كتاب Industrial-Engineering-Calculations-and-Practice
منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Industrial-Engineering-Calculations-and-Practice

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كاتب الموضوعرسالة
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كبير مهندسين
كبير مهندسين


عدد المساهمات : 2044
التقييم : 3386
تاريخ التسجيل : 21/01/2012
العمر : 39
الدولة : مصر
العمل : مدير الصيانة بشركة تصنيع ورق
الجامعة : حلوان

مُساهمةموضوع: كتاب Industrial-Engineering-Calculations-and-Practice    الأحد 06 يناير 2013, 2:54 pm

احبتى فى الله معى اليوم كتاب
Industrial-Engineering-Calculations-and-Practice


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 STEM1-6
IE Catchphrases 1-6
Span and Utility of IE 1-6
Heritage from Industrial Revolution1-7
Historical Accounts 1-8
Chronology of Applications1-10
Importance of IE Calculations 1-14
Importance of Calculations Guide 1-16
Basic Queuing Equations 1-17
Queuing Birth–Death Processes1-21
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 Scale1-23
References 1-23
ix
x Contents
2 Basic Mathematical Calculations
Quadratic Equation 2-1
Overall Mean2-2
Chebyshev’s Theorem 2-2
Permutations2-2
Combinations 2-2
Failure 2-3
Probability Distribution 2-3
Probability2-3
Distribution Function 2-3
Expected Value 2-4
Variance 2-5
Binomial Distribution 2-5
Poisson Distribution2-5
Mean of a Binomial Distribution2-6
Normal Distribution2-6
Cumulative Distribution Function2-6
Population Mean 2-6
Standard Error of the Mean2-6
t-Distribution2-7
Chi-Squared Distribution 2-7
Definition of Set and Notation 2-7
Set Terms and Symbols 2-8
Venn Diagrams2-8
Operations on Sets2-9
De Morgan’s Laws 2-9
Counting the Elements in a Set2-10
Permutations2-10
Combinations 2-11
Probability Terminology2-11
Basic Probability Principles 2-11
Random Variable2-12
Mean Value ˆx or Expected Value μ 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 Roots2-19
Proportion 2-19
Sum of Arithmetic Progression to n Terms 2-20
Sum of Geometric Progression to n Terms2-20
Contents xi
Arithmetic Mean of n Quantities, A2-20
Geometric Mean of n Quantities, G 2-20
Harmonic Mean of n Quantities, H 2-20
Generalized Mean2-20
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 Fractions2-23
Nonrepeated Linear Factors2-23
Repeated Linear Factors 2-24
General terms2-24
Repeated Linear Factors 2-25
Factors of Higher Degree 2-25
Geometry2-25
Triangles 2-25
Right Triangle 2-26
Equilateral Triangle 2-26
General Triangle 2-26
Menelaus’ Theorem2-27
Ceva’s Theorem 2-27
Quadrilaterals 2-27
Rectangle 2-27
Parallelogram 2-27
Rhombus 2-28
Trapezoid2-28
General Quadrilateral 2-28
Theorem2-28
Regular Polygon of n Sides Each of Length b2-28
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 Quadrilateral2-29
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 r2-30
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
Cube2-32
xii Contents
Rectangular Parallelepiped (or Box)2-32
Prism2-32
Truncated Triangular Prism 2-32
Pyramid 2-32
Frustum of a Pyramid2-33
Prismatoid 2-33
Regular Polyhedra2-33
Sphere of Radius r 2-34
Right Circular Cylinder of Radius r and Height h2-34
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 h2-35
Zone and Segment of Two Bases 2-35
Lune 2-36
Spherical Sector2-36
Spherical Triangle and Polygon 2-36
Spheroids2-36
Ellipsoid 2-36
Oblate Spheroid 2-36
Prolate Spheroid2-37
Circular Torus2-37
Formulas from Plane Analytic Geometry2-37
Distance d between Two Points2-37
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 Line2-38
General Equation of a Line2-38
Distance From a Point (x1, y1) to the Line Ax +By +C = 02-38
Angle ψ between Two Lines Having Slopes m1 and m2 2-38
Area of a Triangle with Vertices 2-39
Transformation of Coordinates Involving Pure Translation2-39
Transformation of Coordinates Involving Pure Rotation 2-39
Transformation of Coordinates Involving Translation and Rotation2-39
Polar Coordinates (r, θ) 2-40
Plane Curves2-40
Catenary, Hyperbolic Cosine 2-40
Cardioid 2-40
Circle2-40
Cassinian Curves2-41
Cotangent Curve2-41
Cubical Parabola 2-41
Contents xiii
Cosecant Curve2-41
Cosine Curve2-41
Ellipse 2-41
Gamma Function2-41
Hyperbolic Functions2-41
Inverse Cosine Curve 2-42
Inverse Sine Curve2-42
Inverse Tangent Curve 2-42
Logarithmic Curve2-42
Parabola2-42
Cubical Parabola 2-42
Tangent Curve 2-42
Distance d between Two Points2-43
Logarithmic Identities 2-46
Series Expansions 2-47
Limiting Values2-47
Inequalities2-47
Polynomial Approximations 2-48
Exponential Function Series Expansion 2-49
Fundamental Properties2-49
Definition of General Powers 2-49
Logarithmic and Exponential Functions 2-50
Periodic Property 2-50
Polynomial Approximations2-50
Slopes 2-53
Trigonometric ratios 2-53
Sine Law2-55
Cosine Law 2-56
Algebra 2-56
Expanding 2-56
Factoring2-57
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 Distribution3-3
Geometric Distribution 3-3
xiv Contents
Hypergeometric Distribution 3-3
Negative Binomial Distribution3-4
Poisson Distribution3-4
Rectangular (Discrete Uniform) Distribution 3-4
Continuous Distributions 3-4
Arcsin Distribution3-4
Beta Distribution3-5
Cauchy Distribution 3-5
Chi Distribution3-5
Chi-Square Distribution3-5
Erlang Distribution3-5
Exponential Distribution3-6
Extreme-Value Distribution 3-6
F Distribution 3-6
Gamma Distribution 3-7
Half-Normal Distribution 3-7
Laplace (Double Exponential) Distribution3-7
Logistic Distribution3-7
Lognormal Distribution 3-7
Noncentral Chi-Square Distribution3-8
Noncentral F Distribution 3-8
Noncentral t-Distribution3-8
Normal Distribution3-9
Pareto Distribution 3-9
Rayleigh Distribution 3-9
t-Distribution3-9
Triangular Distribution3-10
Uniform Distribution 3-10
Weibull Distribution 3-10
Distribution Parameters 3-10
Average3-10
Variance 3-11
Standard Deviation3-11
Standard Error 3-11
Skewness3-11
Standardized Skewness3-11
Kurtosis 3-11
Standardized Kurtosis 3-11
Weighted Average 3-11
Estimation and Testing3-11
100(1−α)% Confidence Interval for Mean3-11
100(1−α)% Confidence Interval for Variance 3-11
100(1−α)% Confidence Interval for Difference in Means 3-12
100(1−α)% Confidence Interval for Ratio of Variances 3-12
Contents xv
Normal Probability Plot 3-12
Comparison of Poisson Rates 3-13
Distribution Functions—Parameter Estimation 3-13
Bernoulli3-13
Binomial 3-13
Discrete Uniform3-13
Geometric3-13
Negative Binomial3-13
Poisson3-13
Beta 3-14
Chi-Square3-14
Erlang3-14
Exponential 3-14
F Distribution 3-14
Gamma 3-14
Log–Normal 3-15
Normal3-15
Student’s t 3-15
Triangular3-15
Uniform3-15
Weibull 3-16
Chi-Square Test for Distribution Fitting3-16
Kolmogorov–Smirnov Test3-16
ANOVA 3-16
Notation3-16
Standard Error (Internal) 3-17
Standard Error (Pooled)3-17
Interval Estimates 3-17
Tukey Interval 3-17
Scheffe Interval3-17
Cochran C-Test3-17
Bartlett Test 3-18
Hartley’s Test 3-18
Kruskal–Wallis Test3-18
Adjustment for Ties3-18
Freidman Test 3-18
Regression 3-19
Notation 3-19
Regression Statistics3-19
Predictions3-20
Nonlinear Regression 3-21
Ridge Regression3-21
Quality Control 3-22
For All Quality Control Formulas 3-22
xvi Contents
Subgroup Statistics3-22
X Bar Charts 3-22
Capability Ratios 3-23
R Charts3-24
S Charts3-24
C Charts3-24
U Charts 3-24
P Charts 3-24
NP Charts 3-25
CuSum Chart for the Mean3-25
Multivariate Control Charts3-25
Time-Series Analysis 3-25
Notation 3-25
Autocorrelation at Lag k3-26
Partial Autocorrelation at Lag k3-26
Cross-Correlation at Lag k 3-26
Box-Cox3-26
Periodogram (computed using Fast Fourier Transform) 3-27
Categorical Analysis 3-27
Notation 3-27
Totals 3-27
Chi-Square3-27
Fisher’s Exact Test 3-28
Lambda3-28
Uncertainty Coefficient 3-28
Somer’s D 3-29
Eta 3-29
Contingency Coefficient3-30
Cramer’s V 3-30
Conditional Gamma3-30
Pearson’s R 3-30
Kendall’s Tau b3-30
Tau C 3-30
Probability Terminology 3-30
Basic Probability Principles3-31
Random Variable 3-31
Mean Value ˆx or Expected Value μ3-31
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 Distribution3-32
Geometric Distribution 3-33
Contents xvii
Hypergeometric Distribution 3-33
Negative Binomial Distribution3-33
Poisson Distribution3-34
Rectangular (Discrete Uniform) Distribution 3-34
Continuous Distribution Formulas 3-34
Arcsin Distribution3-34
Beta Distribution3-35
Cauchy Distribution 3-35
Chi Distribution3-35
Chi-Square Distribution3-35
Erlang Distribution3-35
Exponential Distribution3-35
Extreme-Value Distribution 3-36
F Distribution 3-36
Gamma Distribution 3-36
Half-Normal Distribution 3-36
Laplace (Double Exponential) Distribution3-37
Logistic Distribution3-37
Lognormal Distribution 3-37
Noncentral Chi-Square Distribution3-37
Noncentral F Distribution 3-38
Noncentral t-Distribution3-38
Normal Distribution3-38
Pareto Distribution 3-38
Rayleigh Distribution 3-39
t-Distribution3-39
Triangular Distribution3-39
Uniform Distribution 3-39
Weibull Distribution 3-40
Variate Generation Techniques3-40
Notation3-40
Variate Generation Algorithms 3-40
References 3-42
4 Computations with Descriptive Statistics
Sample Average 4-1
Application Areas 4-1
Sample calculations4-1
Sample Variance 4-1
Application Areas 4-1
Sample Calculations4-2
Sample Standard Deviation4-2
Application Areas 4-2
Sample Standard Error of the Mean4-3
xviii Contents
Application Areas 4-3
Skewness4-3
Standardized Skewness4-3
Kurtosis4-4
Standardized Kurtosis4-4
Weighted Average4-4
Estimation and Testing 4-4
100(1−α)% Confidence Interval for Mean4-4
100(1−α)% Confidence Interval for Variance 4-4
100(1−α)% Confidence Interval for Difference
in Means4-4
100(1−α)% Confidence Interval for Ratio
of Variances4-5
Normal Probability Plot 4-5
Comparison of Poisson Rates 4-5
Distribution Functions and Parameter Estimation4-5
Bernoulli Distribution 4-5
Binomial Distribution 4-5
Discrete Uniform Distribution 4-6
Geometric Distribution 4-6
Negative Binomial Distribution4-6
Poisson Distribution4-6
Beta Distribution4-6
Chi-Square Distribution4-6
Erlang Distribution4-6
Exponential Distribution4-7
Application Areas 4-7
F Distribution 4-7
Gamma Distribution 4-7
Log–Normal Distribution 4-7
Normal Distribution4-8
Triangular Distribution4-8
Uniform Distribution 4-8
Weibull Distribution 4-8
Chi-Square Test for Distribution Fitting4-8
Kolmogorov–Smirnov Test4-9
ANOVA 4-9
Notation4-9
Standard Error 4-9
Interval Estimates 4-9
Tukey Interval 4-10
Scheffe Interval4-10
Cochran C-test 4-10
Bartlett Test 4-10
Contents xix
Hartley’s Test 4-10
Kruskal–Wallis Test4-11
Adjustment for ties 4-11
Freidman Test 4-11
Regression 4-12
Notation4-12
Statistical Quality Control4-13
Subgroup Statistics4-13
X-Bar Charts 4-14
Capability Ratios 4-14
R Charts4-15
S Charts4-15
C Charts4-15
U Charts 4-15
P Charts 4-15
NP Charts 4-16
CuSum Chart for the Mean4-16
Time-Series Analysis 4-16
Notation4-16
Autocorrelation at Lag k4-17
Partial Autocorrelation at Lag k4-17
Cross-Correlation at Lag k 4-17
Box-Cox Computation 4-17
Periodogram (Computed using Fast Fourier
Transform)4-18
Categorical Analysis 4-18
Notation4-18
Totals 4-18
Chi-Square4-18
Lambda4-19
Uncertainty Coefficient 4-19
Somer’s D Measure4-20
Eta 4-20
Contingency Coefficient4-21
Cramer’s V Measure 4-21
Conditional Gamma4-21
Pearson’s R Measure4-21
Kendall’s Tau b Measure 4-21
Tau C Measure4-22
Overall Mean4-22
Chebyshev’s Theorem 4-22
Permutation 4-22
Combination 4-22
Failure 4-22
xx Contents
5 Computations for Economic Analysis
Fundamentals of Economic Analysis 5-1
Simple Interest 5-1
Future value5-1
Compound Interest 5-2
Continuous Compound Interest 5-2
Effective Rate5-3
Present Value with Compound Interest5-3
Annuities 5-4
Present value of annuity 5-4
Future value of an annuity 5-4
Amortization of Loans5-5
Interest and Equity Computations 5-5
Equity Break-Even Formula 5-8
Sinking Fund Payment 5-9
Internal Rate of Return5-9
Benefit–Cost Ratio5-9
Simple Payback Period 5-9
Discounted Payback Period 5-10
Economic Methods of Comparing Investment Alternatives5-10
Present Value Analysis 5-10
Annual Value Analysis 5-10
Internal Rate of Return Analysis5-11
External Rate of Return Analysis 5-11
Incremental Analysis5-11
Guidelines for Comparison of
Alternatives 5-12
Asset Replacement and Retention Analysis5-12
Replacement Analysis Computation5-14
Depreciation Methods5-15
Depreciation Terminology5-15
Depreciation Methods5-16
Straight-Line (SL) Method 5-16
Declining Balance (DB) Method5-16
Sums-of-Years’ Digits (SYD) Method5-17
MACRS Method 5-17
Effects of Inflation and Taxes5-18
Foreign Exchange Rates5-21
After-Tax Economic Analysis 5-21
Cost and Value Computations 5-22
Actual Cost of Work Performed5-23
Applied Direct Cost 5-23
Budgeted Cost for Work Performed5-23
Contents 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 Cost5-24
Incremental Cost5-24
Indirect Cost5-24
Life-Cycle Cost5-24
Maintenance Cost 5-24
Marginal Cost5-24
Operating Cost5-24
Opportunity Cost5-25
Overhead Cost5-25
Standard Cost5-25
Sunk Cost 5-25
Total Cost 5-25
Variable cost5-25
Cash-Flow Calculations 5-26
Calculations with Compound Amount Factor 5-26
Calculations with Present Worth Factor5-27
Calculations with Uniform Series Present Worth Factor 5-27
Calculations with Uniform Series Capital Recovery Factor5-28
Calculations with Uniform Series Compound Amount Factor5-29
Calculations with Uniform Series Sinking Fund Factor 5-29
Calculations with Capitalized Cost Formula 5-30
Arithmetic Gradient Series5-31
Internal Rate of Return5-32
Benefit-Cost Ratio Analysis5-33
Simple Payback Period 5-33
Discounted Payback Period 5-34
Time Required to Double Investment5-35
Effects of Inflation on Industrial Project Costing5-36
Mild Inflation 5-40
Moderate Inflation5-40
Severe Inflation 5-40
Hyperinflation5-40
Break-Even Analysis 5-40
Profit Ratio Analysis5-42
Project Cost Estimation 5-46
Optimistic and Pessimistic Cost Estimates 5-47
Cost Performance Index 5-47
Cost Control Limits5-48
Project Balance Computation5-48
xxii Contents
6 Industrial Production Calculations
Learning Curve Models and Computations 6-1
The Average Cost Model6-1
Computational Example6-2
Computational Example6-3
The Unit Cost Model6-4
Productivity Calculations Using Learning Curves 6-5
Determining Average Unit Time6-5
Calculation of the Learning Factor 6-5
Calculating Total Time for a Job6-5
Time Required to Perform a Task for the nth Time6-5
The Improvement Ratio6-5
Computational Example6-5
Solution 6-5
Computation for Improvement Goal in Unit Time 6-6
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 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 Tools6-10
Calculating Pressure 6-11
Finding Required Horsepower 6-11
Machine Accuracy 6-12
Calculating the Goal Dimension6-12
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 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 Cut 6-17
Calculation of Linear Feed for Rectangular Material Removal 6-18
Takt Time for Production Planning6-18
Production Crew Work Rate Analysis 6-19
Production Work Rate Example6-20
Contents xxiii
Case of Multiple Resources Working Together6-20
Computational Examples 6-21
Calculation of Personnel Requirements6-22
Calculation of Machine Requirements6-23
References 6-23
7 Forecasting Calculations
Forecasting Based on Averages7-1
Simple Average Forecast 7-1
Period Moving Average Forecast7-2
Weighted Average Forecast7-2
Weighted T-Period Moving Average Forecast 7-2
Exponential Smoothing Forecast7-3
Regression Analysis 7-3
Regression Relationships7-3
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 Processes7-13
Forecasting for Inventory Control7-15
Economic Order Quantity Model7-15
Quantity Discount 7-16
Calculation of Total Relevant Cost 7-16
Evaluation of the Discount Option7-17
Sensitivity Analysis 7-19
Wagner–Whitin Algorithm 7-20
Notation and Variables7-21
8 Six Sigma and Lean
Concept of Six Sigma8-1
Taguchi Loss Function 8-1
Identification and Elimination of Sources of Defects8-2
Roles and Responsibilities for Six Sigma8-3
Statistical Techniques for Six Sigma8-3
Control Charts 8-4
X and R-Charts 8-4
Data Collection Strategies 8-5
Subgroup Sample Size 8-5
Frequency of Sampling8-6
xxiv Contents
Stable Process 8-6
Out-of-Control Patterns8-6
Calculation of Control Limits 8-7
Plotting Control Charts for Range and Average Charts8-8
Plotting Control Charts for Moving Range and Individual
Control Charts 8-9
Case Example: Plotting of Control Chart8-9
Calculations8-9
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 Index8-21
Potential Abuse of Cp and Cpk 8-22
Lean Principles and Applications8-22
Kaizen of a Process 8-23
Lean Task Value Rating System8-24
9 Risk Computations
Cost Uncertainties 9-1
Schedule Uncertainties 9-2
Performance Uncertainties 9-2
Decision Tables and Trees 9-2
Reliability Calculations9-7
General Reliability Definitions9-8
Exponential Distribution Used as Reliability
Function 9-9
Reliability Formulas9-10
General Reliability Definitions9-10
Exponential Distribution Used as Reliability
Function 9-11
10 Computations for Project Analysis
Planning 10-1
Organizing 10-1
Scheduling10-1
Control 10-2
CPM Scheduling10-2
Advantages for Communication10-3
Advantages for Control 10-3
Advantages for Team Interaction 10-3
Activity Precedence Relationships 10-4
Network Notation10-4
Contents xxv
Forward-Pass Calculations10-5
CPM Example 10-6
Backward-Pass Calculations 10-7
Calculation of Slacks 10-8
Calculations for Subcritical Paths 10-9
Plotting of Gantt Charts10-10
Calculations for Project Crashing 10-13
Calculations for Project Duration Diagnostics10-18
PERT Formulas 10-19
Activity Time Distributions10-19
Project Duration Analysis10-20
Simulation of Project Networks10-24
11 Product Shape and Geometrical Calculations
Equation of a Straight Line 11-1
Quadratic Equation11-2
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
Trigonometry11-7
Law of Sines11-7
Law of Cosines 11-8
Identities 11-8
Complex Numbers11-10
Polar Coordinates11-10
Euler’s Identity 11-11
Roots 11-11
Matrices11-11
Matrix Multiplication 11-11
Matrix Addition 11-11
Identity Matrix 11-11
Matrix Transpose11-11
Matrix Inverse 11-12
Determinants 11-12
Vectors 11-12
Gradient, Divergence, and Curl11-13
Identities 11-13
Progressions and Series11-14
Arithmetic Progression 11-14
xxvi Contents
Geometric Progression 11-14
Properties of Series 11-15
Power Series 11-15
Taylor’s Series 11-16
Differential Calculus 11-16
The Derivative11-16
Test for a Maximum11-16
Test for a Minimum 11-16
Test for a Point of Inflection 11-16
The Partial Derivative11-16
Curvature in Rectangular Coordinates 11-17
The Radius of Curvature 11-17
L’Hospital’s Rule11-17
Integral Calculus11-18
Derivatives and Indefinite Integrals11-18
Derivatives 11-18
Indefinite Integrals11-20
Mensuration of Areas and Volumes 11-21
Nomenclature 11-21
Parabola 11-21
Ellipse11-21
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 Cone11-23
Right Circular Cylinder 11-23
Paraboloid of Revolution11-23
Centroids and Moments of Inertia11-24
Difference Equations11-24
First-Order Linear Difference Equation11-25
Second-Order Linear Difference Equation 11-25
Numerical Methods11-25
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 Rule11-26
Simpson’s Rule/Parabolic Rule (n Must Be
an Even Integer)11-27
Calculation of Best-Fit Circle 11-27
Contents xxvii
12 General Engineering Calculations
Six Simple Machines for Materials Handling12-1
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 Wedge12-2
Machine 6: The Screw12-2
Mechanics: Kinematics 12-3
Scalars and Vectors12-3
Distance and Displacement12-3
Acceleration
Speed and Velocity 12-3
Frequency12-3
Period 12-3
Angular Displacement12-3
Angular Velocity12-4
Angular Acceleration12-4
Rotational Speed 12-4
Uniform Linear Motion 12-4
Uniform Accelerated Linear Motion12-4
Rotational Motion 12-5
Uniform Rotation and a Fixed Axis 12-5
Uniform Accelerated Rotation about a Fixed Axis12-5
Simple Harmonic Motion12-6
Pendulum 12-7
Free Fall 12-7
Vertical Project 12-7
Angled Projections12-8
Horizontal Projection (α = 0)12-8
Sliding Motion on an Inclined Plane12-8
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 Motion12-10
Newton’s Third Law of Motion 12-10
Momentum of Force12-10
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 12-12
xxviii Contents
Torque 12-12
Work12-13
Energy12-13
Conservation of Energy12-14
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 FormulaA-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 FactorsC-1
Volume Conversion Factors C-2
Energy Conversion FactorsC-2
Mass Conversion Factors C-3
Temperature Conversion FactorsC-3
Velocity Conversion FactorsC-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 ExpressionsD-3
Interest TablesD-3
Appendix E: Greek Symbols and Roman Numerals
Greek Symbols  E-1
Roman Numerals E-2
Bibliography     Bibliography-1
Index

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