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

Engineers around the world depend on MATLAB for its power, usability, and outstanding graphics capabilities. Yet too often, engineering students are either left on their own to acquire the background they need to use MATLAB, or they must learn the program concurrently within an advanced course. Both of these options delay students from solving realistic design problems, especially when they do not have a text focused on applications relevant to their field and written at the appropriate level of mathematics.Ideal for use as a short-course textbook and for self-study Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB fills that gap. Accessible after just one semester of calculus, it introduces the many practical analytical and numerical tools that are essential to success both in future studies and in professional life. Sharply focused on the needs of the electrical and computer engineering communities, the text provides a wealth of relevant exercises and design problems. Changes in MATLAB's version 6.0 are included in a special addendum.The lack of skills in fundamental quantitative tools can seriously impede progress in one's engineering studies or career. By working through this text, either in a lecture/lab environment or by themselves, readers will not only begin mastering MATLAB, but they will also hone their analytical and computational skills to a level that will help them to enjoy and succeed in subsequent electrical and computer engineering pursuits.

Contents

INTRODUCTION TO MATLAB AND ITS GRAPHICS CAPABILITIES

• Getting Started
• Basic Algebraic Operations and Functions
• Plotting Points
• M-files
• MATLAB Simple Programming
• Array Operations
• Curve and Surface Plotting
• Polar Plots
• Animation
• Histograms
• Printing and Saving Work in MATLAB
• MATLAB Commands Review

DIFFERENCE EQUATIONS

• Simple Linear Form
• Amortization
• An Iterative Geometric Construct: The Koch Curve
• Solution of Linear Constant Coefficients Difference Equations
• Convolution-Summation of 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 Trigonometric Functions
• Examples with the Logarithmic Function
• Examples with the Exponential Function
• Examples with Hyperbolic Functions and their Inverses
• Commonly Used Signal Processing Functions
• Animation of a Moving Rectangular Pulse
• MATLAB Commands Review

NUMERICAL 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 Solution of ODE
• MATLAB Commands Review

ROOT SOLVING AND OPTIMIZATION METHODS

• Finding the Real Roots of a Function
• Roots of a Polynomial
• Optimization Methods
• 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
• The Transfer Function of a Difference Equation with Constant Coefficients
• MATLAB Commands Review

VECTORS

• Vectors in Two Dimensions
• Dot Product
• Components, Direction Cosines, and Projections
• The Diract Notation and Some General Theorems
• Cross Product and Scalar Triple Product
• Vector Valued Functions
• Line Integrals
• 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
• MATLAB Commands Review

TRANSFORMATIONS

• Two-Dimensional Geometrical Transformations
• Homogeneous Coordinates
• Manipulation of 2-D Images
• Lorentz Transformation
• MATLAB Commands Review

A TASTE OF PROBABILITY THEORY

• Introduction
• Basics
• Addition Laws for Probabilities
• Conditional Probability
• Repeated Trials
• The Poisson and the Normal Distributions
• SUPPLEMENT: REVIEW OF ELEMENTARY FUNCTIONS
• ADDENDUM: MATLAB 6
• APPENDIX: Some Useful Formulae
• SELECTED REFERENCES
• INDEX