Basic Technical Mathematics with Calculus [Rental Edition]

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 Calculus  is a bold revision of this classic bestseller. 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 your 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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Allyn J. Washington received his Masters Degree from Brown University, Providence, Rhode Island. Allyn taught mathematics at Trinity College, Hartford, Connecticut, after graduating Phi Beta Kappa from Trinity. 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 is a founding member of the New York State Mathematics Association of Two Year Colleges and also 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 presently 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, Poughkeepsie, New York. Allyn has authored several textbooks in Technical Mathematics for over 50 years, including this edition of Basic Technical Mathematics with Calculus.

Richard Evans received a Master’s Degree in mathematics from Binghamton University in 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.

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 10

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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