Part 1: Sets, functions, and calculus
by Mary P Attenborough
Mathematics for Electrical Engineering and Computing
- Cover image
- Title page
- Table of Contents
- Copyright page
- Preface
- Acknowledgements
- Part 1: Sets, functions, and calculus
- 1. Sets and functions
- 2. Functions and their graphs
- 2.1 Introduction
- 2.2 The straight line: y = mx + c
- 2.3 The quadratic function: y = ax2+bx+c
- 2.4 The function y = 1/x
- 2.5 The functions y = ax
- 2.6 Graph sketching using simple transformations
- 2.7 The modulus function, y = |x| or y = abs(x)
- 2.8 Symmetry of functions and their graphs
- 2.9 Solving inequalities
- 2.10 Using graphs to find an expression for the function from experimental data
- 2.11 Summary
- 2.12 Exercises
- 3. Problem solving and the art of the convincing argument
- 4. Boolean algebra
- 5. Trigonometric functions and waves
- 5.1 Introduction
- 5.2 Trigonometric functions and radians
- 5.3 Graphs and important properties
- 5.4 Wave functions of time and distance
- 5.5 Trigonometric identities
- 5.6 Superposition
- 5.7 Inverse trigonometric functions
- 5.8 Solving the trigonometric equations sin x = a, cos x= a, tan x = a
- 5.9 Summary
- 5.10 Exercises
- 6. Differentiation
- 7. Integration
- 8. The exponential function
- 9. Vectors
- 9.1 Introduction
- 9.2 Vectors and vector quantities
- 9.3 Addition and subtraction of vectors
- 9.4 Magnitude and direction of a 2D vector–polar co-ordinates
- 9.5 Application of vectors to represent waves (phasors)
- 9.6 Multiplication of a vector by a scalar and unit vectors
- 9.7 Basis vectors
- 9.8 Products of vectors
- 9.9 Vector equation of a line
- 9.10 Summary
- 9.12 Exercises
- 10. Complex numbers
- 10.1 Introduction
- 10.2 Phasor rotation by π/2
- 10.3 Complex numbers and operations
- 10.4 Solution of quadratic equations
- 10.5 Polar form of a complex number
- 10.6 Applications of complex numbers to AC linear circuits
- 10.7 Circular motion
- 10.8 The importance of being exponential
- 10.9 Summary
- 10.10 Exercises
- 11. Maxima and minima and sketching functions
- 12. Sequences and series
- Part 2: Systems
- 13. Systems of linear equations, matrices, and determinants
- 14. Differential equations and difference equations
- 15. Laplace and z transforms
- 15.1 Introduction
- 15.2 The Laplace transform – definition
- 15.3 The unit step function and the (impulse) delta function
- 15.4 Laplace transforms of simple functions and properties of the transform
- 15.5 Solving linear differential equations with constant coefficients
- 15.6 Laplace transforms and systems theory
- 15.7 z transforms
- 15.8 Solving linear difference equations with constant coefficients using z transforms
- 15.9 z transforms and systems theory
- 15.10 Summary
- 15.11 Exercises
- 16. Fourier series
- Part 3: Functions of more than one variable
- Part 4: Graph and language theory
- Part 5: Probability and statistics
- 21. Probability and statistics
- 21.1 Introduction
- 21.2 Population and sample, representation of data, mean, variance and standard deviation
- 21.3 Random systems and probability
- 21.4 Addition law of probability
- 21.5 Repeated trials, outcomes, and probabilities
- 21.6 Repeated trials and probability trees
- 21.7 Conditional probability and probability trees
- 21.8 Application of the probability laws to the probability of failure of an electrical circuit
- 21.9 Statistical modelling
- 21.10 The normal distribution
- 21.11 The exponential distribution
- 21.12 The binomial distribution
- 21.13 The Poisson distribution
- 21.14 Summary
- 21.15 Exercises
- 21. Probability and statistics
- Answers to exercises
- Index
Part 1
Sets, functions, and calculus
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