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9780028008530

Basic Mathematics for Electronics

by ; ; ;
  • ISBN13:

    9780028008530

  • ISBN10:

    0028008537

  • Edition: 7th
  • Format: Hardcover
  • Copyright: 1991-12-16
  • Publisher: Career Education
  • View Upgraded Edition

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Summary

Basic Mathematics for Electronics combines electronictheory and applications with the mathematical principles necessary to solve a wide range of circuit problems. Coverage of mathematical topics reflects current trends in electronics. A complete chapter is devoted to Karnaugh mapping to help students cope with the greater complexity of modern digital circuit devices. Marginal notes indicate areas of special interest in computers and computer usage.To facilitate learning, material is presented in a block form that employs a two-color, single-column format. After the initial chapters, sections may be studied ndependently. As each new topic is introduced, illustrative examples and numerous problems, graded from easy to difficult, are given for reinforcement. Answers to odd-numbered problems are provided in the back of the book. The Answers to Even-Numbered Problems booklet contains answers and selected worked-out solutions. A computerized Test Bank and Transparency Masters are also available with this edition.

Table of Contents

Preface xii
Introduction
1(10)
Mathematics-A Language
1(1)
Mathematics-A Tool
2(1)
Mathematics-A Teacher
2(1)
Methods of Study
2(1)
Rate of Progress
2(1)
Importance of Problems
3(1)
Illustrative Examples
3(1)
Review
3(1)
Section References
3(1)
Abbreviations
3(1)
Significant Figures
4(1)
Metrication
5(1)
Use of Calculators and Computers
5(1)
Electronic Aids to Mathematics for Electronics
5(1)
The Calculator
6(1)
Pocket Calculators
6(1)
Selecting Your Calculator
6(2)
Mathematical Tables
8(1)
Accuracy of Calculators
8(1)
The Computer
9(1)
Computer Facilities
9(1)
Memory
10(1)
Personal? Mainframe? Compatibility?
10(1)
Computers With This Book
10(1)
Dialects
10(1)
Algebra--General Numbers
11(10)
The General Number
11(1)
Signs of Operation
12(1)
The Order of Signs of Operation
12(1)
Algebraic Expressions
13(1)
The Product
13(1)
The Factor
13(1)
Coefficients
13(1)
Primes and Subscripts
13(1)
Evaluation
14(2)
Exponents
16(1)
The Radical Sign
17(1)
Terms
17(2)
Order of Operations
19(1)
Self Tests
19(2)
Self Test
19(2)
Algebra--Addition and Substraction
21(14)
Negative Numbers
21(1)
Practical Need for Negative Numbers
22(1)
The Mathematical Need for Negative Numbers
23(1)
The Absolute Value of a Number
23(1)
Addition of Positive and Negative Numbers
23(3)
The Subtraction of Positive and Negative Numbers
26(2)
Addition and Subtraction of Like Terms
28(1)
Addition and Subtraction of Polynomials
29(1)
Signs of Grouping
30(3)
Inserting Signs of Grouping
33(2)
Self Test
34(1)
Algebra--Multiplication and Division
35(21)
Multiplication of Positive and Negative Numbers
35(2)
Graphical Representation
37(2)
Law of Exponents in Multiplication
39(1)
Multiplication of Monomials
40(1)
Multiplication of Polynomials by Monomials
41(2)
Multiplication of a Polynomial by a Polynomial
43(3)
Division
46(1)
Division of Positive and Negative Numbers
46(1)
Division of Positive and Negative Numbers
46(1)
The Law of Exponents in Division
47(1)
The Zero Exponent
47(1)
The Negative Exponent
48(1)
Division of One Monomial by Another
49(1)
Division of a Polynomial by a Monomial
50(2)
Division of One Polynomial by Another
52(4)
Self Test
55(1)
Equations
56(18)
Definitions
56(1)
Axioms
57(2)
Notation
59(1)
The Solution of Equations
59(1)
Canceling Terms in an Equation
60(1)
Changing Signs in an Equation
61(1)
Checking the Solution
61(1)
Forming and Solving Equations
62(2)
Literal Equations-Formulas
64(5)
Ratio and Proportion
69(2)
Variation and Proportionality
71(3)
Self Test
73(1)
Powers of 10
74(16)
Significant Figures
74(1)
Rounded Numbers
75(1)
Decimals
75(1)
Powers of 10
76(2)
Multiplication With Powers of 10
78(2)
Division With Powers of 10
80(1)
Approximations
80(1)
Combined Multiplication and Division
81(1)
Reciprocals
82(2)
The Power of a Power
84(1)
The Power of a Product
85(1)
The Power of a Fraction
85(1)
The Root of a Power
85(1)
The Root of a Power
85(2)
Addition and Subtraction With Powers of 10
87(3)
Self Test
88(2)
Units and Dimensions 90
90(25)
Systems of Measurement
90(1)
The English System
91(1)
The Sl Metric System
91(1)
The Seven Base Sl Units
92(1)
The Additional Defined Sl Units
93(2)
Some Sl Metric Interrelationships
95(1)
Relations Between the Systems
95(1)
Frequency
96(1)
Ranges of Units
96(1)
Decimal Multipliers
97(1)
Preferred Decimal Multipliers
98(1)
Decimal Conversion Factors
99(2)
Intersystem Conversions
101(5)
Practical Considerations
106(1)
Significant Figures
107(1)
Calculations With Units
108(7)
Self Test
114(1)
Ohm's Law-Series Circuits
115(27)
The Electric Circuit
115(1)
Ohm's Low
115(1)
Methods of Solution
116(4)
Power
120(1)
The Watt
120(1)
Losses
121(1)
Efficiency
121(7)
Resistances in Series
128(5)
Bias Resistors-Field-Effect Transistors
133(4)
Bias Resistors-Transistors
137(5)
Self Test
141(1)
Resistance--Wire Sizes
142(14)
Resistance
142(3)
Microhm-Meter
145(3)
Temperature Effects
148(3)
Wire Measure
151(1)
Factors Governing Wire Size in Practice
151(5)
Self Test
154(2)
Special Products and Factoring
156(24)
Factoring
156(1)
Prime Numbers
156(1)
Square of a Monomial
157(1)
Cube of a Monomial
157(1)
Square Root of a Monomial
158(1)
Cube Root of a Monomial
159(1)
Polynomials With a Common Monomial Factor
160(1)
Square of a Binomial
161(3)
Square Root of a Trinomial
164(1)
Prime Factors of an Expression
165(1)
Product of the Sum and Difference of Two Numbers
166(1)
Factoring the Difference of Two Squares
167(1)
Product of Two Binomials Having a Common Term
167(5)
Factoring Trinomials of the form a2 + bx + c
172(3)
Special Situation Problems
175(5)
Self Test
179(1)
Algebraic Fractions
180(25)
The Degree of a Monomial
180(1)
The Degree of a Polynomial
180(1)
Highest Common Factor
181(1)
Multiple
182(1)
Lowest Common Multiple
182(2)
Definitions
184(1)
Operations on Numerator and Denominator
184(1)
Equivalent Fractions
185(1)
Reduction of Fractions to Their Lowest Terms
186(2)
Signs of Fractions
188(2)
Common Errors in Working With Fractions
190(2)
Changing Mixed Expressions to Fractions
192(1)
Reduction of a Fraction to a Mixed Expression
192(2)
Reduction to the Lowest Common Denominator
194(2)
Addition and Subtraction of Fractions
196(3)
Multiplication of Fractions
199(1)
Division of Fractions
200(2)
Complex Fractions
202(3)
Self Test
204(1)
Fractional Equations
205(20)
Fractional Coefficients
205(3)
Equations Containing Decimals
208(1)
Fractional Equations
209(5)
Literal Equations
214(11)
Self Test
223(2)
Ohm's Law--Parallel Circuits
225(15)
Two Resistance in Parallel
226(4)
Three or More Resistance in Parallel
230(3)
Compound Circuits
233(7)
Self Test
239(1)
Meter Circuits
240(15)
Direct-Current Instrument-Basic Meter Movement
240(1)
Multirange Current Meters
241(3)
Shunting Methods
244(3)
Voltmeters
247(2)
Voltmeters Sensitivity
249(1)
Voltmeter Loading Effects
249(1)
Multirange Voltmeters
250(1)
Ohmmeters
251(1)
Multimeters
252(1)
Digital Meters
253(2)
Self Test
254(1)
Divider Circuits and Wheatstone Bridges
255(13)
Voltage Dividers
255(2)
Voltage Dividers With Loads
257(6)
Current Dividers
263(1)
Wheatstone Bridge Circuits
264(4)
Self Test
267(1)
Graphs
268(23)
Locating Points on a Graph
268(2)
Solving Problems by Means of Graphs
270(4)
Coordinate Notation
274(2)
Graphs of Linear Equations
276(2)
Variables
278(1)
The Graph-Equation Relationships
279(2)
Methods of Plotting
281(4)
Equations Derived From Graphs
285(6)
Self Test
289(2)
Simultaneous Equations
291(18)
Graphical Solution of Simultaneous Linear Equations
291(2)
Solution of Simultaneous Linear Equations by Addition and Subtraction
293(2)
Solution by Substitution
295(2)
Solution by Comparison
297(1)
Fractional Form
297(2)
Fractional Equations
299(1)
Literal Equations in Two Unknowns
300(2)
Equations Containing Three Unknowns
302(1)
Methods of Solution of Problems
303(6)
Self Test
308(1)
Determinants
309(19)
Second-Order Determinants
309(3)
Solution of Equations
312(2)
Consistency of Equations
314(1)
Third-Order Determinants
315(2)
Minors
317(2)
Cofactors
319(2)
Useful Properties of Determinants
321(7)
Self Test
326(2)
Batteries
328(7)
Electromotive Force
328(1)
Batteries
328(2)
Cells in Series
330(1)
Cells in Parallel
331(4)
Self Test
334(1)
Exponents and Radicals
335(23)
Fundamental Laws of Exponents
335(1)
Zero Exponent
336(1)
Negative Exponents
336(1)
Fractional Exponents
337(1)
Radicand
338(1)
Simplification of Radicals
338(1)
Removing a Factor From the Radicand
339(1)
Simplifying Radicals Containing Fractions
340(2)
Addition and Subtraction of Radicals
342(1)
Multiplication of Radicals
343(1)
Division
344(1)
The Operator
345(3)
Indicated Square Roots of Negative Numbers
348(2)
Complex Numbers
350(1)
Addition and Subtraction of Complex Numbers
350(1)
Multiplication of Complex Numbers
351(1)
Division of Complex Numbers
352(1)
Radical Equations
353(5)
Self Test
357(1)
Quadratic Equations
358(29)
Definitions
358(1)
Solution of Pure Quadratic Equations
359(1)
Complete Quadratic Equations-Solution by Factoring
360(3)
Solution by Completing the Square
363(2)
Standard Form
365(1)
The Quadratic Formula
365(2)
Testing Solutions
367(1)
The Graph of a Quadratic Equation-The Parabola
368(8)
Graphical Solutions
376(1)
The Discriminant
376(1)
Maxima and Minima
377(2)
Special Situation Problems
379(8)
Self Test
385(2)
Network Simplification
387(26)
Direction of Current
387(1)
Statement of Kirchhoff's Laws
388(1)
Application of Second Law to Series Circuits
388(4)
Simple Application of Both Laws
392(3)
Further Applications of Kirchhoff's Laws
395(3)
Outline for Solving Networks
398(3)
Equivalent Star and Delta Circuits
401(5)
Thevenin and Norton Equivalents
406(3)
Outline for Thevenin and Norton Solutions
409(4)
Self Test
411(2)
Angles
413(11)
Angles
413(1)
Generation of Angles
414(1)
The Sexagesimal System
415(1)
Angles of Any Magnitude
416(1)
The Circular, or Natural, System
417(2)
Gons and Grads
419(1)
Similar Triangles
420(1)
The Right Triangle
421(3)
Self Test
423(1)
Trigonometric Functions
424(17)
Trigonometric Functions Are Ratios
424(5)
Functions of Complementary Angles
429(1)
Construction of an Angle When One Function Is Given
430(2)
Functions of Any Angle
432(1)
Sign of the Functions
433(2)
Computation of the Functions
435(1)
Functions of 0
436(1)
The Ranges of the Functions
436(2)
Line Representation of the Functions
438(3)
Self Test
440(1)
Trigonometric Values
441(15)
Given an Angle--To Find the Desired Function
441(1)
Inverse Trigonometric Functions
442(1)
Given a Function--To Find the Corresponding Angle
443(1)
Accuracy
444(1)
Functions of Angles Greater Than 90
445(1)
To Find the Functions of an Angle in an Second Quadrant
445(1)
To Find the Function of an Angle in the Third Quadrant
446(1)
To Find the Functions of an Angle in the Fourth of Quadrant
447(1)
To Find the Functions of an Angle Greater than 360
448(1)
To Find the Functions of a Negative Angle
449(1)
To Reduce the Functions of Any Angle to the Functions of an Acute Angle
449(3)
Angles Corresponding to Inverse Functions
452(4)
Self Test
455(1)
Solution of Right Triangles
456(12)
Facts Concerning Right Triangles
456(1)
Procedure for Solution of Right Triangles
457(1)
Given an Acute Angle and a Side Not the Hypotenuse
458(3)
Given an Acute Angle and the Hypotenuse
461(1)
Given the Hypotenuse and One Other Side
462(2)
Given Two Sides Not the Hypotenuse
464(1)
Terms Relating to Miscellaneous Trigonometric Problems
464(2)
The Area of Triangles
466(2)
Self Test
467(1)
Trigonometric Identities and Equations
468(12)
Simple Identities
468(1)
The Pythagorean Identities
469(2)
Low of Sines
471(1)
Law of Cosines
472(3)
The Sum Identities
475(1)
The Difference Identities
476(4)
Self Test
479(1)
Elementary Plane Vectors
480(13)
Vectors
480(1)
Notation
481(1)
Addition of Vectors
482(2)
Components of a Vector
484(3)
Phasors
487(1)
Phasor Summation of Rectangular Components
488(1)
Phasor Summation of Nonrectangular Components
489(4)
Self Test
492(1)
Periodic Functions
493(14)
The Graph of the Sine Curve y = sin x
493(2)
The Graph of the Cosine Curve y = cos x
495(1)
The Graph of the Tangent Curve y = tan x
496(1)
Periodicity
497(1)
Angular Motion
497(1)
Projection of a Point Having Uniform Circular Motion
498(3)
Amplitude
501(1)
Frequency
501(1)
Period
502(1)
Phase
503(1)
Summary
504(3)
Self Test
506(1)
Alternating Currents--Fundamental Ideas
507(14)
Generation of an Alternating Electromotive Force
507(1)
Variation of an Alternating Electromotive Force
508(1)
Vector Representation
509(2)
Cycles, Frequency, and Poles
511(1)
Equations of Voltages and Currents
512(2)
Average Value of Current or Voltage
514(1)
Effective Value of Current or Voltage
515(1)
Phase Relations-Phase Angles
516(5)
Self Test
520(1)
Phasor Algebra
521(11)
Phasor Definitions
521(1)
Addition and Subtraction of Phasors in Rectangular Form
522(1)
Multiplication of Phasors in Rectangular Form
523(1)
Division of Phasors in Rectangular Form
524(1)
Addition And Subtraction of Polar Phasors
525(1)
Multiplication of Polar Phasors
526(1)
Division of Polar Phasors
527(1)
Exponential Form
528(1)
Powers and Roots of Polar Phasors
529(3)
Self Test
531(1)
Alternating Currents-Series Circuits
532(34)
Definitions
532(1)
The Resistive Circuit
533(1)
Power in the Resistive Circuit
534(3)
The Inductive Circuit
537(4)
The Capacitive Circuit
541(3)
Capacitors in Series
544(2)
Power in Circuits Containing Only Inductance or Capacitance
546(1)
Resistance and Inductance in Series
547(3)
Resistance and Capacitance in Series
550(2)
Resistance, Inductance, and Capacitance in Series
552(2)
Power in a Series Circuit
554(1)
Notation for Series Circuits
555(3)
The General Series Circuit
558(4)
Series Resonance
562(1)
Resonant Frequency
563(3)
Self Test
565(1)
Alternating Current-Parallel Circuits
566(26)
Resistance in Parallel
566(1)
Capacitors in Parallel
567(1)
Inductance and Capacitance in Parallel
568(1)
Assumed Voltages
569(1)
Resistance and Inductance in Parallel
570(2)
Resistance and Capacitance in Parallel
572(1)
Resistance, Inductance, and Capacitance in Parallel
573(3)
Phasor Impedances in Parallel
576(2)
Series-Parallel Circuits
578(2)
Parallel Resonance
580(2)
Impedance of Parallel-Resonant Circuits
582(3)
Equivalent Y and Δ Circuits
585(7)
Self Test
590(2)
Logarithms
592(25)
Definition
592(1)
Notation
593(1)
Logarithm of a Product
594(1)
Logarithm of a Product
594(1)
Logarithm of a Quotient
595(1)
Logarithm of a Power
596(1)
Logarithm of a Root
596(1)
Self Test
597(1)
The Common System of Logarithms
597(1)
The Natural System of Logarithms
597(1)
Developing a Table of Logarithms
598(3)
Logarithms From a Calculator
601(1)
To Find the Number Corresponding to a Given Logarithm
601(1)
Change of Base
602(2)
Natural Logarithms
604(1)
Graph of y = log10x
605(1)
Logarithmic Equations
605(1)
Exponential Equations
606(8)
Calculations by Means of Logarithms
614(3)
Self Test A
616(1)
Self Test B
616(1)
Applications of Logarithms
617(24)
Preferred Values
617(2)
Power Ratios--The Decibel
619(2)
Power Reference Levels
621(3)
Current and Voltage Ratios
624(2)
The Merit, or Gain, of an Antenna
626(4)
Transmission Lines
630(1)
The Inductance of a Line
631(1)
The Capacitance of a Line
632(2)
Characteristic Impedances of RF Transmission Lines
634(4)
Graphs Involving Logarithmic Values
638(3)
Self Test
640(1)
Number Systems for Computers
641(35)
Numbers in General
641(1)
Binary Numbers
642(2)
Octal Numbers
644(2)
Systems with Any Radix
646(1)
Conversion Between Systems
646(2)
Binary Addition
648(1)
Subtraction of Binary Numbers
649(1)
Subtraction by Adding Complements
650(1)
Binary Multiplication
651(1)
Binary Division
652(1)
Fractional Binary Numbers
652(4)
Arithmetic Operations With Fractional Binary Numbers
656(4)
Fractional Octal Numbers
660(2)
Hexadecimal Numbering System
662(7)
Fractional Hexadecimal Numbers
669(7)
Self Test
675(1)
Boolean Algebra
676(19)
Symbols of Logic Circuitry
676(1)
Symbols of Mathematical Logic
677(3)
The Axiomatic Tautologies
680(2)
Truth Tables
682(2)
Propositional Investigations
684(2)
Switching Networks
686(4)
Computer Gating Applications
690(2)
NOR Combinations
692(3)
Self Test
693(2)
Karnaugh Maps
695(98)
Karnaugh Maps for a Single Variable
695(4)
The General Karnaugh Map Grouping Within Karnaugh Maps
699(6)
Rollaround of Karnaugh Maps
705(5)
Larger Grouping Within Karnaugh Maps
710(5)
Self Test
714(1)
APPENDICES
A
715(1)
Tables
715(6)
1 Mathematical Symbols
715(1)
2 Letter Symbols
715(1)
3 Abbreviations and Unit Symbols
715(2)
4 Greek Alphabet
717(1)
5 Conversion Factors
717(1)
6 Copper Wire Tables
718(1)
7 Decimal Multipliers
719(1)
8 Rounded Values of Preferred Numbers
720(1)
B Answers to Odd-Numbered Problems
721(57)
C Answers to Self Tests
778(15)
Index 793

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