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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 in the text. The book is intended for a two or three-semester course and is taught primarily to students who plan to pursue 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 easily rearranged to fit the needs of both instructor and 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 :
Author Bio
Washington, Allyn J. : Dutchess Community College
1. Basic Algebraic Operations.
Numbers.
Fundamental 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.
Angles.
4. The Trigonometric Functions.
Angles.
Defining the Trigonometric Functions.
Values of Trigonometric Functions.
The Right Triangle.
Applications of Right Triangles.
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 = b^x and y = logbx.
Properties of Logarithms.
Logarithms to the Base10.
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.
Chapter 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 Series.
The Binomial Theorem.
20. Additional Topics in Trigonometry.
Fundamental Trigonometric Identities.
The Sum and Difference 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 Deviation.
Normal Distributions.
Statistical Process Control.
Linear Regression.
Nonlinear Regression.
Supplementary Topics.
Gaussian Elimination.
Rotation of Axes.
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 Calculators.
Introduction.
The Graphing Calculator.
Graphing Calculator Programs.
Answers to Odd-Numbered Exercises.
Solutions to Practice Test Problems.
Index of Applications.
Index of Writing Exercises.
Index.
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 in the text. The book is intended for a two or three-semester course and is taught primarily to students who plan to pursue 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 easily rearranged to fit the needs of both instructor and 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 :
Author Bio
Washington, Allyn J. : Dutchess Community College
Table of Contents
1. Basic Algebraic Operations.
Numbers.
Fundamental 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.
Angles.
4. The Trigonometric Functions.
Angles.
Defining the Trigonometric Functions.
Values of Trigonometric Functions.
The Right Triangle.
Applications of Right Triangles.
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 = b^x and y = logbx.
Properties of Logarithms.
Logarithms to the Base10.
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.
Chapter 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 Series.
The Binomial Theorem.
20. Additional Topics in Trigonometry.
Fundamental Trigonometric Identities.
The Sum and Difference 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 Deviation.
Normal Distributions.
Statistical Process Control.
Linear Regression.
Nonlinear Regression.
Supplementary Topics.
Gaussian Elimination.
Rotation of Axes.
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 Calculators.
Introduction.
The Graphing Calculator.
Graphing Calculator Programs.
Answers to Odd-Numbered Exercises.
Solutions to Practice Test Problems.
Index of Applications.
Index of Writing Exercises.
Index.