Technical Mathematics

by Ewen, Dale; Gary, Joan S.; Trefzger, James E.

• ISBN13: 9780130488107
• ISBN10: 0130488100
• Edition: 2nd
• Format: Paperback
• Copyright: 2004-06-04
• Publisher: Prentice Hall

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