Understand Electrical and Electronics Maths

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 equations
		Expressing 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 circuit
		Phase 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 mínimums
		The 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 modelling
		Second-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
		Solving for three variables
		Evaluating a determinant of third (or higher) order
		Making it easier
		Data tables
		Describing a matrix
		Working with matrices
		Matrix multiplication
		Order of multiplication
		Identity matrix
		The LED display problem again
		The inverse of a 2 x 2 matrix
		Finding the inverse of a 3x3 matrix
		Testing the inverse
		Another problem
		Row equivalents
	Chapter 14. Beyond the number line
		Using the imagination
		Working with j
		The imaginary number line
		Another approach
		The algebra of complex numbers
		Conjugate complex numbers
		Division of complex numbers
		Complex numbers and quadratic equations
		Complex numbers and vectors
		Polar form
		Negative angles
		Adding complex numbers in polar form
		Multiplying in polar form
		Dividing in polar form
		Powers of complex numbers
		Roots of complex numbers
		Exponential form
		Impedances in equations
		Imaginary numbers solve real problems
	Chapter 15. Analysing waveforms
		Sine waves
		Building the series
		Converting the sines
		Conditions
		Finding the first term
		Finding the cosine terms
		Finding the sine terms
		The final analysis
		Fourier coefficients
		Calculating coefficients
		Symmetry
		Rectified ac
Answers
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 7
	Chapter 8
	Chapter 9
	Chapter 11
	Chapter 13
	Chapter 14
	Chapter 15
Index