Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB

by Manassah; Jamal T.

• ISBN13: 9780849374258
• ISBN10: 0849374251
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-10-20
• Publisher: CRC Press

Summary

Showing how MATLAB® can help solve computational problems in engineering, Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB®, Second Edition explores practical mathematical methods for students, covering numerical techniques of elementary calculus and linear algebra and detailed introductory material on difference equations, complex variables, transformation theory, and probability theory. This integrated approach strengthens students' analytical and computational abilities.Updated to reflect the newest version of MATLAB, this edition features a new layout for enhanced readability. The book covers both linear and nonlinear difference equations, elementary functions, numerical differentiation, integration and ordinary differential equations solving techniques, optimization methods, complex numbers, vectors, matrix algebra and special matrices, geometric and Lorentz transformations, and probability theory.New to the Second Edition:· Updated MATLAB syntax that conforms to MATLAB 7.1· Expanded introductory chapter that reduces the need to refer to MATLAB online help or user manuals· Special advanced sections for students looking for more challenging material· Appendix of symbolic capabilities of MATLABSmoothing the transition from elementary math, physics, and computer science sequences to more advanced engineering concepts, this book helps students master fundamental quantitative tools that allow them to progress to more complex electrical and computer engineering applications.

Table of Contents

Starting with MATLAB and Exploring Its Graphics Capabilities	1	(58)
First Steps	1	(1)
Basic Algebraic Operations and Functions	2	(4)
Plotting Points	6	(4)
Axes Commands	8	(1)
Labeling a Graph	9	(1)
Plotting a Point in 3-D	9	(1)
M-files	10	(1)
MATLAB Simple Programming	11	(5)
The for Iterative Loop	11	(1)
if-else-end Structures	12	(3)
The while Loop	15	(1)
Arrays	16	(6)
Array Relational Operations	17	(1)
Array Algebraic Operations	18	(1)
Combining Arrays Relational and Algebraic Operations: Alternative Syntax to the if Statement	19	(1)
Plotting Arrays	20	(2)
Data Analysis	22	(5)
Manipulation of Data	22	(2)
Displaying Data	24	(1)
Normal Distribution	25	(2)
Parametric Equations	27	(5)
Definition	27	(1)
More Examples	28	(2)
Oscilloscope Graphics	30	(2)
Polar Plots	32	(2)
3-D Plotting	34	(14)
Straight-Edge Geometric Figures	34	(4)
Parametric Equations for a 3-D Curve	38	(2)
Plotting a 3-D Surface	40	(3)
Contour: A Powerful Tool for Exploring 2-D Geometries	43	(5)
Animation	48	(1)
Specialized Plots: Velocity, Gradient, etc.	49	(3)
Velocity Plots from Parametric Equations	49	(1)
Gradient of a Potential	50	(2)
Printing and Saving Work in MATLAB	52	(3)
Printing a Figure	52	(2)
Printing a Program File (Script M-file)	54	(1)
Converting a MATLAB Graphic into an Image File	54	(1)
Saving Values of Variables	54	(1)
Loading the Value of a Variable	54	(1)
Saving a MATLAB Session	54	(1)
Loading workspace.mat	54	(1)
MATLAB Commands Review	55	(4)
Difference Equations	59	(30)
Simple Linear Forms	59	(2)
Amortization	61	(3)
An Iterative Geometric Construct: The Koch Curve	64	(3)
Solution of Linear Constant Coefficients Difference Equations	67	(7)
Homogeneous Solution	68	(2)
Particular Solution	70	(1)
General Solution	70	(4)
Convolution-Summation of a First-Order System with Constant Coefficients	74	(2)
General First-Order Linear Difference Equations	76	(2)
Nonlinear Difference Equations	78	(3)
Computing Irrational Numbers	78	(1)
The Logistic Equation	79	(2)
Fractals and Computer Art	81	(5)
Mira's Model	81	(3)
Henon's Model	84	(2)
Generation of Special Functions from Their Recursion Relations	86	(3)
Elementary Functions and Some of Their Uses	89	(26)
Function Files	89	(2)
Examples with Affine Functions	91	(4)
Application to a Simple Circuit	91	(3)
Further Consideration of Figure 3.1	94	(1)
Examples with Quadratic Functions	95	(1)
Examples with Polynomial Functions	96	(3)
Examples with the Trigonometric Functions	99	(1)
Examples with the Logarithmic Function	100	(3)
Ideal Coaxial Capacitor	100	(1)
The Decibel Scale	101	(1)
Entropy	101	(2)
Examples with the Exponential Function	103	(2)
Application to a Simple RC Circuit	103	(2)
Examples with the Hyperbolic Functions and Their Inverses	105	(1)
Application to the Capacitance of Two Parallel Wires	105	(1)
Commonly Used Signal Processing Functions	105	(6)
Animation of a Moving Rectangular Pulse	111	(1)
Use of the Function Handle	112	(2)
MATLAB Commands Review	114	(1)
Differentiation, Integration, and Solutions of Ordinary Differential Equations	115	(44)
Limits of Indeterminate Forms	115	(2)
Derivative of a Function	117	(2)
Infinite Sums	119	(2)
Numerical Integration	121	(3)
A Better Numerical Differentiator	124	(4)
Application	127	(1)
A Better Numerical Integrator: Simpson's Rule	128	(7)
Numerical Solutions of Ordinary Differential Equations	135	(17)
First-Order Iterator	137	(5)
Higher-Order Iterators: The Runge-Kutta Method	142	(4)
MATLAB ODE Solvers	146	(6)
Integral Equations	152	(6)
MATLAB Commands Review	158	(1)
Root Solving and Optimization Methods	159	(32)
Finding the Real Roots of a Function of One Variable	159	(11)
Graphical Method	159	(1)
Numerical Methods	160	(7)
MATLAB fzero Built-in Function	167	(1)
Application: Zeros of the Zero-Order Bessel Function	168	(2)
Roots of a Polynomial	170	(1)
Optimization Methods for Functions of One Variable	171	(7)
Graphical Method	172	(1)
Numerical Method: The Golden Section Method	173	(2)
MATLAB fminbnd Built-in Function	175	(3)
The Zeros and the Minima of Functions in Two Variables	178	(7)
The MATLAB fsolve Built-in Command	178	(3)
The MATLAB fminsearch Built-in Command	181	(4)
Finding the Minima of Functions with Constraints Present	185	(4)
Lagrange Multipliers	186	(1)
MATLAB fmincon Built-in Function	187	(2)
MATLAB Commands Review	189	(2)
Complex Numbers	191	(44)
Introduction	191	(1)
The Basics	191	(4)
Addition	192	(1)
Multiplication by a Real or Imaginary Number	193	(1)
Multiplication of Two Complex Numbers	193	(2)
Complex Conjugation and Division	195	(2)
Application to Division	196	(1)
Polar Form of Complex Numbers	197	(7)
New Insights into Multiplication and Division of Complex Numbers	198	(2)
Roots of Complex Numbers	200	(1)
The Function y = ejθ	201	(3)
Analytical Solutions of Constant Coefficients ODE	204	(9)
Transient Solutions	205	(2)
Solution in the Presence of a Source: Green Function Technique	207	(3)
Steady-State Solutions	210	(1)
Applications to Circuit Analysis	211	(2)
Phasors	213	(3)
Phasor of Two Added Signals	213	(1)
Total Phasor of Many Signals	214	(2)
Interference and Diffraction of Electromagnetic Waves	216	(4)
The Electromagnetic Wave	216	(1)
Addition of Two Electromagnetic Waves	217	(1)
Generalization to N-waves	218	(2)
Solving ac Circuits with Phasors: The Impedance Method	220	(4)
RLC Circuit Phasor Analysis	221	(1)
The Infinite LC Ladder	222	(2)
Transfer Function for a Difference Equation with Constant Coefficients	224	(10)
MATLAB Commands Review	234	(1)
Vectors	235	(38)
Vectors in Two Dimensions	235	(4)
Addition	235	(1)
Multiplication of a Vector by a Real Number	235	(1)
Cartesian Representation	236	(2)
MATLAB Representation of Vectors	238	(1)
Dot (or Scalar) Product	239	(4)
MATLAB Representation of the Dot Product	241	(2)
Components, Direction Cosines, and Projections	243	(1)
Components	243	(1)
Direction Cosines	243	(1)
Projections	244	(1)
The Dirac Notation and Some General Theorems	244	(5)
Cauchy-Schwartz Inequality	246	(2)
Triangle Inequality	248	(1)
Cross Product and Scalar Triple Product	249	(4)
Cross Product	249	(1)
Geometric Interpretation of the Cross Product	250	(1)
Scalar Triple Product	250	(3)
Tangent, Normal, and Curvature	253	(2)
Velocity and Acceleration Vectors in Polar Coordinates	255	(6)
Line Integral	261	(2)
Infinite-Dimensional Vector Spaces	263	(9)
MATLAB Commands Review	272	(1)
Matrices	273	(70)
Setting Up Matrices	273	(7)
Creating a Matrix by Keying in the Elements	273	(2)
Retrieving Special Matrices from the MATLAB Library	275	(2)
Functional Construction of Matrices	277	(3)
Adding Matrices	280	(1)
Multiplying a Matrix by a Scalar	280	(1)
Multiplying Matrices	281	(1)
Inverse of a Matrix	282	(3)
Solving a System of Linear Equations	285	(3)
Application of Matrix Methods	288	(11)
dc Circuit Analysis	288	(1)
dc Circuit Design	289	(1)
ac Circuit Analysis	290	(1)
Accuracy of a Truncated Taylor Series	291	(3)
Reconstructing a Function from Its Fourier Components	294	(2)
Interpolating the Coefficients of an (n -- 1)- Degree Polynomial from n Points	296	(1)
Least-Squares Fit of Data	297	(1)
Numerical Solution of Fredholm Equations	298	(1)
Eigenvalues and Eigenvectors	299	(6)
Finding the Eigenvalues of a Matrix	299	(3)
Finding the Eigenvalues and Eigenvectors Using MATLAB	302	(3)
The Cayley--Hamilton and Other Analytical Techniques	305	(14)
Cayley--Hamilton Theorem	305	(1)
Solution of Equations of the Form dX/dt = AX	306	(2)
Solution of Equations of the Form dX/dt = AX + B(t)	308	(4)
Pauli Spinors	312	(7)
Special Classes of Matrices	319	(11)
Hermitian Matrices	319	(4)
Unitary Matrices	323	(1)
Unimodular Matrices	324	(6)
Transfer Matrices	330	(4)
Covariance Matrices	334	(7)
Parametric Estimation	336	(3)
Karhunen--Loeve Transform	339	(2)
MATLAB Commands Review	341	(2)
Transformations	343	(22)
Two-Dimensional Geometric Transformations	343	(4)
Construction of Polygonal Figures	343	(1)
Inversion about the Origin and Reflection about the Coordinate Axes	344	(1)
Rotation around the Origin	345	(1)
Scaling	346	(1)
Translation	347	(1)
Homogeneous Coordinates	347	(4)
Manipulation of 2-D Images	351	(4)
Geometrical Manipulation of Images	351	(1)
Digital Image Processing	352	(1)
Encrypting an Image	353	(2)
Lorentz Transformation	355	(3)
Space-Time Coordinates	355	(2)
Addition Theorem for Velocities	357	(1)
Iterative Constructs	358	(5)
The Koch Curve	358	(3)
The Serpenski Curve	361	(2)
MATLAB Commands Review	363	(2)
A Taste of Probability Theory	365	(24)
Introduction	365	(1)
Basics	366	(5)
Addition Laws for Probabilities	371	(4)
Conditional Probability	375	(5)
Total Probability Theorem	377	(1)
Bayes Theorem	377	(3)
Repeated Trials	380	(2)
Generalization of Bernoulli Trials	382	(1)
The Poisson and the Normal Distributions	382	(7)
The Poisson Distribution	383	(2)
The Normal Distribution	385	(4)
Appendix A: Review of Elementary Functions	389	(14)
Affine Functions	389	(1)
Quadratic Functions	390	(5)
Polynomial Functions	395	(1)
Trigonometric Functions	395	(2)
Inverse Trigonometric Functions	397	(1)
The Natural Logarithmic Function	397	(1)
The Exponential Function	398	(1)
The Hyperbolic Functions	399	(2)
The Inverse Hyperbolic Functions	401	(2)
Appendix B: Determinants	403	(4)
Appendix C: Symbolic Calculations with MATLAB	407	(32)
Symbolic Manipulation	408	(9)
Creating Symbolic Expressions	408	(3)
Algebraic Manipulation	411	(3)
Plotting Symbolic Expressions	414	(3)
Symbolic Solution of Algebraic and Transcendental Equations	417	(1)
Symbolic Calculus	418	(5)
Symbolic Linear Algebra	423	(5)
z-Transform and Laplace Transform	428	(11)
z-Transform	428	(3)
Solving Constant Coefficients Linear Difference Equations Using z-Transform	431	(1)
Laplace Transform	432	(4)
Solving Constant Coefficients Linear ODE Using Laplace Transform	436	(3)
Appendix D: Some Useful Formulae	439	(4)
Appendix E: Text Formatting	443	(2)
Selected References	445	(2)
Index	447