Mathematics for Electrical Engineering and Computing
Format: PDF / Kindle (mobi) / ePub
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.
The book is supported with a number of free online resources. On the companion website readers will find:
* over 60 pages of "Background Mathematics" reinforcing introductory material for revision purposes in advance of your first year course
* plotXpose software (for equation solving, and drawing graphs of simple functions, their derivatives, integrals and Fourier transforms)
* problems and projects (linking directly to the software)
In addition, for lecturers only, http://textbooks.elsevier.com features a complete worked solutions manual for the exercises in the book.
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
* Over 60 pages of basic revision material available to download in advance of embarking on a first year course
* Free website support, featuring complete solutions manual, background mathematics, plotXpose software, and further problems and projects enabling students to build on the concepts introduced, and put the theory into practice
−8, so another point is (2, −8). These points on marked on the graph and joined to give the graph as in Figure 2.3(b). Figure 2.3 (a) The graph of y = 4x − 2. (b) The graph of y = −4x . TLFeBOOK 32 Functions and their graphs 2.3 The quadratic function: y = ax 2 + bx + c y = ax 2 + bx + c is a general way of writing a function in which the highest power of x is a squared term. This is called the quadratic function and its graph is called a parabola as shown in Figure 2.4. All the graphs, in
are given in Figure 2.17. TLFeBOOK 40 Functions and their graphs Figure 2.17 Reflections in the line y = x produce the inverse relation. (a) (i) y = 2x ; (ii) y = log2 (x ). The second graph is obtained from the first by reflecting in the dotted line √ y = x . The inverse is a function as there 2 is only one value of y for each value of x. (b) (i) y = √ x ; (ii) y = ± x . The second graph is found by reflecting the first graph in the line y = x . Notice that y = ± x is not a function as there
Consider reflections of the graphs given in Figure 2.36 to determine whether they are even, odd, or neither of these. 2.9. By substituting x → −x in the following functions determine whether they are odd, even, or neither of these: (a) y = −x 2 + x12 where x = 0, (b) y = |x 3 | − x 2 , (c) y = (d) y = −1 x −1 x + log2 (x) where x > 0, + x + x5, (e) y = 6 + x 2 , (f) y = 1 − |x|. 2.10. Draw graphs of the following functions and draw the graph of the inverse relation in each case. Is the
function. So we may write f (x) = 1/x where x = 0 Things to look out for as values that are not allowed as function inputs are : 1. Numbers that would lead to an attempt to divide by zero 2. Numbers that would lead to negative square roots 3. Numbers that would lead to negative inputs to a logarithm. Examples 1.12(a) and (b) require solutions to inequalities which we shall discuss in greater detail in Chapter 2. Here, we shall only look at simple examples and use the same rules as used for
the general term f (n) = 2n. This was found in this case by simple guess work. 1.5 Combining functions The sum, difference, product, and quotient of two functions, f and g Two functions with R as their domain and codomain can be combined using arithmetic operations. We can define the sum of f and g by (f + g) : x → f (x) + g(x) The other operations are defined as follows: (f − g) : x → f (x) − g(x) difference, (f × g) : x → f (x) × g(x) product, (f /g) : x → f (x) g(x) quotient. TLFeBOOK