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Edition/Copyright: 5TH 01
The purpose of this book is to provide an understanding of mathematics as it is applied to electronics. The text may be used in a formal classroom setting or in a self-paced or self-study program. Mathematics Applied to Electronics is for studying technology related to electronics, computers, electromechanics, or automation.
Modern electronics curriculums need the support of a large and diverse amount of mathematics, so the content of this text is a trade-off between a formal proof orientation and the need for expediency in developing a broad, general mathematics ability. The sequence of chapters and topics within each chapter have been planned to be compatible with the electric circuits books currently in use. The scientific calculator is an integral part of the text, and its introduction early in the book enhances the learning process.
NEW TO THE FIFTH EDITION
The book begins with selected topics in prealgebra, number notation, and units of measurement, which are followed by several chapters dealing with the fundamentals of algebra, including the evaluation of formulas. This series of chapters culminates with a chapter devoted to the solution of linear equations, which is followed by a chapter that applies mathematics to electronic circuits.
The text is structured so that each section of theoretical chapters is followed by one or more application chapters. The application chapters reinforce materials previously presented and provide the learner with an opportunity to transfer mathematical skills to electronics concepts. Interspersed throughout the book are chapters and topics dealing with graphing and graphical analysis. These chapters are essential because so much valuable information is presented in graphical form in handbooks and data sheets.
Following chapters dealing with quadratic equations and exponents and radicals are chapters covering logarithmic, exponential, and trigonometric functions. These topics are followed by a series of chapters covering the mathematics of alternating current. The text concludes with chapters dealing with math analysis, computer number systems, and computer logic.
This book has been designed to guide the reader through the learning process by providing a means of coordinating the instruction in the classroom with outside assignments. The reader is helped by hundreds of detailed examples, figures, graphs, and problems. The utilization of the SI system of measurement throughout the text enables the user to make an easy transition to any technology book in use today.
A companion website is available for this text. It contains multiple choice questions for each chapter as well as short answer and/or problem solving questions for Chapters 2-6. This website also contains Syllabus Manager, which instructors can use to easily create and revise syllabi. Syllabus Manager includes direct links into companion website and other online content.
In closing, we wish to thank you, the adopters of this and the previous editions of Mathematics Applied to Electronics, for your helpful comments and suggestions and for your diligence in bringing oversights and omissions to our attention. We acknowledge all of you who have communicated with us, including Roger Harlow, Archie Gillespie, and Anna Spear. We also thank the reviewers of this edition: Nasser Hedayat, Valencia Community College; Barbara Miller, University of Alaska; Saeed A. Shaikh, Miami-Dade Community College; and Stephen Trudeau, Denver Technical College.
Proposals for improvement, questions about problems, or comments on the content may be made by writing us in care of the publisher.
It is our sincere intention to provide high-quality materials for your use. To that end, adopters of the text may request (from the publisher) a complimentary package of materials, including a detailed Instructor's Solutions Manual, Transparency Masters, an extensive Text Item File, and a Windows-based Prentice Hall Test Manager (electronic version of the Test Item File).
Again, thank you for your continued support.
Redondo Beach, California
Harter, James H. : Mesa Community College
Beitzel, Wallace D. : TRW Space and Electronics Group
1. Selected Prealgebra Topics.
Natural Numbers and Number Systems. Signed Numbers. Numerical Expressions and Equations. Order of Operations. Symbols of Grouping. Double Meaning of + and -. Absolute Value of a Signed Number. Combining Signed Numbers. Relational Operators. Multiplying with Signed Numbers. Dividing with Signed Numbers.
2. Number Notation and Operation.
Introduction to Exponents. Number Notation. Numeric Operations and Rounding. Operations with Approximate Numbers. Square Roots, Radicals and Reciprocals. Combined Operations. Powers of Ten and Approximations.
3. Quantities and Units of Measurement.
International System of Units. Selected Physical Quantities. Forming Decimal Multiples and Submultiples of the SI Units. Unit Analysis and Conversion between Systems. Applying Unit Analysis to Energy Cost. Units and Exponents.
4. Algebra Fundamentals I.
Variables, Subscripts, and Primes. Indicating Multiplication. General Numbers. Algebraic Expressions. Products, Factor, and Coefficients. Combining Like Terms. Polynomials. Adding Polynomials.
5. Algebra Fundamentals II.
Multiplying Monomials. Multiplying a Monomial and a Binomial. Multiplying a Monomial and a Polynomial. Subtracting Polynomials. Additional Work with Polynomials. Division of Monomials. Dividing a Polynomial by a Monomial. Factoring Polynomials with a Common Monomial Factor. Evaluating Algebraic Expressions.
6. Solving Equations.
Equations. Finding the Root of an Equation. Using Addition to Transform Equations. Using Multiplication to Transform Equations. Additional Techniques. Equations Containing Parentheses. Solving Formulas. Evaluating Formulas. Forming Equations. Solving Word Problems.
7. Applying Mathematics to Electrical Circuits.
Current, Voltage, and Resistance. Ohm's Law. Resistance in a Series Circuit. Applying Ohm's Law. Summary of the Series Circuit. Power.
Introductory Concepts. Forming Equivalent Fractions. Simplifying Fractions. Multiplying Fractions. Dividing Fractions. Complex Fractions. Adding and Subtracting Fractions. Changing a Mixed Expression to a Fraction. Additional Work with Complex Fractions.
9. Equations Containing Fractions.
Solving Equations Containing Fractions. Solving Fractional Equations. Literal Equations Containing Fractions. Evaluating Formulas.
10. Applying Fractions to Electrical Circuits.
Voltage Division in a Series Circuit. Conductance of the Parallel Circuit. Equivalent Resistance of the Parallel Circuit. Current Division in the Parallel Circuit. Solving Parallel Circuit Problems. Using Network Theorems to Form Equivalent Circuits.
11. Special Products, Factoring, and Equations.
Mentally Multiplying Two Binomials. Product of the Sum and Difference of Two Numbers. Square of a Binomial. Factoring the Difference of Two Squares. Factoring a Perfect Trinomial Square. Factoring By Grouping. Combining Several Types of Factoring. Literal Equations.
12. Applying Mathematics to Electrical Concepts.
Ratio, Percent, and Parts Per Million. Accounting for Empirical Error in Calculations. Efficiency. Proportion. Electrical Conductors.
13. Relations and Functions.
Meaning of a Function. Variables and Constants. Functional Notation. Functional Variation. Simplifying Formulas.
14. Graphs and Graphing Techniques.
Rectangular Coordinates. Graphs of Equations. Graphs of Linear Equations. Deriving a Linear Equation from a Graph. Graphing Empirical Data.
15. Applying Graphs to Electronic Concepts.
Graphic Estimation of Static Parameters. Graphic Estimation of Dynamic Parameters. Graphic Analysis of Linear Circuits. Graphic Analysis of Nonlinear Circuits.
16. Solving Systems of Linear Equations.
Addition or Subtraction Method. Substitution Method. Deriving Electrical Formulas. Determinants of the Second Order. Determinants of the Third Order.
17. Applying Systems of Linear Equations to Electronic Concepts.
Applying Kirchhoff's Voltage Law. Mesh Analysis. Solving Networks by Mesh Analysis.
18. Solving Quadratic Equations.
Introduction. Solving Incomplete Quadratic Equations. Solving Complete Quadratic Equations. Solving Quadratic Equations by the Quadratic Formula. Graphing Quadratic Functions. Applying the Techniques of Solving Quadratic Equations to Electronic Problems.
19. Exponents, Radicals, and Equations.
Laws of Exponents. Zero and Negative Integers as Exponents. Fractional Exponents. Laws of Radicals. Simplifying Radicals. Radical Equations.
20. Logarithmic and Exponential Functions.
Common Logarithms. Common Logarithms and Scientific Notation. Antilogarithms. Logarithms, Products, and Quotients. Logarithms, Powers, and Radicals. Natural Logarithms. Changing Base. Further Properties of Natural Logarithms. Logarithmic Equations. Exponential Equations. Semilog and Log-Log Plots. Nomographs.
21. Applications of Logarithmic and Exponential Equations to Electronic Concepts.
the Decibel. System Calculations. RC and RL Transient Behavior. Preferred Number Series.
22. Angles and Triangles.
Points, Lines, and Angles. Special Angles. Triangles. Right Triangles and the Pythagorean Theorem. Similar Triangles; Trigonometric Functions. Using the Trigonometric Functions to Solve Right Triangles. Inverse Trigonometric Functions. Solving Right Triangles When Two Sides Are Known.
23. Circular Functions.
Angles of Any Magnitude. Circular Functions. Graphs of the Circular Functions. Inverse Circular Functions. The Law of Sines and the Law of Cosines. Polar Coordinates. Converting between Rectangular and Polar Coordinates.
24. Vectors and Phasors.
Scalars and Vectors. Complex Plane. Real and Imaginary Numbers. Complex Numbers. Phasors. Transforming Complex Number Forms. Resolving Systems of Phasors and Vectors.
25. The Mathematics of Phasors.
Addition and Subtraction of Phasor Quantities. Multiplication of Phasor Quantities. Division of Phasor Quantities. Powers and Roots of Phasor Quantities.
26. Fundamentals of Alternating Current.
Alternating-Current Terminology. Resistance. Inductance and Inductive Reactance. Capacitance and Capacitive Reactance. Voltage Phasor for Series Circuits. Current Phasor for Parallel Circuits.
27. Alternating-Current Circuits.
Impedance of Series AC Circuits. Solving Series AC Circuits. Admittance Concepts. Admittance of Parallel AC Circuits.
28. Sinusoidal Alternating Current.
Time and Displacement. Power and Power Factor. Instantaneous Equations and the EI Phasor Diagram.
29. Additional Trigonometric and Exponential Functions.
Auxiliary Trigonometric Functions. Graphs of the Auxiliary Trigonometric Functions. Trigonometric Identities. Hyperbolic Functions. Graphing the Hyperbolic Functions. Hyperbolic Identities. Inverse Hyperbolic Functions.
30. Mathematical Analysis.
Domain and Range. Discontinuities. Functions of Large Numbers. Asymptotes.
31. Computer Number Systems.
Decimal Number Systems. Three Additional Number Systems. Converting Numbers to the Decimal System. Converting Decimal Numbers to Other Systems. Converting between Binary, Octal, and Hexadecimal. Binary Addition and Subtraction. Octal Addition and Subtraction. Hexadecimal Addition and Subtraction. Complements. Binary Arithmetic with Complements. Review.
32. Mathematics of Computer Logic.
Introductory Concepts. Inversion Operator (NOT). Conjunction Operator (AND). Disjunction Operator (OR). Applications of Logic Concepts. Introduction to Karnaugh Maps. DeMorgan's Theorem. Boolean Theorems. Applications.
Glossary of Selected Terms.
Appendix A: Reference Tables.
Appendix B: Answers to Selected Problems.
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