This book provides an introduction to mathematics applied to electronics, computers, electromechanics, and automation. Organized to be compatible with electric circuits books currently in use, the book's content balances a formal proof-orientation against the need for expediency in developing a broad, general mathematics ability. Addresses prealgebra topics, number notation and operation, solving equations, fractions, applying mathematics to electrical concepts, graphs and graphing techniques, vectors, phasors and the mathematics of computer logic. For individuals with little exposure to hard science and little understanding of measured quantities and their precision. nnn
|Publisher:||Prentice Hall Professional Technical Reference|
Table of Contents1. 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.
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.