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More About This Textbook
Overview
This book provides readers with necessary mathematics skills. Mathematics provides the essential framework for and is the basic language of all the technologies. Mathematical, problemsolving, and critical thinking skills are crucial to understanding the changing face of technology. It presents the following major areas: fundamental concepts and measurement; fundamental algebraic concepts; exponential and logarithmic functions; righttriangle trigonometry; the trigonometric functions with formulas and identities; complex numbers; matrices; polynomial and rational functions; basic statistics for process control; and analytic geometry. An excellent learning aid and resource tool for engineers, especially computer software, hardware, and peripheral manufacturers. Its comprehensive appendices make this an excellent desktop reference.
A mathematics textbook covering the skills necessary for careers in technical or engineering fields.
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Table of Contents
1. Fundamental Concepts.
The Real Number System. Zero and Order of Operations. Scientific Notation and Powers of 10. Measurement. Operations with Measurements. Algebraic Expressions. Exponents and Radicals. Multiplication of Algebraic Expressions. Division of Algebraic Expressions. Linear Equations. Formulas. Substitution of Data into Formulas. Applications Involving Linear Equations. Ration and Proportion. Variation.
2. Review of Geometry.
Angles and Lines. Triangles. Quadrilaterals. Circles. Geometric Solids: Areas and Volumes.
3. RightTriangle Trigonometry.
The Trigonometric Ratios. Values of the Trigonometric Ratios. Solving Right Triangles. Applications of the Right Triangle.
4. Equations and Their Graphs.
Functions. Graphing Equations. The Straight Line. Parallel and Perpendicular Lines. The Distance and Midpoint Formulas.
5. Factoring and Algebraic Fractions.
Special Products. Factoring Algebraic Expressions. Other Forms of Factoring. Equivalent Fractions. Multiplication and Division of Algebraic Fractions. Addition and Subtraction of Algebraic Fractions. Complex Fractions. Equations with Fractions.
6. Systems of Linear Equations.
Solving a System of Two Linear Equations. Other Systems of Equations. Solving a System of Three Linear Equations. Determinants. Properties of Determinants. Solving a System of Linear Equations Using Determinants. Partial Fractions.
7. Quadratic Equations.
Solving Quadratic Equations by Factoring. Solving Quadratic Equations by Completing the Square. The Quadratic Formula. Applications.
8. Exponents and Radicals.
Integral Exponents. Fractional Exponents. Simplest Radical Form. Addition and Subtraction of Radicals. Multiplication and Division of Radicals. Equations with Radicals. Equations in Quadratic Form.
9. Exponentials and Logarithms.
The Exponential Function. The Logarithm. Properties of Logarithms. Common Logarithms. Natural Logarithms. Solving Exponential Equations. Solving Logarithmic Equations. Applications: Solving Exponential and Logarithmic Equations. Data Along a Straight Line.
10. Trigonometric Functions.
The Trigonometric Functions. Trigonometric Functions of Any Angle. Radian Measure. Use of Radian Measure.
11. Oblique Triangles and Vectors.
Law of Sines. The Ambiguous Case. Law of Cosines. Applications of Oblique Triangles. Addition of Vectors: Graphical Methods. Addition of Vectors: Trigonometric Methods. Vector Components. Vector Applications.
12. Graphing the Trigonometric Functions.
Graphing the Sine and Cosine Functions. Phase Shift. Graphing the Other Trigonometric Functions. Graphing Composite Curves. Simple Harmonic Motion.
13. Trigonometric Formulas and Identities.
Basic Trigonometric Identities. Formulas for the Sum and the Difference of Two Angles. Double and HalfAngle Formulas. Trigonometric Equations. Inverse Trigonometric Functions.
14. Complex Numbers.
Complex Numbers in Rectangular Form. Trigonometric and Exponential Forms of Complex Numbers. Multiplication and Division of Complex Numbers in Exponential and Trigonometric Forms. Powers and Roots.
15. Matrices.
Basic Operations. Multiplication of Matrices. Finding the Inverse of a Matrix. Solving a System of Equations by a Matrix Method.
16. Polynomials of Higher Degree.
Polynomial Functions. Real Solutions of Polynomial Equations. Complex Solutions of Polynomial Equations.
17. Inequalities and Absolute Value.
Inequalities. Equations and Inequalities Involving Absolute Value. Other Types of Inequalities. Inequalities in Two Variables.
18. Progressions and the Binomial Theorem.
Arithmetic Progressions. Geometric Progressions. The Binomial Theorem.
19. Basic Statistics.
Graphic Presentation of Data. Measures of Central Tendency. Measures of Dispersion. The Normal Distribution. Fitting Curves to Data Sets. Statistical Process Control.
20. Analytic Geometry.
The Circle. The Parabola. The Ellipse. The Hyperbola. Translation of Axes. The General SecondDegree Equation. Systems of Quadratic Equations. Polar Coordinates. Graphs in Polar Coordinates.
Appendix A: Tables.
U.S. Weights and Measures. Conversion Tables. Physical Quantities and their Units.
Appendix B: The Metric System.
Introduction. Length. Mass. Volume and Area. Temperature, Time, Current, and Power. Other Conversions. Appendix B Review.
Appendix C: Using a Graphic Calculator.
Introduction to the Keyboard of the TI83 PLUS. Computational Examples. Graphing Features. Examples of Graphing. Trigonometric Functions and Polar Coordinates. Equation Solving and TABLE Features. The Numeric SOLVER. Matrix Features. LIST Features and Descriptive Statistics. The Line of Best Fit (Linear Regression). Calculus Features. Sequences and Series.
Appendix D: Using an Advanced Graphing Calculator.
Introduction to the TI89 Keyboard. Variables and Editing. The Home Screens Menus. The Keyboard Menus. Graphing Functions. Examples of Graphing. Trig Functions and Polar Coordinates. Numerical GRAPH and TABLE Features. Sequences and Series. The Numeric Solver. Matrix Features. The Data Editor and Descriptive Statistics. The Line of Best Fit (Linear Regression). Symbolic Algebra Features. Basic Calculus Features. Graphing in 3D. Advanced Calculus Features.
Answers to OddNumbered Exercises and Chapter Reviews.
Index.