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Engineering mathematics : a foundation for electronic, electrical, communications and systems engineers

Author: Tony Croft
Publisher: Harlow, England ; New York : Pearson, 2013.
Edition/Format:   Print book : English : 4th edView all editions and formats
Summary:

Engineering Mathematics is the leading undergraduate textbook for Level 1 and 2 mathematics courses for electrical and electronic engineering, systems and communications engineering students. It  Read more...

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Genre/Form: Problems and exercises
Problems, exercises, etc
Problèmes et exercices
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Tony Croft
ISBN: 9780273719779 0273719777
OCLC Number: 808802874
Notes: Previous edition: published as by Anthony Croft, Robert Davison and Martin Hargreaves. 2001.
Includes index.
Description: xviii, 961 pages : illustrations ; 25 cm
Contents: Machine generated contents note: ch. 1 Review of algebraic techniques --
1.1. Introduction --
1.2. Laws of indices --
1.3. Number bases --
1.4. Polynomial equations --
1.5. Algebraic fractions --
1.6. Solution of inequalities --
1.7. Partial fractions --
1.8. Summation notation --
Review exercises 1 --
ch. 2 Engineering functions --
2.1. Introduction --
2.2. Numbers and intervals --
2.3. Basic concepts of functions --
2.4. Review of some common engineering functions and techniques --
Review exercises 2 --
ch. 3 trigonometric functions --
3.1. Introduction --
3.2. Degrees and radians --
3.3. trigonometric ratios --
3.4. sine, cosine and tangent functions --
3.5. sinc x function --
3.6. Trigonometric identities --
3.7. Modelling waves using sin t and cos t --
3.8. Trigonometric equations --
Review exercises 3 --
ch. 4 Coordinate systems --
4.1. Introduction --
4.2. Cartesian coordinate system --
two dimensions --
4.3. Cartesian coordinate system --
three dimensions --
4.4. Polar coordinates --
4.5. Some simple polar curves --
4.6. Cylindrical polar coordinates --
4.7. Spherical polar coordinates --
Review exercises 4 --
ch. 5 Discrete mathematics --
5.1. Introduction --
5.2. Set theory --
5.3. Logic --
5.4. Boolean algebra --
Review exercises 5 --
ch. 6 Sequences and series --
6.1. Introduction --
6.2. Sequences --
6.3. Series --
6.4. binomial theorem --
6.5. Power series --
6.6. Sequences arising from the iterative solution of non-linear equations --
Review exercises 6 --
ch. 7 Vectors --
7.1. Introduction --
7.2. Vectors and scalars: basic concepts --
7.3. Cartesian components --
7.4. Scalar fields and vector fields --
7.5. scalar product --
7.6. vector product --
7.7. Vectors of n dimensions --
Review exercises 7 --
ch. 8 Matrix algebra --
8.1. Introduction --
8.2. Basic definitions --
8.3. Addition, subtraction and multiplication --
8.4. Robot coordinate frames --
8.5. Some special matrices --
8.6. inverse of a 2 x 2 matrix --
8.7. Determinants --
8.8. inverse of a 3 x 3 matrix --
8.9. Application to the solution of simultaneous equations --
8.10. Gaussian elimination --
8.11. Eigenvalues and eigenvectors --
8.12. Analysis of electrical networks --
8.13. Iterative techniques for the solution of simultaneous equations --
8.14. Computer solutions of matrix problems --
Review exercises 8 --
ch. 9 Complex numbers --
9.1. Introduction --
9.2. Complex numbers --
9.3. Operations with complex numbers --
9.4. Graphical representation of complex numbers --
9.5. Polar form of a complex number --
9.6. Vectors and complex numbers --
9.7. exponential form of a complex number --
9.8. Phasors --
9.9. De Moivre's theorem --
9.10. Loci and regions of the complex plane --
Review exercises 9 --
ch. 10 Differentiation --
10.1. Introduction --
10.2. Graphical approach to differentiation --
10.3. Limits and continuity --
10.4. Rate of change at a specific point --
10.5. Rate of change at a general point --
10.6. Existence of derivatives --
10.7. Common derivatives --
10.8. Differentiation as a linear operator --
Review exercises 10 --
ch. 11 Techniques of differentiation --
11.1. Introduction --
11.2. Rules of differentiation --
11.3. Parametric, implicit and logarithmic differentiation --
11.4. Higher derivatives --
Review exercises 11 --
ch. 12 Applications of differentiation --
12.1. Introduction --
12.2. Maximum points and minimum points --
12.3. Points of inflexion --
12.4. Newton-Raphson method for solving equations --
12.5. Differentiation of vectors --
Review exercises 12 --
ch. 13 Integration --
13.1. Introduction --
13.2. Elementary integration --
13.3. Definite and indefinite integrals --
Review exercises 13 --
ch. 14 Techniques of integration --
14.1. Introduction --
14.2. Integration by parts --
14.3. Integration by substitution --
14.4. Integration using partial fractions --
Review exercises 14 --
ch. 15 Applications of integration --
15.1. Introduction --
15.2. Average value of a function --
15.3. Root mean square value of a function --
Review exercises 15 --
ch. 16 Further topics in integration --
16.1. Introduction --
16.2. Orthogonal functions --
16.3. Improper integrals --
16.4. Integral properties of the delta function --
16.5. Integration of piecewise continuous functions --
16.6. Integration of vectors --
Review exercises 16 --
ch. 17 Numerical integration --
17.1. Introduction --
17.2. Trapezium rule --
17.3. Simpson's rule --
Review exercises 17 --
ch. 18 Taylor polynomials, Taylor series and Maclaurin series --
18.1. Introduction --
18.2. Linearization using first-order Taylor polynomials --
18.3. Second-order Taylor polynomials --
18.4. Taylor polynomials of the nth order --
18.5. Taylor's formula and the remainder term --
18.6. Taylor and Maclaurin series --
Review exercises 18 --
ch. 19 Ordinary differential equations I --
19.1. Introduction --
19.2. Basic definitions --
19.3. First-order equations: simple equations and separation of variables --
19.4. First-order linear equations: use of an integrating factor --
19.5. Second-order linear equations --
Review exercises 19 --
ch. 20 Ordinary differential equations II --
20.1. Introduction --
20.2. Analogue simulation --
20.3. Higher order equations --
20.4. State-space models --
20.5. Numerical methods --
20.6. Euler's method --
20.7. Improved Euler method --
20.8. Runge-Kutta method of order 4 --
Review exercises 20 --
ch. 21 Laplace transform --
21.1. Introduction --
21.2. Definition of the Laplace transform --
21.3. Laplace transforms of some common functions --
21.4. Properties of the Laplace transform --
21.5. Laplace transform of derivatives and integrals --
21.6. Inverse Laplace transforms --
21.7. Using partial fractions to find the inverse Laplace transform --
21.8. Finding the inverse Laplace transform using complex numbers --
21.9. convolution theorem --
21.10. Solving linear constant coefficient differential equations using the Laplace transform --
21.11. Transfer functions --
21.12. Poles, zeros and the s plane --
21.13. Laplace transforms of some special functions --
Review exercises 21 --
ch. 22 Difference equations and the z transform --
22.1. Introduction --
22.2. Basic definitions --
22.3. Rewriting difference equations --
22.4. Block diagram representation of difference equations --
22.5. Design of a discrete-time controller --
22.6. Numerical solution of difference equations --
22.7. Definition of the z transform --
22.8. Sampling a continuous signal --
22.9. relationship between the z transform and the Laplace transform --
22.10. Properties of the z transform --
22.11. Inversion of z transforms --
22.12. z transform and difference equations --
Review exercises 22 --
ch. 23 Fourier series --
23.1. Introduction --
23.2. Periodic waveforms --
23.3. Odd and even functions --
23.4. Orthogonality relations and other useful identities --
23.5. Fourier series --
23.6. Half-range series --
23.7. Parseval's theorem --
23.8. Complex notation --
23.9. Frequency response of a linear system --
Review exercises 23 --
ch. 24 Fourier transform --
24.1. Introduction --
24.2. Fourier transform --
definitions --
24.3. Some properties of the Fourier transform --
24.4. Spectra --
24.5. t --
w duality principle --
24.6. Fourier transforms of some special functions --
24.7. relationship between the Fourier transform and the Laplace transform --
24.8. Convolution and correlation --
24.9. discrete Fourier transform --
24.10. Derivation of the d.f.t. --
24.11. Using the d.f.t. to estimate a Fourier transform --
24.12. Matrix representation of the d.f.t. --
24.13. Some properties of the d.f.t. --
24.14. discrete cosine transform --
24.15. Discrete convolution and correlation --
Review exercises 24 --
ch. 25 Functions of several variables --
25.1. Introduction --
25.2. Functions of more than one variable --
25.3. Partial derivatives --
25.4. Higher order derivatives --
25.5. Partial differential equations --
25.6. Taylor polynomials and Taylor series in two variables --
25.7. Maximum and minimum points of a function of two variables --
Review exercises 25 --
ch. 26 Vector calculus --
26.1. Introduction --
26.2. Partial differentiation of vectors --
26.3. gradient of a scalar field --
26.4. divergence of a vector field --
26.5. curl of a vector field --
26.6. Combining the operators grad, div and curl --
26.7. Vector calculus and electromagnetism --
Review exercises 26 --
ch. 27 Line integrals and multiple integrals --
27.1. Introduction --
27.2. Line integrals --
27.3. Evaluation of line integrals in two dimensions --
27.4. Evaluation of line integrals in three dimensions --
27.5. Conservative fields and potential functions --
27.6. Double and triple integrals --
27.7. Some simple volume and surface integrals --
27.8. divergence theorem and Stokes' theorem --
27.9. Maxwell's equations in integral form --
Review exercises 27 --
ch. 28 Probability --
28.1. Introduction --
28.2. Introducing probability --
28.3. Mutually exclusive events: the addition law of probability --
28.4. Complementary events --
28.5. Concepts from communication theory --
28.6. Conditional probability: the multiplication law --
28.7. Independent events --
Review exercises 28 --
ch. 29 Statistics and probability distributions Note continued: 29.1. Introduction --
29.2. Random variables --
29.3. Probability distributions --
discrete variable --
29.4. Probability density functions --
continuous variable --
29.5. Mean value --
29.6. Standard deviation --
29.7. Expected value of a random variable --
29.8. Standard deviation of a random variable --
29.9. Permutations and combinations --
29.10. binomial distribution --
29.11. Poisson distribution --
29.12. uniform distribution --
29.13. exponential distribution --
29.14. normal distribution --
29.15. Reliability engineering --
Review exercises 29.
Responsibility: Anthony Croft [and others].

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