Mathematical Formulas for Industrial and Mechanical Engineering - 1st Edition - ISBN: 9780124201316, 9780124202221

Mathematical Formulas for Industrial and Mechanical Engineering

1st Edition

Authors: Seifedine Kadry
Hardcover ISBN: 9780124201316
eBook ISBN: 9780124202221
Imprint: Elsevier
Published Date: 31st October 2013
Page Count: 144
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Description

  • Preface
  • Biography
  • 1. Symbols and Special Numbers
    • 1.1 Basic Mathematical Symbols
    • 1.2 Basic Algebra Symbols
    • 1.3 Linear Algebra Symbol
    • 1.4 Probability and Statistics Symbols
    • 1.5 Geometry Symbols
    • 1.6 Set Theory Symbols
    • 1.7 Logic Symbols
    • 1.8 Calculus Symbols
    • 1.9 Numeral Symbols
    • 1.10 Greek Alphabet Letters
    • 1.11 Roman Numerals
    • 1.12 Prime Numbers
    • 1.13 Important Numbers in Science (Physical Constants)
    • 1.14 Basic Conversion Formulas
    • 1.15 Basic Area Formulas
    • 1.16 Basic Perimeter Formulas
    • 1.17 Basic Volume Formulas
  • 2. Elementary Algebra
    • 2.1 Sets of Numbers
    • 2.2 Fundamental Properties of Numbers
    • 2.3 Absolute Value
    • 2.4 Basic Properties of Real Numbers
    • 2.5 Laws of Exponents
    • 2.6 Logarithm
    • 2.7 Factorials
    • 2.8 Factors and Expansions
    • 2.9 Solving Algebraic Equations
    • 2.10 Intervals
    • 2.11 Complex Numbers
    • 2.12 The Complex Plane
    • 2.13 Complex Numbers in Polar Form
    • 2.14 Multiplication and Division in Polar Form
    • 2.15 DeMoivre's Theorem
    • 2.16 Euler’s Formula
  • 3. Linear Algebra
    • 3.1 Basic Definitions
    • 3.2 Basic Types of Matrices
    • 3.3 Basic Operations on Matrices
    • 3.4 Properties of Matrix Operations
    • 3.5 Determinants
    • 3.6 Sarrus Rule
    • 3.7 Minors and Cofactors
    • 3.8 Properties of Determinants
    • 3.9 Inverse Matrix
    • 3.10 System of Linear Equations
    • 3.11 Methods of Solution
    • 3.12 Inverse Matrix Method
    • 3.13 Determinant Method (Cramer’s Rule)
  • 4. Analytic Geometry and Trigonometry
    • 4.1 Plane Figures—Perimeter (P), Circumference (C), and Area (A)
    • 4.2 Solid Figures—Surface Area (S) and Volume (V)
    • 4.3 Right Triangle
    • 4.4 Any Triangle
    • 4.5 Degrees or Radians
    • 4.6 Table of Natural Trigonometric Functions
    • 4.7 Trigonometry Identities
    • 4.8 The Inverse Trigonometric Functions
    • 4.9 Solutions of Trigonometric Equations
    • 4.10 Analytic Geometry (in the plane, i.e., 2D)
    • 4.11 Vector
  • 5. Calculus
    • 5.1 Functions and Their Graphs
    • 5.2 Limits of Functions
    • 5.3 Definition and Properties of the Derivative
    • 5.4 Table of Derivatives
    • 5.5 Higher Order Derivatives
    • 5.6 Applications of Derivative
    • 5.7 Indefinite Integral
    • 5.8 Integrals of Rational Function
    • 5.9 Integrals of Irrational Function
    • 5.10 Integrals of Trigonometric Functions
    • 5.11 Integrals of Hyperbolic Functions
    • 5.12 Integrals of Exponential and Logarithmic Functions
    • 5.13 Reduction Formulas Using Integration by Part
    • 5.14 Definite Integral
    • 5.15 Improper Integral
    • 5.16 Continuity of a Function
    • 5.17 Functions and Graphs
    • 5.18 Partial Fractions
    • 5.19 Properties of Trigonometric Functions
    • 5.20 Sequences and Series
    • 5.21 Arithmetic Sequences and Series
    • 5.22 Geometric Sequences and Series
    • 5.23 The Finite Geometric Series
    • 5.24 The Infinite Geometric Series
    • 5.25 Some of Finite and Infinite Series
    • 5.26 Convergence Tests for Series
    • 5.27 Series Tests
    • 5.28 Integral Test
    • 5.29 Comparison Tests
    • 5.30 Ratio Test
    • 5.31 Absolute and Conditional Convergence
    • 5.32 Taylor and Maclaurin Series
    • 5.33 Continuous Fourier Series
    • 5.34 Double Integrals
    • 5.35 Triple Integrals
    • 5.36 First-Order Differential Equations
    • 5.37 Second-Order Differential Equations
    • 5.38 Laplace Transform
    • 5.39 Table of Laplace Transforms
  • 6. Statistics and Probability
    • 6.1 Arithmetic Mean
    • 6.2 Median
    • 6.3 Mode
    • 6.4 Geometric Mean
    • 6.5 Standard Deviation
    • 6.6 Variance
    • 6.7 z-Score
    • 6.8 Coefficient of Variation
    • 6.9 Sample Covariance
    • 6.10 Range
    • 6.11 Central Limit Theorem
    • 6.12 Counting Rule for Combinations
    • 6.13 Counting Rule for Permutations
    • 6.14 Properties of Probability
    • 6.15 Binomial Probability Function
    • 6.16 Expected Value and Variance for the Binomial Distribution
    • 6.17 Poisson Probability Function
    • 6.18 Confidence Intervals
    • 6.19 Sample Size
    • 6.20 Regression and Correlation
    • 6.21 Pearson Product–Moment Correlation Coefficient
    • 6.22 Test Statistic for Hypothesis Tests about a Population Proportion
    • 6.23 Chi-Square Goodness-of-Fit Test Statistic
    • 6.24 Standard Normal Distribution Table
    • 6.25 Table of the Student's t-distribution
    • 6.26 Chi-square Table
    • 6.27 Table of F-statistics, P=0.05
  • 7. Financial Mathematics
    • 7.1 Percentage
    • 7.2 The Number of Payments
    • 7.3 Convert Interest Rate Compounding Bases
    • 7.4 Effective Interest Rate
    • 7.5 The Future Value of a Single Sum
    • 7.6 The Future Value with Compounding
    • 7.7 The Future Value of a Cash Flow Series
    • 7.8 The Future Value of an Annuity
    • 7.9 The Future Value of an Annuity Due
    • 7.10 The Future Value of an Annuity with Compounding
    • 7.11 Monthly Payment
    • 7.12 The Present Value of a Single Sum
    • 7.13 The Present Value with Compounding
    • 7.14 The Present Value of a Cash Flow Series
    • 7.15 The Present Value of an Annuity with Continuous Compounding
    • 7.16 The Present Value of a Growing Annuity with Continuous Compounding
    • 7.17 The Net Present Value of a Cash Flow Series
    • 7.18 Expanded Net Present Value Formula
    • 7.19 The Present Worth Cost of a Cash Flow Series
    • 7.20 The Present Worth Revenue of a Cash Flow Series

Key Features

  • Covers mathematics formulas needed for Industrial and Mechanical Engineering
  • Quick and easy to use reference and study
  • Includes practical examples and figures to help quickly understand concepts

Readership

Students, teachers, researchers, and professionals in all Engineering subjects.

Table of Contents

  • Preface
  • Biography
  • 1. Symbols and Special Numbers
    • 1.1 Basic Mathematical Symbols
    • 1.2 Basic Algebra Symbols
    • 1.3 Linear Algebra Symbol
    • 1.4 Probability and Statistics Symbols
    • 1.5 Geometry Symbols
    • 1.6 Set Theory Symbols
    • 1.7 Logic Symbols
    • 1.8 Calculus Symbols
    • 1.9 Numeral Symbols
    • 1.10 Greek Alphabet Letters
    • 1.11 Roman Numerals
    • 1.12 Prime Numbers
    • 1.13 Important Numbers in Science (Physical Constants)
    • 1.14 Basic Conversion Formulas
    • 1.15 Basic Area Formulas
    • 1.16 Basic Perimeter Formulas
    • 1.17 Basic Volume Formulas
  • 2. Elementary Algebra
    • 2.1 Sets of Numbers
    • 2.2 Fundamental Properties of Numbers
    • 2.3 Absolute Value
    • 2.4 Basic Properties of Real Numbers
    • 2.5 Laws of Exponents
    • 2.6 Logarithm
    • 2.7 Factorials
    • 2.8 Factors and Expansions
    • 2.9 Solving Algebraic Equations
    • 2.10 Intervals
    • 2.11 Complex Numbers
    • 2.12 The Complex Plane
    • 2.13 Complex Numbers in Polar Form
    • 2.14 Multiplication and Division in Polar Form
    • 2.15 DeMoivre's Theorem
    • 2.16 Euler’s Formula
  • 3. Linear Algebra
    • 3.1 Basic Definitions
    • 3.2 Basic Types of Matrices
    • 3.3 Basic Operations on Matrices
    • 3.4 Properties of Matrix Operations
    • 3.5 Determinants
    • 3.6 Sarrus Rule
    • 3.7 Minors and Cofactors
    • 3.8 Properties of Determinants
    • 3.9 Inverse Matrix
    • 3.10 System of Linear Equations
    • 3.11 Methods of Solution
    • 3.12 Inverse Matrix Method
    • 3.13 Determinant Method (Cramer’s Rule)
  • 4. Analytic Geometry and Trigonometry
    • 4.1 Plane Figures—Perimeter (P), Circumference (C), and Area (A)
    • 4.2 Solid Figures—Surface Area (S) and Volume (V)
    • 4.3 Right Triangle
    • 4.4 Any Triangle
    • 4.5 Degrees or Radians
    • 4.6 Table of Natural Trigonometric Functions
    • 4.7 Trigonometry Identities
    • 4.8 The Inverse Trigonometric Functions
    • 4.9 Solutions of Trigonometric Equations
    • 4.10 Analytic Geometry (in the plane, i.e., 2D)
    • 4.11 Vector
  • 5. Calculus
    • 5.1 Functions and Their Graphs
    • 5.2 Limits of Functions
    • 5.3 Definition and Properties of the Derivative
    • 5.4 Table of Derivatives
    • 5.5 Higher Order Derivatives
    • 5.6 Applications of Derivative
    • 5.7 Indefinite Integral
    • 5.8 Integrals of Rational Function
    • 5.9 Integrals of Irrational Function
    • 5.10 Integrals of Trigonometric Functions
    • 5.11 Integrals of Hyperbolic Functions
    • 5.12 Integrals of Exponential and Logarithmic Functions
    • 5.13 Reduction Formulas Using Integration by Part
    • 5.14 Definite Integral
    • 5.15 Improper Integral
    • 5.16 Continuity of a Function
    • 5.17 Functions and Graphs
    • 5.18 Partial Fractions
    • 5.19 Properties of Trigonometric Functions
    • 5.20 Sequences and Series
    • 5.21 Arithmetic Sequences and Series
    • 5.22 Geometric Sequences and Series
    • 5.23 The Finite Geometric Series
    • 5.24 The Infinite Geometric Series
    • 5.25 Some of Finite and Infinite Series
    • 5.26 Convergence Tests for Series
    • 5.27 Series Tests
    • 5.28 Integral Test
    • 5.29 Comparison Tests
    • 5.30 Ratio Test
    • 5.31 Absolute and Conditional Convergence
    • 5.32 Taylor and Maclaurin Series
    • 5.33 Continuous Fourier Series
    • 5.34 Double Integrals
    • 5.35 Triple Integrals
    • 5.36 First-Order Differential Equations
    • 5.37 Second-Order Differential Equations
    • 5.38 Laplace Transform
    • 5.39 Table of Laplace Transforms
  • 6. Statistics and Probability
    • 6.1 Arithmetic Mean
    • 6.2 Median
    • 6.3 Mode
    • 6.4 Geometric Mean
    • 6.5 Standard Deviation
    • 6.6 Variance
    • 6.7 z-Score
    • 6.8 Coefficient of Variation
    • 6.9 Sample Covariance
    • 6.10 Range
    • 6.11 Central Limit Theorem
    • 6.12 Counting Rule for Combinations
    • 6.13 Counting Rule for Permutations
    • 6.14 Properties of Probability
    • 6.15 Binomial Probability Function
    • 6.16 Expected Value and Variance for the Binomial Distribution
    • 6.17 Poisson Probability Function
    • 6.18 Confidence Intervals
    • 6.19 Sample Size
    • 6.20 Regression and Correlation
    • 6.21 Pearson Product–Moment Correlation Coefficient
    • 6.22 Test Statistic for Hypothesis Tests about a Population Proportion
    • 6.23 Chi-Square Goodness-of-Fit Test Statistic
    • 6.24 Standard Normal Distribution Table
    • 6.25 Table of the Student's t-distribution
    • 6.26 Chi-square Table
    • 6.27 Table of F-statistics, P=0.05
  • 7. Financial Mathematics
    • 7.1 Percentage
    • 7.2 The Number of Payments
    • 7.3 Convert Interest Rate Compounding Bases
    • 7.4 Effective Interest Rate
    • 7.5 The Future Value of a Single Sum
    • 7.6 The Future Value with Compounding
    • 7.7 The Future Value of a Cash Flow Series
    • 7.8 The Future Value of an Annuity
    • 7.9 The Future Value of an Annuity Due
    • 7.10 The Future Value of an Annuity with Compounding
    • 7.11 Monthly Payment
    • 7.12 The Present Value of a Single Sum
    • 7.13 The Present Value with Compounding
    • 7.14 The Present Value of a Cash Flow Series
    • 7.15 The Present Value of an Annuity with Continuous Compounding
    • 7.16 The Present Value of a Growing Annuity with Continuous Compounding
    • 7.17 The Net Present Value of a Cash Flow Series
    • 7.18 Expanded Net Present Value Formula
    • 7.19 The Present Worth Cost of a Cash Flow Series
    • 7.20 The Present Worth Revenue of a Cash Flow Series

Details

No. of pages:
144
Language:
English
Copyright:
© Elsevier 2014
Published:
Imprint:
Elsevier
eBook ISBN:
9780124202221
Hardcover ISBN:
9780124201316

About the Author

Seifedine Kadry

Affiliations and Expertise

American University of the Middle East, Kuwait