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Basic Technical Mathematics with Calculus, 7/E
Allyn J. Washington, Dutchess Community College

ISBN-10: 0201356651
ISBN-13:  9780201356656

Publisher:  Addison-Wesley
Copyright:  2000
Format:  Cloth; 963 pp
Published:  11/05/1999


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Description

Technical mathematics is a course pioneered by Allyn Washington, and the seventh edition of this text preserves the author's highly regarded approach to technical math while improving on the integration of technology. The book is intended for a two or three semester course and is taught primarily to students who plan to pursue engineering or other technical fields. The primary strength of the text is the heavy integration of technical applications, which aids the student pursuing a technical career by showing the importance of a strong foundation in algebraic and trigonometric math.

Allyn Washington defined the technical math market when he wrote the first edition of Basic Technical Mathematics over thirty years ago. His continued vision is to provide highly accurate mathematical concepts based on technical applications. The course is designed to allow the student to be simultaneously enrolled in allied technical areas, such as physics or electronics. The material in the text can be rearranged easily to fit the needs of the instructor as well as the students. Above all, the author's vision of this book is to continue to enlighten today's students that an understanding of elementary math is critical in many aspects of life.


Features

  • NEW - <F75BS>NEW! Graphing Calculator. The graphing calculator is used throughout the text in examples and has been more heavily integrated and emphasized than in the previous edition, although it is still not required for the course. This integration includes over 170 new graphing calculator screens pictured in the text. Pg. 98
  • NEW - <F75BS>NEW! Design. A newer, more open design is an important improvement and feature of the seventh edition. The more spacious layout allows for additional graphing calculator screen graphics in the margin, which helps students visualize the graphing technology. Pg. 110
  • NEW - <F75BS>NEW! Applications. Over 300 new technical applications have been added to the seventh edition. A particular strength of the Washington text, the applications challenge students to apply the mathematics to technically-based problems, enforcing the relevancy of mathematics in engineering and other technical fields. Pg. 256
  • NEW - <F75BS>NEW! Word Problems and Solutions. Throughout the text, approximately 120 examples present complete solutions of word problems. These examples are clearly indicated in the margin by the phrase "solving a word problem." In addition, the text includes over 900 word problems within exercise sets. Pg. 257
  • NEW - <F75BS>NEW! Exercises and Figures. The seventh edition includes over 1500 new exercises. Over 200 new figures have been added to help students visualize applications and concepts. Pg. 9
  • NEW - <F75BS>NEW! Writing Exercises. The number of writing exercises has been increased by 40%. A new graphical icon highlights the writing exercises in the text. These exercises reinforce student understanding, as they require students to verbalize their answers using words rather than numbers. Pg. 273
  • Flexibility of Material Coverage. This is an important and critical feature of the Washington approach to technical math. The chapters of the text are easily adapted to the specific needs of the students as well as the instructor. Certain sections or chapters may be omitted without loss of continuity, and chapters may be reordered for a customized syllabus. Notes and suggestions on how to reorder the course are contained in the Answer Book.


Table of Contents

(Most chapters end with Chapter Equations, Review Exercises, and Practice Test.)

1. Basic Algebraic Operations.

Numbers.

Fundamental Laws and Operations of Algebra.

Calculators and Approximate Numbers.

Exponents.

Scientific Notation.

Roots and Radicals.

Addition and Subtraction of Algebraic Expressions.

Multiplication of Algebraic Expressions.

Division of Algebraic Expressions.

Solving Equations.

Formulas and Literal Equations.

Applied Word Problems.



2. Geometry.

Lines and Angles.

Triangles.

Quadrilaterals.

Circles.

Measurement of Irregular Areas.

Solid Geometric Figures.



3. Functions and Graphs.

Introduction to Functions.

More About Functions.

Rectangular Coordinates.

The Graph of a Function.

Graphs on the Graphing Calculator.

Graphs of Functions Defined by Tables of Data.



4. The Trigonometric Functions.

Angles.

Defining the Trigonometric Functions.

Values of Trigonometric Functions.

The Right Triangle.

Applications of Right Triangle.



5. Systems of Linear Equations; Determinants.

Linear Equations.

Graphs of Linear Equations.

Solving Systems of Two Linear Equations in Two Unknowns Graphically.

Solving Systems of Two Linear Equations in Two Unknowns Algebraically.

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

Solving Systems of Three Linear Equations in Three Unknowns Algebraically.

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



6. Factoring and Fractions.

Special Products.

Factoring: Common Factor and Difference of Squares.

Factoring Trinomials.

The Sum and Difference of Cubes.

Equivalent Fractions.

Multiplication and Division of Fractions.

Addition and Subtraction of Fractions.

Equations Involving Fractions.



7. Quadratic Equations.

Quadratic Equations; Solution by Factoring.

Completing the Square.

The Quadratic Formula.

The Graph of the Quadratic Function.



8. Trigonometric Functions of Any Angle.

Signs of the Trigonometric Functions.

Trigonometric Functions of Any Angle.

Radians.

Applications of Radian Measure.



9. Vectors and Oblique Triangles.

Introduction to Vectors.

Components of Vectors.

Vector Addition by Components.

Applications of Vectors.

Oblique Triangles, the Law Of Sines.

The Law of Cosines.



10. Graphs of the Trigonometric Functions.

Graphs of y = a sin x and y = a cos x.

Graphs of y = a sin bx and y = a cos bx.

Graphs of y = a sin (bx + c) and y = a cos (bx + c).

Graphs of y = tan x, y = cot x, y= sec x, y = csc x.

Applications of Trigonometric Graphs.

Composite Trigonometric Curves.



11. Exponents and Radicals.

Simplifying Expressions with Integral Exponents.

Fractional Exponents.

Simplest Radical Forms.

Addition and Subtraction of Radicals.

Multiplication and Division of Radicals.



12. Complex Numbers.

Basic Definitions.

Basic Operations with Complex Numbers.

Graphical Representation of Complex Numbers.

Polar Form of a Complex Number.

Exponential Form of a Complex Number.

Products, Quotients, Powers, and Roots of Complex Numbers.

An Application to Alternating-Current (AC) Circuits.



13. Exponential and Logarithmic Functions.

The Exponential and Logarithmic Functions.

Graphs of y = bx and y = log <MJ18>b x.

Properties of Logarithms.

Logarithms to the Base 10.

Natural Logarithms.

Exponential and Logarithmic Equations.

Graphs on Logarithmic and Semilogarithmic Paper.



14. Additional Types of Equations and Systems of Equations.

Graphical Solution of Systems of Equations.

Algebraic Solution of Systems of Equations.

Equations in Quadratic Form.

Equations with Radicals.



15. Equations of Higher Degree.

The Remainder Theorem and the Factor Theorem.

Synthetic Division.

The Roots of an Equation.

Rational and Irrational Roots.



16. Determinants and Matrices.

Determinants; Expansion by Minors.

Some Properties of Determinants.

Matrices: Definitions and Basic Operations.

Multiplication of Matrices.

Finding the Inverse of a Matrix.

Matrices and Linear Equations.



17. Inequalities.

Properties of Inequalities.

Solving Linear Inequalities.

Solving Nonlinear Inequalities.

Inequalities Involving Absolute Values.

Graphical Solution of Inequalities with Two Variables.



18. Variation.

Ratio and Proportion.

Variation.



19. Sequences and the Binomial Theorem.

Arithmetic Sequences.

Geometric Sequences.

Infinite Geometric Sequences.

The Binomial Theorem.



20. Additional Topics in Trigonometry.

Fundamental Trigonometric Identities.

The Sum and Differences of Formulas.

Double-Angle Formulas.

Half-Angle Formulas.

Solving Trigonometric Equations.

The Inverse Trigonometric Functions.



21. Plane Analytic Geometry.

Basic Definitions.

The Straight Line.

The Circle.

The Parabola.

The Ellipse.

The Hyperbola.

Translation of Axes.

The Second-Degree Equation.

Polar Coordinates.

Curves in Polar Coordinates.



22. Introduction to Statistics.

Frequency Distributions.

Measures of Central Tendency.

Standard Deviations.

Normal Distributions.

Statistical Process Control.

Linear Regression.

Nonlinear Regression.



23. The Derivative.

Limits.

The Slope of a Tangent to a Curve.

The Derivative.

The Derivative as an Instantaneous Rate of Change.

Derivatives of Polynomials.

Derivatives of Products and Quotients of Functions.

The Derivative of a Power of a Function.

Differentiation of Implicit Functions.

Higher Derivatives.



24. Applications of the Derivatives.

Tangents and Normals.

Newton's Method for Solving Equations.

Curvilinear Motion.

Related Rates.

Using Derivatives in Curve Sketching.

More on Curve Sketching.

Applied Maximum and Minimum Problems.

Differentials and Linear Approximations.



25. Integration.

Antiderivatives.

The Indefinite Integral.

The Area Under a Curve.

The Definite Integral.

Numerical Integration: The Trapezoidal Rule.

Simpson's Rule.



26. Applications of Integration.

Applications of the Indefinite Integral.

Areas by Integration.

Volumes by Integration.

Centroids.

Moments of Inertia.

Other Applications.



27. Differentiation of Transcendental Functions.

Derivatives of the Sine and Cosine Functions.

Derivatives of the Other Trigonometric Functions.

Derivatives of the Inverse Trigonometric Functions.

Applications.

Derivative of the Logarithmic Function.

Derivative of the Exponential Function.

Applications.



28. Methods of Integration.

The General Power Formula.

The Basic Logarithmic Form.

The Exponential Form.

Basic Trigonometric Forms.

Other Trigonometric Forms.

Inverse Trigonometric Forms.

Integration by Parts.

Integration by Trigonometric Substitution.

Integration by Partial Fractions: Nonrepeated Linear Factors.

Integration by Partial Fractions: Other Cases.

Integration by Use of Tables.



29. Expansion of Functions in Series.

Infinite Series.

Maclaurin Series.

Certain Operations with Series.

Computations by Use of Series Expansions.

Taylor Series.

Introduction to Fourier Series.

More on Fourier Series.



30. Differential Equations.

Solutions of Differential Equations.

Separation of Variables.

Integrating Combinations.

The Linear Differential Equations of the First Order.

Elementary Applications.

Higher-Order Homogeneous Equations.

Auxiliary Equations with Repeated or Complex Roots.

Solutions on Nonhomogeneous Equations.

Applications of Higher-Order Equations.

Laplace Transforms.

Solving Differential Equations by Laplace Transforms.



Supplementary Topics.

Gaussian Elimination.

Rotation of Axes.

Functions of Two Variables.

Curves and Surfaces in Three Dimensions.

Partial Derivatives.

Double Integrals.

Numerical Solutions to Differential Equations.



Appendix A. Study Aids.

Introduction.

Suggestions for Study.

Solving Word Problems.



Appendix B. Units of Measurement: The Metric System.

Introduction.

Reductions and Conversions.



Appendix C. Scientific and Graphing Calculator.

Introduction.

The Graphing Calculator.

Graphing Calculator Problems.



Appendix D. Newton's Method (in 1740).


Appendix E. A Table of Integrals.


Answers to Odd-Numbered Exercises.


Solutions to Practice Test Problems.


Index of Applications.


Index of Writing Problems.


Index.


Next Edition(s)

  • Basic Technical Mathematics with Calculus, 9/E
    Washington
    ©2009  |  Addison-Wesley  |  Cloth; 1152 pp  |  Instock
    ISBN-10: 0138142262  |  ISBN-13: 9780138142261
    Brief Description  |  More Info



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©2000  |  Addison-Wesley  |  On-line Supplement  |  Live
ISBN-10: 0201658585  |  ISBN-13: 9780201658583
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