You are previewing Technical Mathematics, Sixth Edition.
O'Reilly logo
Technical Mathematics, Sixth Edition

Book Description

This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish, refine, and fill in where needed. Much has been rewritten to be even cleaner and clearer, new features have been introduced, and some peripheral topics have been removed.

The authors continue to provide real-world, technical applications that promote intuitive reader learning. Numerous fully worked examples and boxed and numbered formulas give students the essential practice they need to learn mathematics. Computer projects are given when appropriate, including BASIC, spreadsheets, computer algebra systems, and computer-assisted drafting. The graphing calculator has been fully integrated and calculator screens are given to introduce computations. Everything the technical student may need is included, with the emphasis always on clarity and practical applications.

Table of Contents

  1. Dedication
  2. Copyright
  3. Preface
  4. About the Authors
  5. Review of Numerical Computation
    1. The Real Numbers
    2. Addition and Subtraction
    3. Multiplication
    4. Division
    5. Powers and Roots
    6. Combined Operations
    7. Scientific Notation and Engineering Notation
    8. Units of Measurement
    9. Percentage
    10. CHAPTER 1 REVIEW PROBLEMS
  6. Introduction to Algebra
    1. Algebraic Expressions
    2. Adding and Subtracting Polynomials
    3. Laws of Exponents
    4. Multiplying a Monomial by a Monomial
    5. Multiplying a Monomial and a Multinomial
    6. Multiplying a Binomial by a Binomial
    7. Multiplying a Multinomial by a Multinomial
    8. Raising a Multinomial to a Power
    9. Dividing a Monomial by a Monomial
    10. Dividing a Polynomial by a Monomial
    11. Dividing a Polynomial by a Polynomial
    12. CHAPTER 2 REVIEW PROBLEMS
  7. Simple Equations and Word Problems
    1. Solving a Simple Equation
    2. Solving Word Problems
    3. Uniform Motion Applications
    4. Money Problems
    5. Applications Involving Mixtures
    6. Statics Applications
    7. Applications to Work, Fluid Flow, and Energy Flow
    8. CHAPTER 3 REVIEW PROBLEMS
  8. Functions
    1. Functions and Relations
    2. More on Functions
    3. CHAPTER 4 REVIEW PROBLEMS
  9. Graphs
    1. Rectangular Coordinates
    2. Graphing an Equation
    3. Graphing a Function by Calculator
    4. The Straight Line
    5. Solving an Equation Graphically
    6. CHAPTER 5 REVIEW PROBLEMS
  10. Geometry
    1. Straight Lines and Angles
    2. Triangles
    3. Quadrilaterals
    4. The Circle
    5. Polyhedra
    6. Cylinder, Cone, and Sphere
    7. CHAPTER 6 REVIEW PROBLEMS
  11. Right Triangles and Vectors
    1. The Trigonometric Functions
    2. Solving a Right Triangle
    3. Applications of the Right Triangle
    4. An Angle in Standard Position
    5. Introduction to Vectors
    6. Applications of Vectors
    7. CHAPTER 7 REVIEW PROBLEMS
  12. Oblique Triangles and Vectors
    1. Trigonometric Functions of Any Angle
    2. Finding the Angle When the Trigonometric Function Is Known
    3. Law of Sines
    4. Law of Cosines
    5. Applications
    6. Non-Perpendicular Vectors
    7. CHAPTER 8 REVIEW PROBLEMS
  13. Systems of Linear Equations
    1. Systems of Two Linear Equations
    2. Applications
    3. Other Systems of Equations
    4. Systems of Three Equations
    5. CHAPTER 9 REVIEW PROBLEMS
  14. Matrices and Determinants
    1. Introduction to Matrices
    2. Solving Systems of Equations by the Unit Matrix Method
    3. Second-Order Determinants
    4. Higher-Order Determinants
    5. CHAPTER 10 REVIEW PROBLEMS
  15. Factoring and Fractions
    1. Common Factors
    2. Difference of Two Squares
    3. Factoring Trinomials
    4. Other Factorable Expressions
    5. Simplifying Fractions
    6. Multiplying and Dividing Fractions
    7. Adding and Subtracting Fractions
    8. Complex Fractions
    9. Fractional Equations
    10. Literal Equations and Formulas
    11. CHAPTER 11 REVIEW PROBLEMS
  16. Quadratic Equations
    1. Solving a Quadratic Equation Graphically and by Calculator
    2. Solving a Quadratic by Formula
    3. Applications
    4. CHAPTER 12 REVIEW PROBLEMS
  17. Exponents and Radicals
    1. Integral Exponents
    2. Simplification of Radicals
    3. Operations with Radicals
    4. Radical Equations
    5. CHAPTER 13 REVIEW PROBLEMS
  18. Radian Measure, Arc Length, and Rotation
    1. Radian Measure
    2. Arc Length
    3. Uniform Circular Motion
    4. CHAPTER 14 REVIEW PROBLEMS
  19. Trigonometric, Parametric, and Polar Graphs
    1. Graphing the Sine Wave by Calculator
    2. Manual Graphing of the Sine Wave
    3. The Sine Wave as a Function of Time
    4. Graphs of the Other Trigonometric Functions
    5. Graphing a Parametric Equation
    6. Graphing in Polar Coordinates
    7. CHAPTER 15 REVIEW PROBLEMS
  20. Trigonometric Identities and Equations
    1. Fundamental Identities
    2. Sum or Difference of Two Angles
    3. Functions of Double Angles and Half-Angles
    4. Evaluating a Trigonometric Expression
    5. Solving a Trigonometric Equation
    6. CHAPTER 16 REVIEW PROBLEMS
  21. Ratio, Proportion, and Variation
    1. Ratio and Proportion
    2. Similar Figures
    3. Direct Variation
    4. The Power Function
    5. Inverse Variation
    6. Functions of More Than One Variable
    7. CHAPTER 17 REVIEW PROBLEMS
  22. Exponential and Logarithmic Functions
    1. The Exponential Function
    2. Logarithms
    3. Properties of Logarithms
    4. Solving an Exponential Equation
    5. Solving a Logarithmic Equation
    6. CHAPTER 18 REVIEW PROBLEMS
  23. Complex Numbers
    1. Complex Numbers in Rectangular Form
    2. Complex Numbers in Polar Form
    3. Complex Numbers on the Calculator
    4. Vector Operations Using Complex Numbers
    5. Alternating Current Applications
    6. CHAPTER 19 REVIEW PROBLEMS
  24. Sequences, Series, and the Binomial Theorem
    1. Sequences and Series
    2. Arithmetic and Harmonic Progressions
    3. Geometric Progressions
    4. Infinite Geometric Progressions
    5. The Binomial Theorem
    6. CHAPTER 20 REVIEW PROBLEMS
  25. Introduction to Statistics and Probability
    1. Definitions and Terminology
    2. Frequency Distributions
    3. Numerical Description of Data
    4. Introduction to Probability
    5. The Normal Curve
    6. Standard Errors
    7. Process Control
    8. Regression
    9. CHAPTER 21 REVIEW PROBLEMS
  26. Analytic Geometry
    1. The Straight Line
    2. Equation of a Straight Line
    3. The Circle
    4. The Parabola
    5. The Ellipse
    6. The Hyperbola
    7. CHAPTER 22 REVIEW PROBLEMS
  27. Summary of Facts and Formulas
  28. Conversion Factors
  29. Table of Integrals
  30. Answers to Selected Problems
    1. CHAPTER 1
    2. CHAPTER 2
    3. CHAPTER 3
    4. CHAPTER 4
    5. CHAPTER 5
    6. CHAPTER 6
    7. CHAPTER 7
    8. CHAPTER 8
    9. CHAPTER 9
    10. CHAPTER 10
    11. CHAPTER 11
    12. CHAPTER 12
    13. CHAPTER 13
    14. CHAPTER 14
    15. CHAPTER 15
    16. CHAPTER 16
    17. CHAPTER 17
    18. CHAPTER 18
    19. CHAPTER 19
    20. CHAPTER 20
    21. CHAPTER 21
    22. CHAPTER 22