
Kurtosis4-4
Standardized Kurtosis4-4
Weighted Average4-4
Estimation and Testing4-4
100(1−α)% Confidence Interval for Mean4-4
100(1−α)% Confidence Interval for Variance4-4
100(1−α)% Confidence Interval for Difference
in Means4-4
100(1−α)% Confidence Interval for Ratio
of Variances4-5
Normal Probability Plot4-5
Comparison of Poisson Rates4-5
Distribution Functions and Parameter Estimation4-5
Bernoulli Distribution4-5
Binomial Distribution4-5
Discrete Uniform Distribution4-6
Geometric Distribution4-6
Negative Binomial Distribution4-6
Poisson Distribution4-6
Beta Distribution4-6
Chi-Square Distribution4-6
ErlangDistribution4-6
Exponential Distribution4-7
Application Areas4-7
FDistribution4-7
Gamma Distribution4-7
Log–Normal Distribution4-7
Normal Distribution4-8
Triangular Distribution4-8
Uniform Distribution4-8
Weibull Distribution4-8
Chi-Square Test for Distribution Fitting4-8
Kolmogorov–Smirnov Test4-9
ANOVA4-9
Notation4-9
Standard Error4-9
Interval Estimates4-9
Tukey Interval4-10
Scheffe Interval4-10
CochranC-test4-10
Bartlett Test4-10
Contents xix
Hartley’s Test4-10
Kruskal–Wallis Test4-11
Adjustment for ties4-11
Freidman Test4-11
Regression4-12
Notation4-12
Statistical Quality Control4-13
Subgroup Statistics4-13
X-Bar Charts4-14
Capability Ratios4-14
R Charts4-15
S Charts4-15
C Charts4-15
U Charts4-15
P Charts4-15
NP Charts4-16
CuSum Chart for the Mean4-16
Time-Series Analysis4-16
Notation4-16
Autocorrelation at Lagk4-17
Partial Autocorrelation at Lagk4-17
Cross-Correlation at Lagk4-17
Box-Cox Computation4-17
Periodogram (Computed using Fast Fourier
Transform)4-18
Categorical Analysis4-18
Notation4-18
Totals4-18
Chi-Square4-18
Lambda4-19
UncertaintyCoefficient4-19
Somer’sDMeasure4-20
Eta 4-20
Contingency Coefficient4-21
Cramer’s V Measure4-21
Conditional Gamma4-21
Pearson’sRMeasure4-21
Kendall’s TaubMeasure4-21
TauCMeasure4-22
Overall Mean4-22
Chebyshev’s Theorem4-22
Permutation4-22
Combination4-22
Failure4-22
xx Contents
5Computations for Economic Analysis
Fundamentals of Economic Analysis5-1
Simple Interest5-1
Future value5-1
Compound Interest5-2
Continuous Compound Interest5-2
Effective Rate5-3
Present Value with Compound Interest5-3
Annuities5-4
Present value of annuity5-4
Future value of an annuity5-4
Amortization of Loans5-5
Interest and Equity Computations5-5
Equity Break-Even Formula5-8
Sinking Fund Payment5-9
Internal Rate of Return5-9
Benefit–Cost Ratio5-9
Simple Payback Period5-9
Discounted Payback Period5-10
Economic Methods of Comparing Investment Alternatives5-10
Present Value Analysis5-10
Annual Value Analysis5-10
Internal Rate of Return Analysis5-11
External Rate of Return Analysis5-11
Incremental Analysis5-11
Guidelines for Comparison of
Alternatives5-12
Asset Replacement and Retention Analysis5-12
ReplacementAnalysis Computation5-14
Depreciation Methods5-15
Depreciation Terminology5-15
Depreciation Methods5-16
Straight-Line (SL) Method5-16
Declining Balance (DB) Method5-16
Sums-of-Years’ Digits (SYD) Method5-17
MACRS Method5-17
Effects of Inflation and Taxes5-18
Foreign Exchange Rates5-21
After-Tax Economic Analysis5-21
Cost and Value Computations5-22
Actual Cost of Work Performed5-23
Applied Direct Cost5-23
Budgeted Cost for Work Performed5-23
Contents xxi
Budgeted Cost for Work Scheduled5-23
Direct Cost5-23
Economies of Scale5-23
Estimated Cost at Completion5-23
First Cost5-24
Fixed Cost5-24
Incremental Cost5-24
Indirect Cost5-24
Life-Cycle Cost5-24
Maintenance Cost5-24
Marginal Cost5-24
Operating Cost5-24
Opportunity Cost5-25
Overhead Cost5-25
Standard Cost5-25
Sunk Cost5-25
Total Cost5-25
Variable cost5-25
Cash-Flow Calculations5-26
Calculations with Compound Amount Factor5-26
Calculations with Present Worth Factor5-27
Calculations with Uniform Series Present Worth Factor5-27
Calculations with Uniform Series Capital Recovery Factor5-28
Calculations with Uniform Series Compound Amount Factor5-29
Calculations with Uniform Series Sinking Fund Factor5-29
Calculations with Capitalized Cost Formula5-30
ArithmeticGradient Series5-31
Internal Rate of Return5-32
Benefit-Cost Ratio Analysis5-33
Simple Payback Period5-33
Discounted Payback Period5-34
Time Required to Double Investment5-35
Effects of Inflation on Industrial Project Costing5-36
Mild Inflation5-40
Moderate Inflation5-40
Severe Inflation5-40
Hyperinflation5-40
Break-Even Analysis5-40
Profit Ratio Analysis5-42
Project Cost Estimation5-46
Optimistic and Pessimistic Cost Estimates5-47
Cost Performance Index5-47
Cost Control Limits5-48
Project Balance Computation5-48
xxii Contents
6Industrial Production Calculations
Learning Curve Models and Computations6-1
The Average Cost Model6-1
Computational Example6-2
Computational Example6-3
The Unit Cost Model6-4
Productivity Calculations Using Learning Curves6-5
Determining Average Unit Time6-5
Calculation of the Learning Factor6-5
Calculating Total Time for a Job6-5
Time Required to Perform a Task for thenth Time6-5
The Improvement Ratio6-5
Computational Example6-5
Solution6-5
Computation for Improvement Goal in Unit Time6-6
Computation of Machine Output Capacities6-6
Machine Utilization Ratio: Determining How Often a
Machine Is Idle6-6
Calculating Number of Machines Needed to Meet Output6-7
Alternate Forms for Machine Formula6-7
Calculating Buffer Production to Allow for Defects6-8
Adjusting Machine Requirements to Allow for Rejects6-9
Output Computations for Sequence of Machines6-9
Calculating Forces on Cutting Tools6-10
Calculating Pressure6-11
Finding Required Horsepower6-11
Machine Accuracy6-12
Calculatingthe Goal Dimension6-12
Drill Thrust6-13
Drill Torque6-14
Drill Horsepower6-14
Calculating Speed and Rotation of Machines6-14
Shaft Speed6-15
Surface Speed6-15
Tool Feed per Revolution6-16
Tool Feed per Minute6-16
Tool Feed per Tooth6-17
Computation to Find the Volume of Material Removed6-17
Time Rate for Material Removal in a Rectangular Cut6-17
Calculation of Linear Feed for Rectangular Material Removal6-18
Takt Time for Production Planning6-18
Production Crew Work Rate Analysis6-19
Production Work Rate Example6-20
Contents xxiii
Case of Multiple Resources Working Together6-20
Computational Examples6-21
Calculation of Personnel Requirements6-22
Calculation of Machine Requirements6-23
References6-23
7Forecasting Calculations
Forecasting Based on Averages7-1
Simple Average Forecast7-1
Period Moving Average Forecast7-2
Weighted Average Forecast7-2
WeightedT-Period Moving Average Forecast7-2
Exponential Smoothing Forecast7-3
Regression Analysis7-3
Regression Relationships7-3
Prediction7-4
Control7-4
Procedure for Regression Analysis7-5
Coefficient of Determination7-5
Residual Analysis7-7
Time-Series Analysis7-9
Stationarity and Data Transformation7-10
Moving Average Processes7-12
Autoregressive Processes7-13
Forecasting for Inventory Control7-15
Economic Order Quantity Model7-15
Quantity Discount7-16
Calculation of Total Relevant Cost7-16
Evaluation of the Discount Option7-17
Sensitivity Analysis7-19
Wagner–Whitin Algorithm7-20
Notation and Variables7-21
8Six Sigma and Lean
Concept of Six Sigma8-1
Taguchi Loss Function8-1
Identification and Elimination of Sources of Defects8-2
Roles and Responsibilities for Six Sigma8-3
Statistical Techniques for Six Sigma8-3
Control Charts8-4
XandR-Charts8-4
Data Collection Strategies8-5
Subgroup Sample Size8-5
Frequency of Sampling8-6
xxiv Contents
Stable Process8-6
Out-of-Control Patterns8-6
Calculation of Control Limits8-7
Plotting Control Charts for Range and Average Charts8-8
Plotting Control Charts for Moving Range and Individual
Control Charts8-9
Case Example: Plotting of Control Chart8-9
Calculations8-9
Trend Analysis8-14
Process Capability Analysis for Six Sigma8-18
Capable Process (Cp) 8-18
Capability Index (Cp
k
) 8-19
Process Capability Example8-20
Possible Applications of Process Capability Index8-21
Potential Abuse ofCp and Cp
k
8-22
Lean Principles and Applications8-22
Kaizen of a Process8-23
Lean Task Value Rating System8-24
9Risk Computations
Cost Uncertainties9-1
Schedule Uncertainties9-2
Performance Uncertainties9-2
Decision Tables and Trees9-2
Reliability Calculations9-7
General Reliability Definitions9-8
Exponential Distribution Used as Reliability
Function9-9
Reliability Formulas9-10
General Reliability Definitions9-10
Exponential Distribution Used as Reliability
Function9-11
10Computations for Project Analysis
Planning10-1
Organizing10-1
Scheduling10-1
Control10-2
CPM Scheduling10-2
Advantages for Communication10-3
Advantages for Control10-3
Advantages for Team Interaction10-3
Activity Precedence Relationships10-4
Network Notation10-4
Contents xxv
Forward-Pass Calculations10-5
CPM Example10-6
Backward-Pass Calculations10-7
Calculation of Slacks10-8
Calculations for Subcritical Paths10-9
Plotting of Gantt Charts10-10
Calculations for Project Crashing10-13
Calculations for Project Duration Diagnostics10-18
PERT Formulas10-19
Activity Time Distributions10-19
Project Duration Analysis10-20
Simulation of Project Networks10-24
11Product Shape and Geometrical Calculations
Equation of a Straight Line11-1
Quadratic Equation11-2
Conic Sections11-2
Case 1 of Conic Section:e=1 (Parabola)11-3
Case 2 of Conic Section:e<1 (Ellipse)11-3
Case 3 Hyperbola:e>1 11-4
Case 4e=1 (Circle)11-5
Conic Section Equation11-6
Quadric Surface (Sphere)11-6
Identities11-7
Trigonometry11-7
Law of Sines11-7
Law of Cosines11-8
Identities11-8
Complex Numbers11-10
Polar Coordinates11-10
Euler’s Identity11-11
Roots11-11
Matrices11-11
Matrix Multiplication11-11
Matrix Addition11-11
Identity Matrix11-11
Matrix Transpose11-11
Matrix Inverse11-12
Determinants11-12
Vectors11-12
Gradient, Divergence, and Curl11-13
Identities11-13
Progressions and Series11-14
Arithmetic Progression11-14
xxvi Contents
Geometric Progression11-14
Properties of Series11-15
Power Series11-15
Taylor’s Series11-16
Differential Calculus11-16
The Derivative11-16
Test for a Maximum11-16
Test for a Minimum11-16
Test for a Point of Inflection11-16
The Partial Derivative11-16
Curvature in Rectangular Coordinates11-17
The Radius of Curvature11-17
L’Hospital’s Rule11-17
Integral Calculus11-18
Derivatives and Indefinite Integrals11-18
Derivatives11-18
Indefinite Integrals11-20
Mensuration of Areas and Volumes11-21
Nomenclature11-21
Parabola11-21
Ellipse11-21
Circular Segment11-22
Circular Sector11-22
Sphere11-22
Parallelogram11-22
Regular Polygon (nEqualSides)11-23
Prismoid11-23
Right Circular Cone11-23
Right Circular Cylinder11-23
Paraboloid of Revolution11-23
Centroids and Moments of Inertia11-24
Difference Equations11-24
First-Order Linear Difference Equation11-25
Second-Order Linear Difference Equation11-25
Numerical Methods11-25
Newton’s Method for Root Extraction11-25
Newton’s Method of Minimization11-25
Numerical Integration11-26
Euler’s or Forward Rectangular Rule11-26
Trapezoidal Rule11-26
Simpson’s Rule/Parabolic Rule (nMust Be
an Even Integer)11-27
Calculation of Best-Fit Circle11-27
Contents xxvii
12General Engineering Calculations
Six Simple Machines for Materials Handling12-1
Machine 1: The Lever12-1
Machine 2: Wheel and Axle12-1
Machine 3: The Pulley12-2
Machine 4: The Inclined Plane12-2
Machine 5: The Wedge12-2
Machine 6: The Screw12-2
Mechanics: Kinematics12-3
Scalars and Vectors12-3
Distance and Displacement12-3
Acceleration12-3
Speed and Velocity12-3
Frequency12-3
Period12-3
Angular Displacement12-3
Angular Velocity12-4
Angular Acceleration12-4
Rotational Speed12-4
Uniform Linear Motion12-4
Uniform Accelerated Linear Motion12-4
Rotational Motion12-5
Uniform Rotation and a Fixed Axis12-5
Uniform Accelerated Rotation about a Fixed Axis12-5
Simple Harmonic Motion12-6
Pendulum12-7
Free Fall12-7
VerticalProject12-7
Angled Projections12-8
Horizontal Projection (α=0)12-8
Sliding Motion on an Inclined Plane12-8
Rolling Motion on an Inclined Plane12-9
Mechanics: Dynamics12-10
Newton’s First Law of Motion12-10
Newton’s Second Law of Motion12-10
Newton’s Third Law of Motion12-10
Momentum of Force12-10
Impulse of Force12-11
Law of Conservation of Momentum12-11
Friction12-11
General Law of Gravity12-11
Gravitational Force12-12
Centrifugal Force12-12
Centripetal Force12-12
xxviii Contents
Torque12-12
Work12-13
Energy12-13
Conservation of Energy12-14
Power12-14
Appendix A: Mathematical Patterns, Series, and Formulae
Number Sequence and PatternsA-1
Closed-Form Mathematical ExpressionsA-3
Derivation of the Quadratic FormulaA-7
Appendix B: Measurement Units, Notation, and Constants
Common NotationB-1
Scientific ConstantsB-3
Numbers and PrefixesB-3
Appendix C: Conversion Factors
Area Conversion FactorsC-1
Volume Conversion FactorsC-2
Energy Conversion FactorsC-2
Mass Conversion FactorsC-3
Temperature Conversion FactorsC-3
Velocity Conversion FactorsC-4
Pressure Conversion FactorsC-4
Distance Conversion FactorsC-5
Physical Science EquationsC-6
English and Metric SystemsC-7
Household Measurement ConversionC-7
Appendix D: Factors and Tables
Formulas for Interest FactorD-1
Summation Formulas for Closed-Form ExpressionsD-3
Interest TablesD-3
Appendix E: Greek Symbols and Roman Numerals
Greek Symbols E-1
Roman Numerals E-2
BibliographyBibliography-1
Index


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