Basic Mathematics for Electronics

by Cooke, Nelson M.; Adams, Herbert F.; Dell, Peter B.; Moore, T. Adair

• ISBN13: 9780028008530
• ISBN10: 0028008537
• Edition: 7th
• Format: Hardcover
• Copyright: 1991-12-16
• Publisher: Career Education

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