[share_ebook] CRC Press - Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB

Description

*Introduces the computational and graphics capabilities of MATLAB
*Discusses simple algorithms to numerically implement the basic operations of calculus and linear algebra
*Contains additional mathematical material necessary to understand intermediate electrical engineering courses
*Provides scientists and professional engineers with a quick reference to use MATLAB as a problem-solving tool
*Includes numerous exercises and examples that offer a glimpse into fascinating problems encountered in engineering practice as well as end-of-chapter MATLAB definitions

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 MATLAB

Smoothing 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

PREFACE TO FIRST EDITION
PREFACE TO SECOND EDITION

STARTING WITH MATLAB AND EXPLORING ITS GRAPHICS CAPABILITIES
First Steps
Basic Algebraic Operations and Functions
Plotting Points
M-Files
MATLAB Simple Programming
Arrays
Data Analysis
Parametric Equations
Polar Plots
3-D Plotting
Animation
Specialized Plots: Velocity, Gradient, etc.
Printing and Saving Work in MATLAB
MATLAB Commands Review

DIFFERENCE EQUATIONS
Simple Linear Forms
Amortization
An Iterative Geometric Construct: The Koch Curve
Solution of Linear Constant Coefficients Difference Equations
Convolution-Summation of a First-Order System with Constant Coefficients
General First-Order Linear Difference Equations
Nonlinear Difference Equations
Fractals and Computer Art
Generation of Special Functions from Their Recursion Relations

ELEMENTARY FUNCTIONS AND SOME OF THEIR USES
Function Files
Examples with Affine Functions
Examples with Quadratic Functions
Examples with Polynomial Functions
Examples with the Trigonometric Functions
Examples with the Logarithmic Function
Examples with the Exponential Function
Examples with the Hyperbolic Functions and Their Inverses
Commonly Used Signal Processing Functions
Animation of a Moving Rectangular Pulse
Use of the Function Handle
MATLAB Commands Review

DIFFERENTIATION, INTEGRATION, AND SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
Limits of Indeterminate Forms
Derivative of a Function
Infinite Sums
Numerical Integration
A Better Numerical Differentiator
A Better Numerical Integrator: Simpson's Rule
Numerical Solutions of Ordinary Differential Equations
Integral Equations
MATLAB Commands Review

ROOT SOLVING AND OPTIMIZATION METHODS
Finding the Real Roots of a Function of One Variable
Roots of a Polynomial
Optimization Methods for Functions of One Variable
The Zeros and the Minima of Functions in Two Variables
Finding the Minima of Functions with Constraints Present
MATLAB Commands Review

COMPLEX NUMBERS
Introduction
The Basics
Complex Conjugation and Division
Polar Form of Complex Numbers
Analytical Solutions of Constant Coefficients ODE
Phasors
Interference and Diffraction of Electromagnetic Waves
Solving ac Circuits with Phasors: The Impedance Method
Transfer Function for a Difference Equation with Constant Coefficients
MATLAB Commands Review

VECTORS
Vectors in Two Dimensions
Dot (or Scalar) Product
Components, Direction Cosines, and Projections
The Dirac Notation and Some General Theorems
Cross Product and Scalar Triple Product
Tangent, Normal, and Curvature
Velocity and Acceleration Vectors in Polar Coordinates
Line Integral
Infinite-Dimensional Vector Spaces
MATLAB Commands Review

MATRICES
Setting up Matrices
Adding Matrices
Multiplying a Matrix by a Scalar
Multiplying Matrices
Inverse of a Matrix
Solving a System of Linear Equations
Application of Matrix Methods
Eigenvalues and Eigenvectors
The Cayley-Hamilton and Other Analytical Techniques
Special Classes of Matrices
Transfer Matrices
Covariance Matrices
MATLAB Commands Review

TRANSFORMATIONS
Two-Dimensional Geometric Transformations
Homogeneous Coordinates
Manipulation of 2-D Images
Lorentz Transformation
Iterative Constructs
MATLAB Commands Review

A TASTE OF PROBABILITY THEORY
Introduction
Basics
Addition Laws for Probabilities
Conditional Probability
Repeated Trials
Generalization of Bernoulli Trials
The Poisson and the Normal Distributions

APPENDIX A: REVIEW OF ELEMENTARY FUNCTIONS
APPENDIX B: DETERMINANTS
APPENDIX C: SYMBOLIC CALCULATIONS WITH MATLAB®
APPENDIX D: SOME USEFUL FORMULAE
APPENDIX E: TEXT FORMATTING

SELECTED REFERENCES
INDEX

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