Handbook of Industrial Engineering Equations,Formulas, and Calculations

Handbook of Industrial Engineering Equations,Formulas, and Calculations
اسم المؤلف
Adedeji B.Badiru, Olufemi A.Omitaomu
التاريخ
3 يناير 2018
المشاهدات
التقييم
Loading...

Handbook of Industrial Engineering Equations,Formulas, and Calculations
Adedeji B.Badiru
Olufemi A.Omitaomu
Contents
Preface . xxix
Authors xxxi
1 Computational Foundations of Industrial Engineering
Efficacy of Mathematical Modeling .1-1
Industrial Engineering and Computations 1-1
Definition and Applications .1-5
Orientation to STEM .1-6
IE Catchphrases .1-6
Span and Utility of IE 1-6
Heritage from Industrial Revolution 1-7
Historical Accounts .1-8
Chronology of Applications 1-10
Importance of IE Calculations 1-14
Importance of Calculations Guide .1-16
Basic Queuing Equations 1-17
Queuing Birth–Death Processes .1-21
Laws of Motion of Queuing Birth and Death 1-21
Queuing Birth–Death Law 1 .1-21
Queuing Birth–Death Law 2 .1-21
Queuing Birth–Death Law 3 .1-21
Data Types for Computational Analysis 1-22
Nominal Scale 1-22
Ordinal Scale 1-22
Interval Scale 1-22
Ration Scale 1-23
Cardinal Scale .1-23
References 1-23
ixx Contents
2 Basic Mathematical Calculations
Quadratic Equation .2-1
Overall Mean 2-2
Chebyshev’s Theorem .2-2
Permutations 2-2
Combinations 2-2
Failure .2-3
Probability Distribution 2-3
Probability 2-3
Distribution Function .2-3
Expected Value 2-4
Variance .2-5
Binomial Distribution .2-5
Poisson Distribution 2-5
Mean of a Binomial Distribution 2-6
Normal Distribution 2-6
Cumulative Distribution Function .2-6
Population Mean .2-6
Standard Error of the Mean 2-6
t-Distribution .2-7
Chi-Squared Distribution .2-7
Definition of Set and Notation .2-7
Set Terms and Symbols .2-8
Venn Diagrams 2-8
Operations on Sets .2-9
De Morgan’s Laws .2-9
Counting the Elements in a Set .2-10
Permutations 2-10
Combinations 2-11
Probability Terminology .2-11
Basic Probability Principles 2-11
Random Variable .2-12
Mean Value xˆ or Expected Value ? .2-12
Series Expansions 2-12
Mathematical Signs and Symbols .2-15
Greek Alphabets 2-16
Algebra .2-17
Laws of Algebraic Operations .2-17
Special Products and Factors 2-17
Powers and Roots .2-19
Proportion 2-19
Sum of Arithmetic Progression to n Terms .2-20
Sum of Geometric Progression to n Terms 2-20Contents xi
Arithmetic Mean of n Quantities, A .2-20
Geometric Mean of n Quantities, G .2-20
Harmonic Mean of n Quantities, H .2-20
Generalized Mean 2-20
Solution of Quadratic Equations 2-21
Solution of Cubic Equations .2-21
Trigonometric Solution of the Cubic Equation .2-22
Solution of Quadratic Equations 2-23
Partial Fractions .2-23
Nonrepeated Linear Factors 2-23
Repeated Linear Factors 2-24
General terms .2-24
Repeated Linear Factors 2-25
Factors of Higher Degree 2-25
Geometry 2-25
Triangles .2-25
Right Triangle 2-26
Equilateral Triangle .2-26
General Triangle 2-26
Menelaus’ Theorem .2-27
Ceva’s Theorem .2-27
Quadrilaterals 2-27
Rectangle 2-27
Parallelogram .2-27
Rhombus 2-28
Trapezoid 2-28
General Quadrilateral 2-28
Theorem .2-28
Regular Polygon of n Sides Each of Length b .2-28
Circle of radius r 2-28
Regular Polygon of n sides Inscribed in a Circle of Radius r 2-29
Regular Polygon of n Sides Circumscribing a Circle of Radius r .2-29
Cyclic Quadrilateral .2-29
Prolemy’s Theorem .2-29
Cyclic-Inscriptable Quadrilateral .2-30
Sector of Circle of Radius r .2-30
Radius of a Circle Inscribed in a Triangle of Sides a, b, and c 2-30
Radius of a Circle Circumscribing a Triangle of Sides a, b, and c 2-30
Segment of a Circle of Radius r .2-30
Ellipse of Semimajor Axis a and Semiminor Axis b 2-31
Segment of a Parabola .2-31
Planar Areas by Approximation .2-31
Solids Bounded By Planes .2-31
Cube 2-32xii Contents
Rectangular Parallelepiped (or Box) .2-32
Prism .2-32
Truncated Triangular Prism .2-32
Pyramid 2-32
Frustum of a Pyramid 2-33
Prismatoid 2-33
Regular Polyhedra 2-33
Sphere of Radius r 2-34
Right Circular Cylinder of Radius r and Height h .2-34
Circular Cylinder of Radius r and Slant Height  2-35
Cylinder of Cross-Sectional Area A and Slant Height  2-35
Right Circular Cone of Radius r and Height h 2-35
Spherical Cap of Radius r and Height h .2-35
Frustum of a Right Circular Cone of Radii a and b and Height h 2-35
Zone and Segment of Two Bases 2-35
Lune 2-36
Spherical Sector 2-36
Spherical Triangle and Polygon 2-36
Spheroids 2-36
Ellipsoid 2-36
Oblate Spheroid .2-36
Prolate Spheroid .2-37
Circular Torus 2-37
Formulas from Plane Analytic Geometry 2-37
Distance d between Two Points 2-37
Slope m of Line Joining Two Points .2-37
Equation of a Line Joining Two Points 2-37
Equation of a Line in Terms of x-intercept a = 0 and y-intercept b = 0 2-38
Normal Form for Equation of a Line 2-38
General Equation of a Line 2-38
Distance From a Point (x1, y1) to the Line Ax + By + C = 0 2-38
Angle ? between Two Lines Having Slopes m1 and m2 .2-38
Area of a Triangle with Vertices .2-39
Transformation of Coordinates Involving Pure Translation 2-39
Transformation of Coordinates Involving Pure Rotation 2-39
Transformation of Coordinates Involving Translation and Rotation 2-39
Polar Coordinates (r, ?) .2-40
Plane Curves .2-40
Catenary, Hyperbolic Cosine 2-40
Cardioid .2-40
Circle .2-40
Cassinian Curves 2-41
Cotangent Curve 2-41
Cubical Parabola 2-41Contents xiii
Cosecant Curve 2-41
Cosine Curve 2-41
Ellipse .2-41
Gamma Function .2-41
Hyperbolic Functions 2-41
Inverse Cosine Curve 2-42
Inverse Sine Curve .2-42
Inverse Tangent Curve 2-42
Logarithmic Curve .2-42
Parabola 2-42
Cubical Parabola 2-42
Tangent Curve .2-42
Distance d between Two Points 2-43
Logarithmic Identities .2-46
Series Expansions 2-47
Limiting Values 2-47
Inequalities .2-47
Polynomial Approximations 2-48
Exponential Function Series Expansion 2-49
Fundamental Properties 2-49
Definition of General Powers .2-49
Logarithmic and Exponential Functions .2-50
Periodic Property .2-50
Polynomial Approximations .2-50
Slopes 2-53
Trigonometric ratios .2-53
Sine Law 2-55
Cosine Law .2-56
Algebra .2-56
Expanding 2-56
Factoring .2-57
Roots of a Quadratic Equation .2-57
Law of exponents .2-57
Logarithms .2-58
3 Statistical Distributions, Methods, and Applications
Discrete Distributions .3-1
Bernoulli Distribution .3-1
Beta Binomial Distribution .3-1
Beta Pascal Distribution 3-3
Binomial Distribution .3-3
Discrete Weibull Distribution .3-3
Geometric Distribution .3-3xiv Contents
Hypergeometric Distribution .3-3
Negative Binomial Distribution 3-4
Poisson Distribution 3-4
Rectangular (Discrete Uniform) Distribution .3-4
Continuous Distributions .3-4
Arcsin Distribution 3-4
Beta Distribution 3-5
Cauchy Distribution 3-5
Chi Distribution .3-5
Chi-Square Distribution 3-5
Erlang Distribution 3-5
Exponential Distribution .3-6
Extreme-Value Distribution .3-6
F Distribution 3-6
Gamma Distribution .3-7
Half-Normal Distribution .3-7
Laplace (Double Exponential) Distribution .3-7
Logistic Distribution 3-7
Lognormal Distribution 3-7
Noncentral Chi-Square Distribution 3-8
Noncentral F Distribution 3-8
Noncentral t-Distribution .3-8
Normal Distribution 3-9
Pareto Distribution 3-9
Rayleigh Distribution 3-9
t-Distribution .3-9
Triangular Distribution .3-10
Uniform Distribution 3-10
Weibull Distribution .3-10
Distribution Parameters 3-10
Average .3-10
Variance .3-11
Standard Deviation 3-11
Standard Error .3-11
Skewness .3-11
Standardized Skewness 3-11
Kurtosis 3-11
Standardized Kurtosis .3-11
Weighted Average .3-11
Estimation and Testing 3-11
100(1??)% Confidence Interval for Mean 3-11
100(1 ? ?)% Confidence Interval for Variance .3-11
100(1 ? ?)% Confidence Interval for Difference in Means 3-12
100(1 ? ?)% Confidence Interval for Ratio of Variances .3-12Contents xv
Normal Probability Plot 3-12
Comparison of Poisson Rates .3-13
Distribution Functions—Parameter Estimation .3-13
Bernoulli .3-13
Binomial .3-13
Discrete Uniform .3-13
Geometric .3-13
Negative Binomial 3-13
Poisson 3-13
Beta .3-14
Chi-Square 3-14
Erlang 3-14
Exponential 3-14
F Distribution 3-14
Gamma .3-14
Log–Normal .3-15
Normal 3-15
Student’s t .3-15
Triangular .3-15
Uniform 3-15
Weibull .3-16
Chi-Square Test for Distribution Fitting 3-16
Kolmogorov–Smirnov Test .3-16
ANOVA .3-16
Notation 3-16
Standard Error (Internal) 3-17
Standard Error (Pooled) 3-17
Interval Estimates 3-17
Tukey Interval 3-17
Scheffe Interval .3-17
Cochran C-Test 3-17
Bartlett Test 3-18
Hartley’s Test .3-18
Kruskal–Wallis Test .3-18
Adjustment for Ties .3-18
Freidman Test 3-18
Regression 3-19
Notation .3-19
Regression Statistics .3-19
Predictions 3-20
Nonlinear Regression 3-21
Ridge Regression 3-21
Quality Control 3-22
For All Quality Control Formulas 3-22xvi Contents
Subgroup Statistics .3-22
X Bar Charts .3-22
Capability Ratios 3-23
R Charts 3-24
S Charts .3-24
C Charts 3-24
U Charts .3-24
P Charts 3-24
NP Charts .3-25
CuSum Chart for the Mean .3-25
Multivariate Control Charts 3-25
Time-Series Analysis .3-25
Notation .3-25
Autocorrelation at Lag k 3-26
Partial Autocorrelation at Lag k 3-26
Cross-Correlation at Lag k 3-26
Box-Cox 3-26
Periodogram (computed using Fast Fourier Transform) .3-27
Categorical Analysis 3-27
Notation .3-27
Totals 3-27
Chi-Square 3-27
Fisher’s Exact Test .3-28
Lambda .3-28
Uncertainty Coefficient .3-28
Somer’s D .3-29
Eta .3-29
Contingency Coefficient 3-30
Cramer’s V .3-30
Conditional Gamma 3-30
Pearson’s R .3-30
Kendall’s Tau b .3-30
Tau C 3-30
Probability Terminology .3-30
Basic Probability Principles .3-31
Random Variable .3-31
Mean Value xˆ or Expected Value ? 3-31
Discrete Distribution Formulas 3-32
Bernoulli Distribution .3-32
Beta Binomial Distribution .3-32
Beta Pascal Distribution 3-32
Binomial Distribution .3-32
Discrete Weibull Distribution .3-32
Geometric Distribution .3-33Contents xvii
Hypergeometric Distribution .3-33
Negative Binomial Distribution 3-33
Poisson Distribution 3-34
Rectangular (Discrete Uniform) Distribution .3-34
Continuous Distribution Formulas 3-34
Arcsin Distribution 3-34
Beta Distribution 3-35
Cauchy Distribution 3-35
Chi Distribution .3-35
Chi-Square Distribution 3-35
Erlang Distribution 3-35
Exponential Distribution .3-35
Extreme-Value Distribution .3-36
F Distribution 3-36
Gamma Distribution .3-36
Half-Normal Distribution .3-36
Laplace (Double Exponential) Distribution .3-37
Logistic Distribution 3-37
Lognormal Distribution 3-37
Noncentral Chi-Square Distribution 3-37
Noncentral F Distribution 3-38
Noncentral t-Distribution .3-38
Normal Distribution 3-38
Pareto Distribution 3-38
Rayleigh Distribution 3-39
t-Distribution .3-39
Triangular Distribution .3-39
Uniform Distribution 3-39
Weibull Distribution .3-40
Variate Generation Techniques 3-40
Notation 3-40
Variate Generation Algorithms 3-40
References 3-42
4 Computations with Descriptive Statistics
Sample Average .4-1
Application Areas 4-1
Sample calculations 4-1
Sample Variance 4-1
Application Areas 4-1
Sample Calculations .4-2
Sample Standard Deviation .4-2
Application Areas 4-2
Sample Standard Error of the Mean .4-3xviii Contents
Application Areas 4-3
Skewness .4-3
Standardized Skewness 4-3
Kurtosis .4-4
Standardized Kurtosis 4-4
Weighted Average 4-4
Estimation and Testing .4-4
100(1 ? ?)% Confidence Interval for Mean .4-4
100(1 ? ?)% Confidence Interval for Variance .4-4
100(1 ? ?)% Confidence Interval for Difference
in Means .4-4
100(1 ? ?)% Confidence Interval for Ratio
of Variances 4-5
Normal Probability Plot 4-5
Comparison of Poisson Rates .4-5
Distribution Functions and Parameter Estimation .4-5
Bernoulli Distribution .4-5
Binomial Distribution .4-5
Discrete Uniform Distribution .4-6
Geometric Distribution .4-6
Negative Binomial Distribution 4-6
Poisson Distribution 4-6
Beta Distribution 4-6
Chi-Square Distribution 4-6
Erlang Distribution 4-6
Exponential Distribution .4-7
Application Areas 4-7
F Distribution 4-7
Gamma Distribution .4-7
Log–Normal Distribution .4-7
Normal Distribution 4-8
Triangular Distribution .4-8
Uniform Distribution 4-8
Weibull Distribution .4-8
Chi-Square Test for Distribution Fitting 4-8
Kolmogorov–Smirnov Test .4-9
ANOVA .4-9
Notation 4-9
Standard Error .4-9
Interval Estimates 4-9
Tukey Interval 4-10
Scheffe Interval .4-10
Cochran C-test .4-10
Bartlett Test 4-10Contents xix
Hartley’s Test .4-10
Kruskal–Wallis Test .4-11
Adjustment for ties 4-11
Freidman Test 4-11
Regression 4-12
Notation 4-12
Statistical Quality Control .4-13
Subgroup Statistics .4-13
X-Bar Charts 4-14
Capability Ratios 4-14
R Charts 4-15
S Charts .4-15
C Charts 4-15
U Charts .4-15
P Charts 4-15
NP Charts .4-16
CuSum Chart for the Mean .4-16
Time-Series Analysis .4-16
Notation 4-16
Autocorrelation at Lag k 4-17
Partial Autocorrelation at Lag k 4-17
Cross-Correlation at Lag k 4-17
Box-Cox Computation 4-17
Periodogram (Computed using Fast Fourier
Transform) .4-18
Categorical Analysis 4-18
Notation 4-18
Totals 4-18
Chi-Square 4-18
Lambda .4-19
Uncertainty Coefficient .4-19
Somer’s D Measure 4-20
Eta .4-20
Contingency Coefficient 4-21
Cramer’s V Measure 4-21
Conditional Gamma 4-21
Pearson’s R Measure 4-21
Kendall’s Tau b Measure .4-21
Tau C Measure .4-22
Overall Mean 4-22
Chebyshev’s Theorem .4-22
Permutation .4-22
Combination 4-22
Failure .4-22xx Contents
5 Computations for Economic Analysis
Fundamentals of Economic Analysis .5-1
Simple Interest .5-1
Future value 5-1
Compound Interest .5-2
Continuous Compound Interest 5-2
Effective Rate 5-3
Present Value with Compound Interest .5-3
Annuities 5-4
Present value of annuity 5-4
Future value of an annuity 5-4
Amortization of Loans .5-5
Interest and Equity Computations .5-5
Equity Break-Even Formula .5-8
Sinking Fund Payment 5-9
Internal Rate of Return 5-9
Benefit–Cost Ratio .5-9
Simple Payback Period 5-9
Discounted Payback Period 5-10
Economic Methods of Comparing Investment Alternatives 5-10
Present Value Analysis 5-10
Annual Value Analysis 5-10
Internal Rate of Return Analysis .5-11
External Rate of Return Analysis 5-11
Incremental Analysis .5-11
Guidelines for Comparison of
Alternatives 5-12
Asset Replacement and Retention Analysis .5-12
Replacement Analysis Computation 5-14
Depreciation Methods .5-15
Depreciation Terminology 5-15
Depreciation Methods .5-16
Straight-Line (SL) Method 5-16
Declining Balance (DB) Method .5-16
Sums-of-Years’ Digits (SYD) Method 5-17
MACRS Method 5-17
Effects of Inflation and Taxes 5-18
Foreign Exchange Rates .5-21
After-Tax Economic Analysis .5-21
Cost and Value Computations .5-22
Actual Cost of Work Performed .5-23
Applied Direct Cost .5-23
Budgeted Cost for Work Performed .5-23Contents xxi
Budgeted Cost for Work Scheduled .5-23
Direct Cost .5-23
Economies of Scale 5-23
Estimated Cost at Completion 5-23
First Cost 5-24
Fixed Cost .5-24
Incremental Cost 5-24
Indirect Cost .5-24
Life-Cycle Cost .5-24
Maintenance Cost 5-24
Marginal Cost .5-24
Operating Cost .5-24
Opportunity Cost .5-25
Overhead Cost 5-25
Standard Cost .5-25
Sunk Cost .5-25
Total Cost .5-25
Variable cost .5-25
Cash-Flow Calculations 5-26
Calculations with Compound Amount Factor 5-26
Calculations with Present Worth Factor 5-27
Calculations with Uniform Series Present Worth Factor .5-27
Calculations with Uniform Series Capital Recovery Factor 5-28
Calculations with Uniform Series Compound Amount Factor 5-29
Calculations with Uniform Series Sinking Fund Factor .5-29
Calculations with Capitalized Cost Formula .5-30
Arithmetic Gradient Series 5-31
Internal Rate of Return 5-32
Benefit-Cost Ratio Analysis .5-33
Simple Payback Period 5-33
Discounted Payback Period 5-34
Time Required to Double Investment 5-35
Effects of Inflation on Industrial Project Costing 5-36
Mild Inflation .5-40
Moderate Inflation .5-40
Severe Inflation 5-40
Hyperinflation 5-40
Break-Even Analysis 5-40
Profit Ratio Analysis 5-42
Project Cost Estimation 5-46
Optimistic and Pessimistic Cost Estimates 5-47
Cost Performance Index .5-47
Cost Control Limits .5-48
Project Balance Computation .5-48xxii Contents
6 Industrial Production Calculations
Learning Curve Models and Computations 6-1
The Average Cost Model .6-1
Computational Example 6-2
Computational Example 6-3
The Unit Cost Model .6-4
Productivity Calculations Using Learning Curves 6-5
Determining Average Unit Time 6-5
Calculation of the Learning Factor .6-5
Calculating Total Time for a Job .6-5
Time Required to Perform a Task for the nth Time 6-5
The Improvement Ratio 6-5
Computational Example 6-5
Solution 6-5
Computation for Improvement Goal in Unit Time 6-6
Computation of Machine Output Capacities .6-6
Machine Utilization Ratio: Determining How Often a
Machine Is Idle 6-6
Calculating Number of Machines Needed to Meet Output 6-7
Alternate Forms for Machine Formula 6-7
Calculating Buffer Production to Allow for Defects .6-8
Adjusting Machine Requirements to Allow for Rejects 6-9
Output Computations for Sequence of Machines .6-9
Calculating Forces on Cutting Tools 6-10
Calculating Pressure 6-11
Finding Required Horsepower .6-11
Machine Accuracy .6-12
Calculating the Goal Dimension .6-12
Drill Thrust 6-13
Drill Torque .6-14
Drill Horsepower .6-14
Calculating Speed and Rotation of Machines 6-14
Shaft Speed .6-15
Surface Speed .6-15
Tool Feed per Revolution 6-16
Tool Feed per Minute 6-16
Tool Feed per Tooth 6-17
Computation to Find the Volume of Material Removed 6-17
Time Rate for Material Removal in a Rectangular Cut .6-17
Calculation of Linear Feed for Rectangular Material Removal 6-18
Takt Time for Production Planning .6-18
Production Crew Work Rate Analysis .6-19
Production Work Rate Example .6-20Contents xxiii
Case of Multiple Resources Working Together .6-20
Computational Examples 6-21
Calculation of Personnel Requirements .6-22
Calculation of Machine Requirements .6-23
References 6-23
7 Forecasting Calculations
Forecasting Based on Averages .7-1
Simple Average Forecast .7-1
Period Moving Average Forecast 7-2
Weighted Average Forecast .7-2
Weighted T-Period Moving Average Forecast 7-2
Exponential Smoothing Forecast 7-3
Regression Analysis .7-3
Regression Relationships .7-3
Prediction .7-4
Control .7-4
Procedure for Regression Analysis .7-5
Coefficient of Determination 7-5
Residual Analysis .7-7
Time-Series Analysis .7-9
Stationarity and Data Transformation .7-10
Moving Average Processes 7-12
Autoregressive Processes .7-13
Forecasting for Inventory Control 7-15
Economic Order Quantity Model .7-15
Quantity Discount .7-16
Calculation of Total Relevant Cost .7-16
Evaluation of the Discount Option .7-17
Sensitivity Analysis 7-19
Wagner–Whitin Algorithm 7-20
Notation and Variables 7-21
8 Six Sigma and Lean
Concept of Six Sigma .8-1
Taguchi Loss Function 8-1
Identification and Elimination of Sources of Defects 8-2
Roles and Responsibilities for Six Sigma 8-3
Statistical Techniques for Six Sigma .8-3
Control Charts .8-4
X and R-Charts 8-4
Data Collection Strategies .8-5
Subgroup Sample Size .8-5
Frequency of Sampling 8-6xxiv Contents
Stable Process .8-6
Out-of-Control Patterns 8-6
Calculation of Control Limits .8-7
Plotting Control Charts for Range and Average Charts 8-8
Plotting Control Charts for Moving Range and Individual
Control Charts .8-9
Case Example: Plotting of Control Chart .8-9
Calculations 8-9
Trend Analysis .8-14
Process Capability Analysis for Six Sigma .8-18
Capable Process (Cp) .8-18
Capability Index (Cpk) .8-19
Process Capability Example 8-20
Possible Applications of Process Capability Index 8-21
Potential Abuse of C
p and Cpk .8-22
Lean Principles and Applications .8-22
Kaizen of a Process 8-23
Lean Task Value Rating System 8-24
9 Risk Computations
Cost Uncertainties .9-1
Schedule Uncertainties 9-2
Performance Uncertainties .9-2
Decision Tables and Trees 9-2
Reliability Calculations 9-7
General Reliability Definitions 9-8
Exponential Distribution Used as Reliability
Function .9-9
Reliability Formulas .9-10
General Reliability Definitions 9-10
Exponential Distribution Used as Reliability
Function .9-11
10 Computations for Project Analysis
Planning .10-1
Organizing .10-1
Scheduling 10-1
Control .10-2
CPM Scheduling 10-2
Advantages for Communication .10-3
Advantages for Control .10-3
Advantages for Team Interaction .10-3
Activity Precedence Relationships .10-4
Network Notation 10-4Contents xxv
Forward-Pass Calculations 10-5
CPM Example 10-6
Backward-Pass Calculations .10-7
Calculation of Slacks .10-8
Calculations for Subcritical Paths 10-9
Plotting of Gantt Charts 10-10
Calculations for Project Crashing 10-13
Calculations for Project Duration Diagnostics 10-18
PERT Formulas .10-19
Activity Time Distributions 10-19
Project Duration Analysis .10-20
Simulation of Project Networks 10-24
11 Product Shape and Geometrical Calculations
Equation of a Straight Line .11-1
Quadratic Equation .11-2
Conic Sections .11-2
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 4 e = 1 (Circle) 11-5
Conic Section Equation 11-6
Quadric Surface (Sphere) 11-6
Identities .11-7
Trigonometry .11-7
Law of Sines 11-7
Law of Cosines .11-8
Identities .11-8
Complex Numbers .11-10
Polar Coordinates 11-10
Euler’s Identity .11-11
Roots .11-11
Matrices 11-11
Matrix Multiplication 11-11
Matrix Addition .11-11
Identity Matrix .11-11
Matrix Transpose .11-11
Matrix Inverse 11-12
Determinants .11-12
Vectors .11-12
Gradient, Divergence, and Curl 11-13
Identities .11-13
Progressions and Series .11-14
Arithmetic Progression .11-14xxvi Contents
Geometric Progression 11-14
Properties of Series 11-15
Power Series .11-15
Taylor’s Series 11-16
Differential Calculus .11-16
The Derivative 11-16
Test for a Maximum 11-16
Test for a Minimum 11-16
Test for a Point of Inflection .11-16
The Partial Derivative 11-16
Curvature in Rectangular Coordinates 11-17
The Radius of Curvature .11-17
L’Hospital’s Rule 11-17
Integral Calculus 11-18
Derivatives and Indefinite Integrals .11-18
Derivatives .11-18
Indefinite Integrals .11-20
Mensuration of Areas and Volumes 11-21
Nomenclature 11-21
Parabola 11-21
Ellipse 11-21
Circular Segment .11-22
Circular Sector .11-22
Sphere .11-22
Parallelogram .11-22
Regular Polygon (n Equal Sides) .11-23
Prismoid .11-23
Right Circular Cone .11-23
Right Circular Cylinder .11-23
Paraboloid of Revolution .11-23
Centroids and Moments of Inertia .11-24
Difference Equations .11-24
First-Order Linear Difference Equation .11-25
Second-Order Linear Difference Equation 11-25
Numerical Methods .11-25
Newton’s Method for Root Extraction .11-25
Newton’s Method of Minimization 11-25
Numerical Integration .11-26
Euler’s or Forward Rectangular Rule .11-26
Trapezoidal Rule 11-26
Simpson’s Rule/Parabolic Rule (n Must Be
an Even Integer) 11-27
Calculation of Best-Fit Circle .11-27Contents xxvii
12 General Engineering Calculations
Six Simple Machines for Materials Handling 12-1
Machine 1: The Lever 12-1
Machine 2: Wheel and Axle 12-1
Machine 3: The Pulley .12-2
Machine 4: The Inclined Plane .12-2
Machine 5: The Wedge 12-2
Machine 6: The Screw 12-2
Mechanics: Kinematics .12-3
Scalars and Vectors 12-3
Distance and Displacement .12-3
Acceleration .12-3
Speed and Velocity 12-3
Frequency .12-3
Period .12-3
Angular Displacement .12-3
Angular Velocity 12-4
Angular Acceleration .12-4
Rotational Speed 12-4
Uniform Linear Motion 12-4
Uniform Accelerated Linear Motion 12-4
Rotational Motion .12-5
Uniform Rotation and a Fixed Axis .12-5
Uniform Accelerated Rotation about a Fixed Axis 12-5
Simple Harmonic Motion .12-6
Pendulum .12-7
Free Fall 12-7
Vertical Project 12-7
Angled Projections .12-8
Horizontal Projection (? = 0) .12-8
Sliding Motion on an Inclined Plane 12-8
Rolling Motion on an Inclined Plane .12-9
Mechanics: Dynamics .12-10
Newton’s First Law of Motion 12-10
Newton’s Second Law of Motion 12-10
Newton’s Third Law of Motion 12-10
Momentum of Force 12-10
Impulse of Force 12-11
Law of Conservation of Momentum 12-11
Friction .12-11
General Law of Gravity .12-11
Gravitational Force 12-12
Centrifugal Force .12-12
Centripetal Force .12-12xxviii Contents
Torque 12-12
Work .12-13
Energy .12-13
Conservation of Energy .12-14
Power 12-14
Appendix A: Mathematical Patterns, Series, and Formulae
Number Sequence and Patterns A-1
Closed-Form Mathematical Expressions A-3
Derivation of the Quadratic Formula A-7
Appendix B: Measurement Units, Notation, and Constants
Common Notation . B-1
Scientific Constants B-3
Numbers and Prefixes B-3
Appendix C: Conversion Factors
Area Conversion Factors C-1
Volume Conversion Factors C-2
Energy Conversion Factors C-2
Mass Conversion Factors . C-3
Temperature Conversion Factors C-3
Velocity Conversion Factors C-4
Pressure Conversion Factors . C-4
Distance Conversion Factors . C-5
Physical Science Equations C-6
English and Metric Systems . C-7
Household Measurement Conversion C-7
Appendix D: Factors and Tables
Formulas for Interest Factor D-1
Summation Formulas for Closed-Form Expressions .D-3
Interest Tables .D-3
Appendix E: Greek Symbols and Roman Numerals
Greek Symbols E-1
Roman Numerals E-2
Bibliography . Bibliography-1
Index Index-1 Prefac
كلمة سر فك الضغط : books-world.net
The Unzip Password : books-world.net

التعليقات

اترك تعليقاً

لن يتم نشر عنوان بريدك الإلكتروني. الحقول الإلزامية مشار إليها بـ *

Time limit is exhausted. Please reload CAPTCHA.