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Understand electrical and electronics maths
1 online resource (316 pages) : illustrations
Understand Electrical and Electronics Maths covers elementary maths and the aspects of electronics. The book discusses basic maths including quotients, algebraic fractions, logarithms, types of equations and balancing of equations. The text also describes the main features and functions of graphs and the solutions to simpler types of electronics problems. The book then tackles the applications of polar coordinates in electronics, limits, differentiation and integration, and the applications of maths of rates of change in electronics. The activities of an electronic circuit; techniques of math.
Front Cover; Understand Electrical and Electronics Maths; Copyright Page; Contents; Preface; Symbols for mathematical operators; Symbols for equality and inequality; Part One -- Basic Maths; Chapter 1. About numbers; Types of numbers; Factors; Highest common factor; Lowest common multiple; Factors of polynomials; Chapter 2. Quotients; Handling fractions; Algebraic fractions; Partial fractions; Chapter 3. Logs and other topics; Indices; Logarithms; Vectors; Chapter 4. Making sense of equations; Types of equations; Balancing equations; Changing the subject; Quadratic equations.
Simultaneous equationsExpressing results; Chapter 5. Looking at graphs; Graph variables; Coordinates; Straight-line graphs; Gradient/intercept equation; Steepness; Testing a point; Distance between two points; Recognizing graphs; Graphs with log scales; Trig ratios; Other graphs; Important points; Functions; Chapter 6. From theory to practice; P.d. across a resistor; Resistance; Current through a resistor; Resistors in parallel; Currents in a resistor network; Potential divider; Flux density; Decibels; Induced emf; Alternating current; Phasors; Inductive impedance; Capacitative impedance.
RLC series resonant circuitPhase angle in RLC series circuit; Charging a capacitor; Part Two -- Maths Topics; Chapter 7. Distance and direction; Types of coordinate; Polar coordinates; Circular motion; Vectors; Circular motion, vectors and sine waves; From sine waves to vectors; Rectangular to polar; Polar to rectangular; Chapter 8. Limits; Limits at zero; Limits at infinity; Using a calculator; Chapter 9. Rates of change; Pin-pointing the gradient; Simplifying the symbols; Finding dy/dx; A function from a function; Looking for tlie rules; Other symbols; Using the rules; Useful derivatives.
Maximums and mínimumsThe Chain Rule; Differentiation of a product; Differentiating a quotient; Partial differentials; Percentage changes; Rates of change; Chapter 10. Summing it up; Tidying up; Working in reverse; Standard integrals; Dealing with the constant of integration; Integrating ratios; Integration by substitution; More examples of substitution; Integrating by parts; Integration and averages; Integrating sine waves; Modified sine waves; Root mean square (rms) values; Chapter 11. Equations for actions; A simple model; Growth and decay; Solving the decay equation; First-order equations.
More modellingSecond-order equations; Solving with positive discriminant; Solving with zero discriminant; Solving with negative discriminant; A second-order model; Chapter 12. Practical differentials; Euler's method; Operator D; Solving a differential equation; Imaginary roots; Higher-order equations; The Laplace transformation; Transforming differential equations; Inverse transformation; More transforming routines; Transforming integrals; Initial value; Final value; Chapter 13. Systematic solutions; Elimination in theory; Evaluating determinants; Solving equations by using determinants.