Book description
Mathematics for Electrical Engineering and Computing embraces many applications of modern mathematics, such as Boolean Algebra and Sets and Functions, and also teaches both discrete and continuous systems - particularly vital for Digital Signal Processing (DSP). In addition, as most modern engineers are required to study software, material suitable for Software Engineering - set theory, predicate and prepositional calculus, language and graph theory - is fully integrated into the book.Excessive technical detail and language are avoided, recognising that the real requirement for practising engineers is the need to understand the applications of mathematics in everyday engineering contexts. Emphasis is given to an appreciation of the fundamental concepts behind the mathematics, for problem solving and undertaking critical analysis of results, whether using a calculator or a computer.The text is backed up by numerous exercises and worked examples throughout, firmly rooted in engineering practice, ensuring that all mathematical theory introduced is directly relevant to real-world engineering. The book includes introductions to advanced topics such as Fourier analysis, vector calculus and random processes, also making this a suitable introductory text for second year undergraduates of electrical, electronic and computer engineering, undertaking engineering mathematics courses.Dr Attenborough is a former Senior Lecturer in the School of Electrical, Electronic and Information Engineering at South Bank University. She is currently Technical Director of The Webbery - Internet development company, Co. Donegal, Ireland.- Fundamental principles of mathematics introduced and applied in engineering practice, reinforced through over 300 examples directly relevant to real-world engineering
Table of contents
- 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
Product information
- Title: Mathematics for Electrical Engineering and Computing
- Author(s):
- Release date: June 2003
- Publisher(s): Newnes
- ISBN: 9780080473406
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