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Technical Mathematics

ISBN: 9780766828018 | 0766828018
Edition: 4th
Format: Paperback
Publisher: Cengage Learning
Pub. Date: 10/12/2001

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SummaryTable of ContentsAuthor Biography
Available in both hard- and soft-cover editions, Technical Mathematics underscores the importance of algebra, geometry, and trigonometry in today's sophisticated, state-of-the-art trade/technical work environments. It integrates practice problems and examples directly into its explanations of math concepts and eliminates the need to labor through theoretical derivations and formal proofs. With new, step-by-step examples and applications problems drawn directly from a variety of diverse occupational fields, this edition also features expanded co... MORE
... MORE
Prefacexv
SECTION I Fundamentals of General Mathematics1(164)
Whole Numbers
2(29)
Place Value
2(1)
Expanding Whole Numbers
3(1)
Estimating (Approximating)
4(1)
Addition of Whole Numbers
5(1)
Subtraction of Whole Numbers
6(2)
Problem Solving-Word Problem Practical Applications
8(1)
Adding and Subtracting Whole Numbers in Practical Applications
8(2)
Multiplication of Whole Numbers
10(3)
Division of Whole Numbers
13(3)
Multiplying and Dividing Whole Numbers in Practical Applications
16(3)
Combined Operations of Whole Numbers
19(1)
Combined Operations of Whole Numbers in Practical Applications
20(7)
Unit Exercise and Problem Review
23(4)
Computing with a Calculator: Whole Numbers
27(4)
Common Fractions
31(46)
Definitions
31(1)
Fractional Parts
32(1)
A Fraction as an Indicated Division
33(1)
Equivalent Fractions
33(1)
Expressing Fractions in Lowest Terms
33(1)
Expressing Mixed Numbers as Improper Fractions
34(1)
Expressing Improper Fractions as Mixed Numbers
35(1)
Use of Common Fractions in Practical Applications
36(2)
Addition of Common Fractions
38(4)
Subtraction of Common Fractions
42(3)
Adding and Subtracting Common Fractions in Practical Applications
45(4)
Multiplication of Common Fractions
49(4)
Multiplying Common Fractions in Practical Applications
53(3)
Division of Common Fractions
56(3)
Dividing Common Fractions in Practical Applications
59(2)
Combined Operations With Common Fractions
61(2)
Combined Operations of Common Fractions in Practical Applications
63(8)
Unit Exercise and Problem Review
66(5)
Computing with a Calculator: Fractions and Mixed Numbers
71(6)
Decimal Fractions
77(48)
Meaning of Fractional Parts
78(1)
Reading Decimal Fractions
78(1)
Simplified Method of Reading Decimal Fractions
79(1)
Writing Decimal Fractions
79(1)
Rounding Decimal Fractions
80(1)
Expressing Common Fractions as Decimal Fractions
80(1)
Expressing Decimal Fractions as Common Fractions
81(1)
Decimal Fractions in Practical Applications
82(1)
Adding Decimal Fractions
83(1)
Subtracting Decimal Fractions
84(1)
Adding and Subtracting Decimal Fractions in Practical Applications
85(3)
Multiplying Decimal Fractions
88(2)
Multiplying Decimal Fractions in Practical Applications
90(3)
Dividing Decimal Fractions
93(2)
Dividing Decimal Fractions in Practical Applications
95(3)
Powers and Roots of Decimal Fractions
98(3)
Decimal Fraction Powers and Roots in Practical Applications
101(4)
Table of Decimal Equivalents
105(2)
Combined Operations of Decimal Fractions
107(2)
Combined Operations of Decimal Fractions in Practical Applications
109(10)
Unit Exercise and Problem Review
112(7)
Computing with a Calculator: Decimals
119(6)
Percents
125(16)
Definition of Percent
125(1)
Expressing Decimal Fractions as Percents
126(1)
Expressing Common Fractions and Mixed Numbers as Percents
126(1)
Expressing Percents as Decimal Fractions
127(1)
Expressing Percents as Common Fractions
128(1)
Types of Simple Percentage Problems
128(2)
Finding Percentage in Practical Applications
130(2)
Finding Percent (Rate) in Practical Applications
132(2)
Finding the Base in Practical Applications
134(1)
More Complex Percentage Practical Applications
135(6)
Unit Exercise and Problem Review
138(3)
Graphs: Bar and Line
141(24)
Types and Structure of Graphs
141(1)
Reading Bar Graphs
142(4)
Drawing Bar Graphs
146(2)
Line Graphs
148(1)
Reading Line Graphs
149(1)
Reading Combined-Data Line Graphs
150(5)
Drawing Line Graphs
155(1)
Drawing Broken-Line Graphs
155(2)
Drawing Straight-Line Graphs
157(1)
Drawing Curved-Line Graphs
158(7)
Unit Exercise and Problem Review
160(5)
SECTION II Measurement165(82)
Precision, Accuracy, and Tolerance
166(16)
Exact and Approximate (Measurement) Numbers
166(1)
Degree of Precision of Measuring Instruments
167(1)
Common Linear Measuring Instruments
167(1)
Degree of Precision of a Measurement Number
168(1)
Degrees of Precision in Adding and Subtracting Measurement Numbers
169(1)
Significant Digits
170(1)
Accuracy
171(1)
Accuracy in Multiplying and Dividing Measurement Numbers
171(1)
Absolute and Relative Error
172(1)
Tolerance (Linear)
173(1)
Unilateral and Bilateral Tolerance with Clearance and Interference Fits
174(8)
Unit Exercise and Problem Review
177(5)
Measurement Units
182(40)
Customary Linear Units
183(1)
Expressing Equivalent Units of Measure
183(3)
Arithmetic Operations with Compound Numbers
186(4)
Customary Linear Measure Practical Applications
190(3)
Metric Units of Linear Measure
193(1)
Expressing Equivalent Units within the Metric System
194(2)
Arithmetic Operations with Metric Lengths
196(1)
Metric Linear Measure Practical Applications
196(2)
Customary Units of Surface Measure (Area)
198(1)
Customary Area Measure Practical Applications
199(1)
Metric Units of Surface Measure (Area)
200(2)
Arithmetic Operations with Metric Area Units
202(1)
Metric Area Measure Practical Applications
202(1)
Customary Units of Volume (Cubic Measure)
203(1)
Customary Volume Practical Applications
204(1)
Metric Units of Volume (Cubic Measure)
205(2)
Arithmetic Operations with Metric Volume Units
207(1)
Metric Volume Practical Applications
207(1)
Customary and Metric Units of Capacity
208(1)
Customary and Metric Capacity Practical Applications
209(1)
Customary and Metric Units of Weight (Mass)
210(2)
Customary and Metric Weight Practical Applications
212(1)
Compound Units
212(2)
Compound Units Practical Applications
214(8)
Unit Exercise and Problem Review
216(6)
Steel Rules and Vernier Calipers
222(13)
Types of Steel Rules
222(1)
Reading Fractional Measurements
222(2)
Measurements that do not Fall on Rule Graduations
224(1)
Reading Decimal-Inch Measurements
225(1)
Reading Metric Measurements
226(1)
Vernier Calipers: Types and Description
227(2)
Reading Measurements on a Customary Vernier Caliper
229(2)
Reading Measurements on a Metric Vernier Caliper
231(4)
Unit Exercise and Problem Review
233(2)
Micrometers
235(12)
Description of a Customary Outside Micrometer
235(1)
Reading a Customary Micrometer
236(1)
The Customary Vernier Micrometer
237(1)
Reading a Customary Vernier Micrometer
238(2)
Description of a Metric Micrometer
240(1)
Reading a Metric Micrometer
240(1)
The Metric Vernier Micrometer
241(1)
Reading a Metric Vernier Micrometer
242(5)
Unit Exercise and Problem Review
244(3)
SECTION III Fundamentals of Algebra247(168)
Introduction to Algebra
248(11)
Symbolism
248(1)
Algebraic Expressions
248(3)
Evaluation of Algebraic Expressions
251(8)
Unit Exercise and Problem Review
256(3)
Signed Numbers
259(21)
Meaning of Signed Numbers
259(1)
The Number Scale
260(2)
Operations Using Signed Numbers
262(1)
Absolute Value
262(1)
Addition of Signed Numbers
263(3)
Subtraction of Signed Numbers
266(1)
Multiplication of Signed Numbers
267(1)
Division of Signed Numbers
268(1)
Powers of Signed Numbers
269(3)
Roots of Signed Numbers
272(2)
Combined Operations of Signed Numbers
274(6)
Unit Exercise and Problem Review
276(4)
Basic Algebraic Operations
280(39)
Definitions
280(1)
Addition
281(2)
Subtraction
283(3)
Multiplication
286(3)
Division
289(4)
Powers
293(2)
Roots
295(3)
Removal of Parentheses
298(1)
Combined Operations
298(2)
Scientific Notation
300(5)
Metric Prefixes Applied to Very Large and Very Small Numbers
305(3)
Basic Structure of the Binary Numeration System
308(11)
Unit Exercise and Problem Review
312(7)
Simple Equations
319(23)
Expression of Equality
319(1)
Writing Equations from Word Statements
320(2)
Checking the Equation
322(2)
Principles of Equality
324(1)
Solution of Equations by the Subtraction Principle of Equality
324(3)
Solution of Equations by the Addition Principle of Equality
327(3)
Solution of Equations by the Division Principle of Equality
330(2)
Solution of Equations by the Multiplication Principle of Equality
332(3)
Solution of Equations by the Root Principle of Equality
335(2)
Solution of Equations by the Power Principle of Equality
337(5)
Unit Exercise and Problem Review
339(3)
Complex Equations
342(14)
Equations Consisting of Combined Operations
342(4)
Solving for the Unknown in Formulas
346(1)
Substituting Values Directly in Given Formulas
346(3)
Rearranging Formulas
349(7)
Unit Exercise and Problem Review
353(3)
Ratio and Proportion
356(16)
Description of Ratios
356(1)
Order of Terms of Ratios
357(2)
Description of Proportions
359(4)
Direct Proportions
363(2)
Inverse Proportions
365(7)
Unit Exercise and Problem Review
368(4)
The Cartesian Coordinate System and Graphs of Linear Equations
372(9)
Description of the Cartesian (Rectangular) Coordinate System
372(1)
Graphing a Linear Equation
373(2)
Slope of a Linear Equation
375(1)
Slope Intercept Equation of a Straight Line
376(1)
Determining an Equation, Given Two Points
377(1)
Describing a Straight Line
378(3)
Unit Exercise and Problem Review
379(2)
Systems of Equations
381(16)
Graphical Method of Solving Systems of Equations
381(2)
Substitution Method of Solving Systems of Equations
383(1)
Addition or Subtraction Method of Solving Systems of Equations
384(4)
Types of Systems of Equations
388(1)
Writing and Solving Systems of Equations From Word Statements, Number Problems, and Practical Applications
389(8)
Unit Exercise and Problem Review
395(2)
Quadratic Equations
397(18)
General or Standard Form of Quadratic Equations
397(1)
Incomplete Quadratic Equations
398(4)
Complete Quadratic Equations
402(2)
Practical Applications of Complete Quadratic Equations
404(5)
Word Problems Involving Complete Quadratic Equations. Equations Not Given
409(6)
Unit Exercise and Problem Review
413(2)
SECTION IV Fundamentals of Plane Geometry415(120)
Introduction to Plane Geometry
416(6)
Plane Geometry
416(1)
Axioms and Postulates
417(3)
Points and Lines
420(2)
Unit Exercise
421(1)
Angular Measure
422(20)
Units of Angular Measure
422(1)
Units of Angular Measure in Degrees, Minutes, and Seconds
423(1)
Expressing Degrees, Minutes, and Seconds as Decimal Degrees
424(1)
Expressing Decimal Degrees as Degrees, Minutes, and Seconds
424(2)
Arithmetic Operations on Angular Measure in Degrees, Minutes, and Seconds
426(8)
Simple Semicircular Protractor
434(1)
Circle Graphs
435(3)
Complements and Supplements of Scale Readings
438(4)
Unit Exercise and Problem Review
439(3)
Angular Geometric Principles
442(13)
Naming Angles
442(1)
Types of Angles
442(1)
Angles Formed by a Transversal
443(2)
Theorems and Corollaries
445(10)
Unit Exercise and Problem Review
452(3)
Triangles
455(16)
Types of Triangles
456(2)
Angles of a Triangle
458(4)
Isosceles and Equilateral Triangles
462(1)
Isosceles Triangle Practical Application
462(1)
Equilateral Triangle Practical Application
463(1)
The Pythagorean Theorem
464(1)
Pythagorean Theorem Practical Applications
464(7)
Unit Exercise and Problem Review
467(4)
Congruent and Similar Figures
471(14)
Congruent Figures
471(2)
Similar Figures
473(3)
Similar Triangles Practical Applications
476(9)
Unit Exercise and Problem Review
481(4)
Polygons
485(14)
Types of Polygons
485(2)
Types of Quadrilaterals
487(2)
Polygon Interior and Exterior Angles
489(1)
Polygon Interior and Exterior Angles Practical Applications
489(5)
Trapezoid Median Practical Applications
494(5)
Unit Exercise and Problem Review
496(3)
Circles
499(36)
Definitions
499(2)
Circumference Formula
501(1)
Arc Length Formula
502(2)
Radian Measure
504(2)
Circle Postulates
506(1)
Chords, Arcs, and Central Angles
507(1)
Circle Chord Bisector Practical Application
508(3)
Circle Tangents and Chord Segments
511(1)
Circle Tangent Practical Application
512(1)
Tangents From a Common Point Practical Application
513(3)
Angles Formed Inside and on a Circle
516(1)
Inscribed Angles Practical Application
516(1)
Tangent and Chord Practical Application
517(3)
Angles Outside a Circle
520(1)
Internally and Externally Tangent Circles
521(1)
Internally Tangent Circles Practical Application
522(2)
Externally Tangent Circles Practical Application
524(11)
Unit Exercise and Problem Review
528(7)
SECTION V Geometric Figures: Areas and Volumes535(76)
Areas of Common Polygons
536(22)
Areas of Rectangles
536(3)
Areas of Parallelograms
539(4)
Areas of Trapezoids
543(4)
Areas of Triangles Given the Base and Height
547(2)
Areas of Triangles Given Three Sides
549(9)
Unit Exercise and Problem Review
553(5)
Areas of Circles, Sectors, Segments, and Ellipses
558(14)
Areas of Circles
558(1)
Ratio of Two Circles
559(3)
Areas of Sectors
562(2)
Areas of Segments
564(2)
Areas of Ellipses
566(6)
Unit Exercise and Problem Review
568(4)
Prisms and Cylinders: Volumes, Surface Areas, and Weights
572(13)
Prisms
572(1)
Volumes of Prisms
572(3)
Cylinders
575(1)
Volumes of Cylinders
576(2)
Computing Heights and Bases of Prisms and Cylinders
578(2)
Lateral Areas and Surface Areas of Right Prisms and Cylinders
580(5)
Unit Exercise and Problem Review
583(2)
Pyramids and Cones: Volumes, Surface Areas, and Weights
585(16)
Pyramids
585(1)
Cones
586(1)
Volumes of Regular Pyramids and Right Circular Cones
586(2)
Computing Heights and Bases of Regular Pyramids and Right Circular Cones
588(1)
Lateral Areas and Surface Areas of Regular Pyramids and Right Circular Cones
589(3)
Frustums of Pyramids and Cones
592(1)
Volumes of Frustums of Regular Pyramids and Right Circular Cones
593(2)
Lateral Areas and Surface Areas of Frustums of Regular Pyramids and Right Circular Cones
595(6)
Unit Exercise and Problem Review
599(2)
Spheres and Composite Figures: Volumes, Surface Areas, and Weights
601(10)
Spheres
601(1)
Surface Area of a Sphere
602(1)
Volume of a Sphere
602(2)
Volumes and Surface Areas of Composite Solid Figures
604(7)
Unit Exercise and Problem Review
609(2)
SECTION VI Fundamentals of Trigonometry611(108)
Introduction to Trigonometric Functions
612(10)
Ratio of Right Triangle Sides
612(1)
Identifying Right Triangle Sides by Name
613(1)
Trigonometric Functions: Ratio Method
614(2)
Customary and Metric Units of Angular Measure
616(1)
Determining Functions of Given Angles and Determining Angles of Given Functions
616(6)
Unit Exercise and Problem Review
620(2)
Trigonometric Functions with Right Triangles
622(12)
Variation of Functions
622(2)
Functions of Complementary Angles
624(2)
Determining an Unknown Angle When Two Sides of a Right Triangle Are Known
626(2)
Determining an Unknown Side When an Acute Angle and One Side of a Right Triangle are Known
628(6)
Unit Exercise and Problem Review
632(2)
Practical Applications with Right Triangles
634(28)
Solving Problems Stated in Word Form
634(5)
Solving Problems Given in Picture Form that Require Auxiliary Lines
639(9)
Solving Complex Problems that Require Auxiliary Lines
648(14)
Unit Exercise and Problem Review
657(5)
Functions of Any Angle, Oblique Triangles
662(35)
Cartesian (Rectangular) Coordinate System
662(1)
Determining Functions of Angles in Any Quadrant
663(3)
Alternating Current Applications
666(3)
Determining Functions of Angles Greater Than 360°
669(1)
Instantaneous Voltage Related to Time Application
670(1)
Solving Oblique Triangles
671(1)
Law of Sines
671(1)
Solving Problems Given Two Angles and a Side, Using the Law of Sines
672(2)
Solving Problems Given Two Sides and an Angle Opposite One of the Given Sides, Using the Law of Sines
674(4)
Law of Cosines (Given Two Sides and the Included Angle)
678(1)
Solving Problems Given Two Sides and the Included Angle, Using the Law of Cosines
678(3)
Law of Cosines (Given Three Sides)
681(1)
Solving Problems Given Three Sides, Using the Law of Cosines
682(3)
Practical Applications of Oblique Trigonometry
685(12)
Unit Exercise and Problem Review
692(5)
Vectors
697(22)
Scalar and Vector Quantities
697(1)
Description and Naming Vectors
697(1)
Vector Ordered Pair Notation
698(1)
Vector Length and Angle Notation
699(1)
Adding Vectors
699(2)
Graphic Addition of Vectors
701(4)
Addition of Vectors Using Trigonometry
705(6)
General (Component Vector) Procedure for Vectors Using Trigonometry
711(8)
Unit Exercise and Problem Review
716(3)
Appendix A United States Customary and Metric Units of Measure719(2)
Appendix B Formulas for Areas (A) of Plane Figures721(1)
Appendix C Formulas for Volumes and Areas of Solid Figures722(1)
Appendix D Answers to Odd-Numbered Exercises723(32)
Index755
Robert D. Smith is an Associate Professor Emeritus of Industrial Technology at Central Connecticut State University in New Britain, Connecticut

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