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Technical Mathematics,9780130488107
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Technical Mathematics

by ; ;
Edition:
2nd
ISBN13:

9780130488107

ISBN10:
0130488100
Format:
Paperback
Pub. Date:
6/4/2004
Publisher(s):
Prentice Hall
List Price: $225.19

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Summary

//-->4881K-2, 0-13-048810-0, Ewen, Dale, Gary, Joan S., Trefzger, James E., Technical Mathematics, 2/E//-->This book provides readers with necessary mathematics skills. Mathematics provides the essential framework for and is the basic language of all the technologies. Mathematical, problem-solving, 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; right-triangle 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.

Table of Contents

Fundamental Concepts
1(76)
Introduction
1(1)
The Real Number System
1(5)
Zero and Order of Operations
6(3)
Scientific Notation and Powers of 10
9(5)
Measurement
14(3)
Operations with Measurements
17(4)
Algebraic Expressions
21(5)
Exponents and Radicals
26(5)
Multiplication of Algebraic Expressions
31(4)
Division of Algebraic Expressions
35(3)
Linear Equations
38(4)
Formulas
42(3)
Substitution of Data into Formulas
45(5)
Applications Involving Linear Equations
50(5)
Ratio and Proportion
55(5)
Variation
60(17)
Chapter 1 Summary
65(5)
Chapter 1 Review
70(3)
Chapter 1 Special NASA Application: Spare Parts for the Space Shuttle
73(2)
Chapter 1 Application: Precision-Machined Computer Disks
75(2)
Review of Geometry
77(37)
Introduction
77(1)
Angles and Lines
77(5)
Triangles
82(8)
Quadrilaterals
90(5)
Circles
95(5)
Geometric Solids: Areas and Volumes
100(14)
Chapter 2 Summary
107(3)
Chapter 2 Review
110(2)
Chapter 2 Special NASA Application: Window-to-Wall Ratio
112(2)
Right-Triangle Trigonometry
114(31)
Introduction
114(1)
The Trigonometric Ratios
114(10)
Values of the Trigonometric Ratios
124(6)
Solving Right Triangles
130(4)
Applications of the Right Triangle
134(11)
Chapter 3 Summary
142(1)
Chapter 3 Review
143(2)
Equations and Their Graphs
145(35)
Introduction
145(1)
Functions
145(5)
Graphing Equations
150(9)
The Straight Line
159(7)
Parallel and Perpendicular Lines
166(4)
The Distance and Midpoint Formulas
170(10)
Chapter 4 Summary
173(1)
Chapter 4 Review
174(2)
Chapter 4 Special NASA Application: The Space Shuttle Landing, Part I
176(4)
Factoring and Algebraic Fractions
180(32)
Introduction
180(1)
Special Products
180(3)
Factoring Algebraic Expressions
183(6)
Other Forms of Factoring
189(3)
Equivalent Fractions
192(3)
Multiplication and Division of Algebraic Fractions
195(3)
Addition and Subtraction of Algebraic Fractions
198(4)
Complex Fractions
202(3)
Equations with Fractions
205(7)
Chapter 5 Summary
209(2)
Chapter 5 Review
211(1)
Systems of Linear Equations
212(49)
Introduction
212(1)
Solving a System of Two Linear Equations
212(10)
Other Systems of Equations
222(2)
Solving a System of Three Linear Equations
224(6)
Determinants
230(5)
Properties of Determinants
235(3)
Solving a System of Linear Equations Using Determinants
238(6)
Partial Fractions
244(17)
Chapter 6 Summary
251(4)
Chapter 6 Review
255(2)
Chapter 6 Application: Kirchhoff's Laws for Electric Circuits
257(4)
Quadratic Equations
261(17)
Introduction
261(1)
Solving Quadratic Equations by Factoring
261(3)
Solving Quadratic Equations by Completing the Square
264(3)
The Quadratic Formula
267(4)
Applications
271(7)
Chapter 7 Summary
275(1)
Chapter 7 Review
276(2)
Exponents and Radicals
278(26)
Introduction
278(1)
Integral Exponents
278(3)
Fractional Exponents
281(3)
Simplest Radical Form
284(7)
Addition and Subtraction of Radicals
291(2)
Multiplication and Division of Radicals
293(3)
Equations with Radicals
296(4)
Equations in Quadratic Form
300(4)
Chapter 8 Summary
302(1)
Chapter 8 Review
303(1)
Exponentials and Logarithms
304(43)
Introduction
304(1)
The Exponential Function
304(4)
The Logarithm
308(3)
Properties of Logarithms
311(4)
Common Logarithms
315(4)
Natural Logarithms
319(5)
Solving Exponential Equations
324(3)
Solving Logarithmic Equations
327(2)
Applications: Solving Exponential and Logarithmic Equations
329(6)
Data Along a Straight Line
335(12)
Chapter 9 Summary
341(1)
Chapter 9 Review
342(3)
Chapter 9 Special NASA Application: The Space Shuttle Landing, Part II
345(2)
Trigonometric Functions
347(26)
Introduction
347(1)
The Trigonometric Functions
347(7)
Trigonometric Functions of Any Angle
354(6)
Radian Measure
360(6)
Use of Radian Measure
366(7)
Chapter 10 Summary
370(1)
Chapter 10 Review
371(2)
Oblique Triangles and Vectors
373(48)
Introduction
373(1)
Law of Sines
373(6)
The Ambiguous Case
379(4)
Law of Cosines
383(4)
Applications of Oblique Triangles
387(5)
Addition of Vectors: Graphical Methods
392(6)
Addition of Vectors: Trigonometric Methods
398(2)
Vector Components
400(6)
Vector Applications
406(15)
Chapter 11 Summary
413(2)
Chapter 11 Review
415(3)
Chapter 11 Special NASA Application: Vector Analysis of Wind Changes Affecting Shuttle Launch
418(3)
Graphing the Trigonometric Functions
421(24)
Introduction
421(1)
Graphing the Sine and Cosine Functions
421(5)
Phase Shift
426(4)
Graphing the Other Trigonometric Functions
430(3)
Graphing Composite Curves
433(2)
Simple Harmonic Motion
435(10)
Chapter 12 Summary
441(1)
Chapter 12 Review
441(2)
Chapter 12 Special NASA Application: Fitting a Sine Curve to Energy Use Data
443(2)
Trigonometric Formulas and Identities
445(31)
Introduction
445(1)
Basic Trigonometric Identities
445(6)
Formulas for the Sum and the Difference of Two Angles
451(5)
Double- and Half-Angle Formulas
456(6)
Trigonometric Equations
462(3)
Inverse Trigonometric Functions
465(11)
Chapter 13 Summary
473(1)
Chapter 13 Review
474(2)
Complex Numbers
476(22)
Introduction
476(1)
Complex Numbers in Rectangular Form
476(6)
Trigonometric and Exponential Forms of Complex Numbers
482(4)
Multiplication and Division of Complex Numbers in Exponential and Trigonometric Forms
486(4)
Powers and Roots
490(8)
Chapter 14 Summary
495(2)
Chapter 14 Review
497(1)
Matrices
498(28)
Introduction
498(1)
Basic Operations
498(5)
Multiplication of Matrices
503(5)
Finding the Inverse of a Matrix
508(8)
Solving a System of Equations by a Matrix Method
516(10)
Chapter 15 Summary
520(1)
Chapter 15 Review
521(3)
Chapter 15 Application: Matrices Used to Encode Information
524(2)
Polynomials of Higher Degree
526(16)
Introduction
526(1)
Polynomial Functions
526(5)
Real Solutions of Polynomial Equations
531(4)
Complex Solutions of Polynomial Equations
535(7)
Chapter 16 Summary
540(1)
Chapter 16 Review
541(1)
Inequalities and Absolute Value
542(19)
Introduction
542(1)
Inequalities
542(8)
Equations and Inequalities Involving Absolute Value
550(3)
Other Types of Inequalities
553(3)
Inequalities in Two Variables
556(5)
Chapter 17 Summary
559(1)
Chapter 17 Review
559(2)
Progressions and the Binomial Theorem
561(13)
Introduction
561(1)
Arithmetic Progressions
561(3)
Geometric Progressions
564(4)
The Binomial Theorem
568(6)
Chapter 18 Summary
572(1)
Chapter 18 Review
573(1)
Basic Statistics
574(34)
Introduction
574(1)
Graphical Presentation of Data
574(5)
Measures of Central Tendency
579(3)
Measures of Dispersion
582(4)
The Normal Distribution
586(3)
Fitting Curves to Data Sets
589(6)
Statistical Process Control
595(13)
Chapter 19 Summary
600(1)
Chapter 19 Review
601(3)
Chapter 19 Application: Statistics in the Manufacturing Process
604(4)
Analytic Geometry
608(51)
Introduction
608(1)
The Circle
608(5)
The Parabola
613(8)
The Ellipse
621(4)
The Hyperbola
625(6)
Translation of Axes
631(5)
The General Second-Degree Equation
636(2)
Systems of Quadratic Equations
638(3)
Polar Coordinates
641(8)
Graphs in Polar Coordinates
649(10)
Chapter 20 Summary
655(2)
Chapter 20 Review
657(2)
APPENDIX A Tables
659(4)
Table 1 U.S. Weights and Measures
659(1)
Table 2 Conversion Tables
660(2)
Table 3 Physical Quantities and Their Units
662(1)
APPENDIX B The Metric System
663(24)
B.1 Introduction
663(3)
B.2 Length
666(4)
B.3 Mass
670(2)
B.4 Volume and Area
672(5)
B.5 Temperature, Time, Current, and Power
677(6)
B.6 Other Conversions
683(4)
Appendix B Review
685(2)
APPENDIX C Using a Graphing Calculator
687(29)
C.1 Introduction to The TI-83 Keyboard
687(3)
C.2 Computational Examples
690(3)
C.3 Graphing Features
693(2)
C.4 Examples of Graphing
695(6)
C.5 Trigonometric Functions and Polar Coordinates
701(4)
C.6 Equation-Solving and Table Features
705(3)
C.7 The Numeric Solver
708(2)
C.8 Matrix Features
710(2)
C.9 List Features and Descriptive Statistics
712(2)
C.10 The Line of Best Fit (Linear Regression)
714(2)
APPENDIX D Using an Advanced Graphing Calculator
716(39)
D.1 Introduction to The TI-89 Keyboard
716(3)
D.2 Variables and Editing
719(1)
D.3 The Home Screen Menus
720(2)
D.4 The Keyboard Menus
722(5)
D.5 Graphing Functions
727(2)
D.6 Examples of Graphing
729(8)
D.7 Trig Functions and Polar Coordinates
737(4)
D.8 Numerical Graph and Table Features
741(3)
D.9 Sequences and Series
744(1)
D.10 The Numeric Solver
745(2)
D.11 Matrix Features
747(1)
D.12 The Data Editor and Descriptive Statistics
748(1)
D.13 The Line of Best Fit (Linear Regression)
749(1)
D.14 Symbolic Algebra Features
750(5)
Answers to Odd-Numbered Exercises and Chapter Reviews 755(52)
Index 807


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