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Basic Technical Mathematics with Calculus, 11th edition

Published by Pearson (July 14, 2021) © 2018

  • Allyn J. Washington Dutchess Community College
  • Richard Evans Corning Community College
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For courses in technical and pre-engineering technical programs or other programs for which coverage of basic mathematics is required.

The best-seller in technical mathematics gets an “Oh, wow!” update

The 11th Edition of Basic Technical Mathematics with Calculusis a bold revision of this classic best-seller. The text now sports an engaging full-color design, and new co-author Rich Evans has introduced a wealth of relevant applications and improvements, many based on user feedback. The text is supported by an all-new online graphing calculator manual, accessible at point-of-use via short URLs. The new edition continues to feature a vast number of applications from technical and pre-engineering fields–including computer design, electronics, solar energy, lasers fiber optics, and the environment–and aims to develop students’ understanding of mathematical methods without simply providing a collection of formulas. The authors start the text by establishing a solid background in algebra and trigonometry, recognizing the importance of these topics for success in solving applied problems.

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Table of Contents

  1. Basic Algebraic Operations
    • 1.1 Numbers
    • 1.2 Fundamental Operations of Algebra
    • 1.3 Calculators and Approximate Numbers
    • 1.4 Exponents and Unit Conversions
    • 1.5 Scientific Notation
    • 1.6 Roots and Radicals
    • 1.7 Addition and Subtraction of Algebraic Expressions
    • 1.8 Multiplication of Algebraic Expressions
    • 1.9 Division of Algebraic Expressions
    • 1.10 Solving Equations
    • 1.11 Formulas and Literal Equations
    • 1.12 Applied Word Problems
  2. Geometry
    • 2.1 Lines and Angles
    • 2.2 Triangles
    • 2.3 Quadrilaterals
    • 2.4 Circles
    • 2.5 Measurement of Irregular Areas
    • 2.6 Solid Geometric Figures
  3. Functions and Graphs
    • 3.1 Introduction to Functions
    • 3.2 More about Functions
    • 3.3 Rectangular Coordinates
    • 3.4 The Graph of a Function
    • 3.5 Graphs on the Graphing Calculator
    • 3.6 Graphs of Functions Defined by Tables of Data
  4. The Trigonometric Functions
    • 4.1 Angles
    • 4.2 Defining the Trigonometric Functions
    • 4.3 Values of the Trigonometric Functions
    • 4.4 The Right Triangle
    • 4.5 Applications of Right Triangles
  5. Systems of Linear Equations Determinants
    • 5.1 Linear Equations and Graphs of Linear Functions
    • 5.2 Systems of Equations and Graphical Solutions
    • 5.3 Solving Systems of Two Linear Equations in Two Unknowns Algebraically
    • 5.4 Solving Systems of Two Linear Equations in Two Unknowns by Determinants
    • 5.5 Solving Systems of Three Linear Equations in Three Unknowns Algebraically
    • 5.6 Solving Systems of Three Linear Equations in Three Unknowns by Determinants
  6. Factoring and Fractions
    • 6.1 Factoring: Greatest Common Factor and Difference of Squares
    • 6.2 Factoring Trinomials
    • 6.3 The Sum and Difference of Cubes
    • 6.4 Equivalent Fractions
    • 6.5 Multiplication and Division of Fractions
    • 6.6 Addition and Subtraction of Fractions
    • 6.7 Equations Involving Fractions
  7. Quadratic Equations
    • 7.1 Quadratic Equations; Solution by Factoring
    • 7.2 Completing the Square
    • 7.3 The Quadratic Formula
    • 7.4 The Graph of the Quadratic Function
  8. Trigonometric Functions of Any Angle
    • 8.1 Signs of the Trigonometric Functions
    • 8.2 Trigonometric Functions of Any Angle
    • 8.3 Radians
    • 8.4 Applications of Radian Measure
  9. Vectors and Oblique Triangles
    • 9.1 Introduction to Vectors
    • 9.2 Components of Vectors
    • 9.3 Vector Addition by Components
    • 9.4 Applications of Vectors
    • 9.5 Oblique Triangles, the Law of Sines
    • 9.6 The Law of Cosines
  10. Graphs of the Trigonometric Functions
    • 10.1 Graphs of y = a sin x and y = a cos x
    • 10.2 Graphs of y = a sin bx and y = a cos bx
    • 10.3 Graphs of y = a sin (bx + c) and y = a cos (bx + c)
    • 10.4 Graphs of y = tan x, y = cot x, y = sec x, y = csc x
    • 10.5 Applications of the Trigonometric Graphs
    • 10.6 Composite Trigonometric Curves
  11. Exponents and Radicals
    • 11.1 Simplifying Expressions with Integer Exponents
    • 11.2 Fractional Exponents
    • 11.3 Simplest Radical Form
    • 11.4 Addition and Subtraction of Radicals
    • 11.5 Multiplication and Division of Radicals
  12. Complex Numbers
    • 12.1 Basic Definitions
    • 12.2 Basic Operations with Complex Numbers
    • 12.3 Graphical Representation of Complex Numbers
    • 12.4 Polar Form of a Complex Number
    • 12.5 Exponential Form of a Complex Number
    • 12.6 Products, Quotients, Powers, and Roots of Complex Numbers
    • 12.7 An Application to Alternating-current (ac) Circuits
  13. Exponential and Logarithmic Functions
    • 13.1 Exponential Functions
    • 13.2 Logarithmic Functions
    • 13.3 Properties of Logarithms
    • 13.4 Logarithms to the Base
    • 13.5 Natural Logarithms
    • 13.6 Exponential and Logarithmic Equations
    • 13.7 Graphs on Logarithmic and Semilogarithmic Paper
  14. Additional Types of Equations and Systems of Equations
    • 14.1 Graphical Solution of Systems of Equations
    • 14.2 Algebraic Solution of Systems of Equations
    • 14.3 Equations in Quadratic Form
    • 14.4 Equations with Radicals
  15. Equations of Higher Degree
    • 15.1 The Remainder and Factor Theorems; Synthetic Division
    • 15.2 The Roots of an Equation
    • 15.3 Rational and Irrational Roots
  16. Matrices; Systems of Linear Equations
    • 16.1 Matrices: Definitions and Basic Operations
    • 16.2 Multiplication of Matrices
    • 16.3 Finding the Inverse of a Matrix
    • 16.4 Matrices and Linear Equations
    • 16.5 Gaussian Elimination
    • 16.6 Higher-order Determinants
  17. Inequalities
    • 17.1 Properties of Inequalities
    • 17.2 Solving Linear Inequalities
    • 17.3 Solving Nonlinear Inequalities
    • 17.4 Inequalities Involving Absolute Values
    • 17.5 Graphical Solution of Inequalities with Two Variables
    • 17.6 Linear Programming
  18. Variation
    • 18.1 Ratio and Proportion
    • 18.2 Variation
  19. Sequences and the Binomial Theorem
    • 19.1 Arithmetic Sequences
    • 19.2 Geometric Sequences
    • 19.3 Infinite Geometric Series
    • 19.4 The Binomial Theorem
  20. Additional Topics in Trigonometry
    • 20.1 Fundamental Trigonometric Identities
    • 20.2 The Sum and Difference Formulas
    • 20.3 Double-Angle Formulas
    • 20.4 Half-Angle Formulas
    • 20.5 Solving Trigonometric Equations
    • 20.6 The Inverse Trigonometric Functions
  21. Plane Analytic Geometry
    • 21.1 Basic Definitions
    • 21.2 The Straight Line
    • 21.3 The Circle
    • 21.4 The Parabola
    • 21.5 The Ellipse
    • 21.6 The Hyperbola
    • 21.7 Translation of Axes
    • 21.8 The Second-degree Equation
    • 21.9 Rotation of Axes
    • 21.10 Polar Coordinates
    • 21.11 Curves in Polar Coordinates
  22. Introduction to Statistics
    • 22.1 Graphical Displays of Data
    • 22.2 Measures of Central Tendency
    • 22.3 Standard Deviation
    • 22.4 Normal Distributions
    • 22.5 Statistical Process Control
    • 22.6 Linear Regression
    • 22.7 Nonlinear Regression
  23. The Derivative
    • 23.1 Limits
    • 23.2 The Slope of a Tangent to a Curve
    • 23.3 The Derivative
    • 23.4 The Derivative as an Instantaneous Rate of Change
    • 23.5 Derivatives of Polynomials
    • 23.6 Derivatives of Products and Quotients of Functions
    • 23.7 The Derivative of a Power of a Function
    • 23.8 Differentiation of Implicit Functions
    • 23.9 Higher Derivatives
  24. Applications of the Derivative
    • 24.1 Tangents and Normals
    • 24.2 Newton’s Method for Solving Equations
    • 24.3 Curvilinear Motion
    • 24.4 Related Rates
    • 24.5 Using Derivatives in Curve Sketching
    • 24.6 More on Curve Sketching
    • 24.7 Applied Maximum and Minimum Problems
    • 24.8 Differentials and Linear Approximations
  25. Integration
    • 25.1 Antiderivatives
    • 25.2 The Indefinite Integral
    • 25.3 The Area Under a Curve
    • 25.4 The Definite Integral
    • 25.5 Numerical Integration: The Trapezoidal Rule
    • 25.6 Simpson's Rule
  26. Applications of Integration
    • 26.1 Applications of the Indefinite Integral
    • 26.2 Areas by Integration
    • 26.3 Volumes by Integration
    • 26.4 Centroids
    • 26.5 Moments of Inertia
    • 26.6 Other Applications
  27. Differentiation of Transcendental Functions
    • 27.1 Derivatives of the Sine and Cosine Functions
    • 27.2 Derivatives of the Other Trigonometric Functions
    • 27.3 Derivatives of the Inverse Trigonometric Functions
    • 27.4 Applications
    • 27.5 Derivative of the Logarithmic Function
    • 27.6 Derivative of the Exponential Function
    • 27.7 L’Hospital’s Rule
    • 27.8 Applications
  28. Methods of Integration
    • 28.1 The Power Rule for Integration
    • 28.2 The Basic Logarithmic Form
    • 28.3 The Exponential Form
    • 28.4 Basic Trigonometric Forms
    • 28.5 Other Trigonometric Forms
    • 28.6 Inverse Trigonometric Forms
    • 28.7 Integration by Parts
    • 28.8 Integration by Trigonometric Substitution
    • 28.9 Integration by Partial Fractions: Non-repeated Linear Factors
    • 28.10 Integration by Partial Fractions: Other Cases
    • 28.11 Integration by Use of Tables
  29. Partial Derivatives and Double Integrals
    • 29.1 Functions of Two Variables
    • 29.2 Curves and Surfaces in Three Dimensions
    • 29.3 Partial Derivatives
    • 29.4 Double Integrals
  30. Expansion of Functions in Series
    • 30.1 Infinite Series
    • 30.2 Maclaurin Series
    • 30.3 Operations with Series
    • 30.4 Computations by Use of Series Expansions
    • 30.5 Taylor Series
    • 30.6 Introduction to Fourier Series
    • 30.7 More About Fourier Series
  31. Differential Equations
    • 31.1 Solutions of Differential Equations
    • 31.2 Separation of Variables
    • 31.3 Integrating Combinations
    • 31.4 The Linear Differential Equation of the First Order
    • 31.5 Numerical Solutions of First-order Equations
    • 31.6 Elementary Applications
    • 31.7 Higher-order Homogeneous Equations
    • 31.8 Auxiliary Equation with Repeated or Complex Roots
    • 31.9 Solutions of Nonhomogeneous Equations
    • 31.10 Applications of Higher-order Equations
    • 31.11 Laplace Transforms
    • 31.12 Solving Differential Equations by Laplace Transforms

Appendix A Solving Word Problems

Appendix B Units of Measurement

Appendix C Newton’s Method

Appendix D A Table of Integrals

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