Basic Technical Mathematics with Calculus
12th Edition
Published on 15. January 2022
Book
Hardback
1136 pages
978-0-13-758262-4 (ISBN)
Description
Basic Technical Mathematics with Calculus focuses on the essentials you need, with no added theory or side trips. It supports understanding of mathematical techniques and how they apply on the job in fields like computer design, electronics, solar energy, lasers, and the environment. A vast number of applications create a solid foundation in algebra and trigonometry and demonstrate their applicability in various technical fields. Plenty of solved examples, problem sets, and practice exercises help reinforce skills. End-of-chapter review and test prep help you succeed on quizzes and exams. Additionally, the authors point out common errors, frequently misunderstood topics, and essential material.
More details
Edition
12th edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
College/higher education
ISBN-13
978-0-13-758262-4 (9780137582624)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Persons
About our authors The late Allyn J. Washington received his Master's Degree from Brown University. He was Professor of Mathematics at Dutchess Community College (Poughkeepsie, New York) where he served as the Mathematics Department Head as well as Dean of the College. Allyn was a founding member of the New York State Mathematics Association of Two-Year Colleges and a founding member of the American Mathematics Association of Two-Year Colleges. He was awarded an Honorary Doctorate Degree by State University of New York. He is listed in Who's Who in America. The Allyn J. Washington Center for Science and Art Building is named in his honor at Dutchess Community College. Allyn authored several textbooks in Technical Mathematics, including Basic Technical Mathematics.
Richard Evans received a Master's Degree in mathematics from Binghamton University (Binghamton, New York). He is currently a professor of mathematics at Corning Community College, where he has taken an active role in the college's governance system, including having chaired the mathematics department as well as the College Association. He is a long-standing member of the New York Mathematics Association of Two-Year Colleges and has attended and presented at many of these annual conferences. Rich has a strong background in applied mathematics and has taken two sabbatical leaves involving real-world applications of math in business and industry. In his free time, Rich enjoys spending time with his family, playing guitar, and boating in the Finger Lakes.
Richard Evans received a Master's Degree in mathematics from Binghamton University (Binghamton, New York). He is currently a professor of mathematics at Corning Community College, where he has taken an active role in the college's governance system, including having chaired the mathematics department as well as the College Association. He is a long-standing member of the New York Mathematics Association of Two-Year Colleges and has attended and presented at many of these annual conferences. Rich has a strong background in applied mathematics and has taken two sabbatical leaves involving real-world applications of math in business and industry. In his free time, Rich enjoys spending time with his family, playing guitar, and boating in the Finger Lakes.
Content
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Review Exercises and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
Exponential and Logarithmic Functions
13.1 Exponential Functions
13.2 Logarithmic Functions
13.3 Properties of Logarithms
13.4 Logarithms to the Base 10
13.5 Natural Logarithms
13.6 Exponential and Logarithmic Equations
13.7 Graphs on Logarithmic and Semilogarithmic Paper
Key Formulas and Equations, Review Exercises, and Practice Test
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
Review Exercises and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
Variation
18.1 Ratio and Proportion
18.2 Variation
Key Formulas and Equations, Review Exercises, and Practice Test
Sequences and the Binomial Theorem
19.1 Arithmetic Sequences
19.2 Geometric Sequences
19.3 Infinite Geometric Series
19.4 The Binomial Theorem
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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?
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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?
Key Formulas and Equations, Review Exercises, and Practice Test
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'Hopital's Rule
27.8 ?Applications
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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?
Key Formulas and Equations, Review Exercises, and Practice Test
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
APPENDICES
Solving Word Problems
Units of Measurement
Newton's Method
A Table of Integrals
Binary and Hexadecimal Numbers (online at bit.ly/3h1t3lt)
Photo Credits Answers to Odd-Numbered Exercises and Chapter Review Exercises Solutions to Practice Test Problems Index of Applications Index
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Review Exercises and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
Exponential and Logarithmic Functions
13.1 Exponential Functions
13.2 Logarithmic Functions
13.3 Properties of Logarithms
13.4 Logarithms to the Base 10
13.5 Natural Logarithms
13.6 Exponential and Logarithmic Equations
13.7 Graphs on Logarithmic and Semilogarithmic Paper
Key Formulas and Equations, Review Exercises, and Practice Test
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
Review Exercises and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
Variation
18.1 Ratio and Proportion
18.2 Variation
Key Formulas and Equations, Review Exercises, and Practice Test
Sequences and the Binomial Theorem
19.1 Arithmetic Sequences
19.2 Geometric Sequences
19.3 Infinite Geometric Series
19.4 The Binomial Theorem
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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?
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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?
Key Formulas and Equations, Review Exercises, and Practice Test
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'Hopital's Rule
27.8 ?Applications
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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
Key Formulas and Equations, Review Exercises, and Practice Test
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?
Key Formulas and Equations, Review Exercises, and Practice Test
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
APPENDICES
Solving Word Problems
Units of Measurement
Newton's Method
A Table of Integrals
Binary and Hexadecimal Numbers (online at bit.ly/3h1t3lt)
Photo Credits Answers to Odd-Numbered Exercises and Chapter Review Exercises Solutions to Practice Test Problems Index of Applications Index