## Description

**For courses in Introductory Technical Math. **

** **

This tried-and-true text from Allyn Washington preserves the author's highly regarded approach to technical math, while enhancing the integration of technology. Appropriate for a three- to four- semester course, *BASIC TECHNICAL MATHEMATICS WITH CALCULUS* shows how algebra, trigonometry, and basic calculus are used on the job. It addresses a vast number of technical and pre-engineering fields, including computer design, electronics, solar energy, lasers fiber optics, and the environment. Known for its exceptional problem sets and applied material, the book offers practice exercises, writing exercises, word problems, and practice tests. This edition features more technical applications, over 2300 new exercises, additional graphing calculator screens and the innovative MyLab websites.

## Table of Contents

Each chapter contains: Equations, Quick Chapter Review, Review Exercises, Practice Test

**1. Basic Algebraic Operations**

1.1 Numbers

1.2 Fundamental Operations of Algebra

1.3 Calculators and Approximate Numbers

1.4 Exponents

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

5.2 Graphs of Linear Functions

5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

**6. Factoring and Fractions**

6.1 Special Products

6.2 Factoring: Common Factor and Difference of Squares

6.3 Factoring Trinomials

6.4 The Sum and Difference of Cubes

6.5 Equivalent Fractions

6.6 Multiplication and Division of Fractions

6.7 Addition and Subtraction of Fractions

6.8 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 Trignometric Curves

**11. Exponents and Radicals**

11.1 Simplifying Expressions with Integral Exponents

11.2 Fractional Exponents

11.3 Simplest Radical Form

11.3 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 Frequency Distributions

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 Standard Deviation

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 Funtions

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 Appilcations

**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 General Power Formula

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: Nonrepeated 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: The Metric System

B.1 Introduction

B.2 Reductions and Conversions

Appendix C: The Graphing Calculator

C.1 Introduction

C.2 The Graphing Calculator

C.3 Graphing Calculator Programs

C.4 The Advanced Graphing Calculator

Appendix D: Newton's Method

Appendix E: A Table of Integrals

Answers to Odd-Numbered Exercises and Quick Chapter Reviews

Solutions to Practice Test Problems

Index of Applications

Index of Writing Exercises

Index

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Basic Technical Mathematics with Calculus, CourseSmart eText, 10th Edition

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