[资料]一本经典的matlab工程科学计算教程

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

1. Introduction to MATLAB® and Its Graphics Capabilities
1.1 Getting Started
1.2 Basic Algebraic Operations and Functions
1.3 Plotting Points
1.3.1 Axes Commands
1.3.2 Labeling a Graph
1.3.3 Plotting a Point in 3-D
1.4 M-files
1.5 MATLAB Simple Programming
1.5.1 Iterative Loops
1.5.2 If-Else-End Structures
1.6 Array Operations
1.7 Curve and Surface Plotting
1.7.1 x-y Parametric Plot
1.7.2 More Parametric Plots in 2-D
1.7.3 Plotting a 3-D Curve
1.7.4 Plotting a 3-D Surface
1.8 Polar Plots
1.9 Animation
1.10 Histograms
1.11 Printing and Saving Work in MATLAB
1.12 MATLAB Commands Review
2. Difference Equations
2.1 Simple Linear Forms
2.2 Amortization
2.3 An Iterative Geometric Construct: The Koch Curve
2.4 Solution of Linear Constant Coefficients Difference
Equations
2.4.1 Homogeneous Solution
2.4.2 Particular Solution
2.4.3 General Solution
2.5 Convolution-Summation of a First-Order System with
Constant Coefficients
2.6 General First-Order Linear Difference Equations*
2.7 Nonlinear Difference Equations
2.7.1 Computing Irrational Numbers
2.7.2 The Logistic Equation
2.8 Fractals and Computer Art
2.8.1 Mira’s Model
2.8.2 Hénon’s Model
2.9 Generation of Special Functions from Their Recursion
Relations*
3. Elementary Functions and Some of Their Uses
3.1 Function Files
3.2 Examples with Affine Functions
3.3 Examples with Quadratic Functions
3.4 Examples with Polynomial Functions
3.5 Examples with Trigonometric Functions
3.6 Examples with the Logarithmic Function
3.6.1 Ideal Coaxial Capacitor
3.6.2 The Decibel Scale
3.6.3 Entropy
3.7 Examples with the Exponential Function
3.8 Examples with the Hyperbolic Functions and Their
Inverses
3.8.1 Capacitance of Two Parallel Wires
3.9 Commonly Used Signal Processing Functions
3.10 Animation of a Moving Rectangular Pulse
3.11 MATLAB Commands Review
4. Numerical Differentiation, Integration, and Solutions of
Ordinary Differential Equations
4.1 Limits of Indeterminate Forms
4.2 Derivative of a Function
4.3 Infinite Sums
4.4 Numerical Integration
4.5 A Better Numerical Differentiator
4.6 A Better Numerical Integrator: Simpson’s Rule
4.7 Numerical Solutions of Ordinary Differential Equations
4.7.1 First-Order Iterator
4.7.2 Higher-Order Iterators: The Runge-Kutta
Method*
4.7.3 MATLAB ODE Solvers
4.8 MATLAB Commands Review
5. Root Solving and Optimization Methods
5.1 Finding the Real Roots of a Function
5.1.1 Graphical Method
5.1.2 Numerical Methods
5.1.3 MATLAB fsolve and fzero Built-in Functions
5.2 Roots of a Polynomial
5.3 Optimization Methods
5.3.1 Graphical Method
5.3.2 Numerical Methods
5.3.3 MATLAB fmin and fmins Built-in Function
5.4 MATLAB Commands Review
6. Complex Numbers
6.1 Introduction
6.2 The Basics
6.2.1 Addition
6.2.2 Multiplication by a Real or Imaginary Number
6.2.3 Multiplication of Two Complex Numbers
6.3 Complex Conjugation and Division
6.3.1 Division
6.4 Polar Form of Complex Numbers
6.4.1 New Insights into Multiplication and Division
of Complex Numbers
6.5 Analytical Solutions of Constant Coefficients ODE
6.5.1 Transient Solutions
6.5.2 Steady-State Solutions
6.5.3 Applications to Circuit Analysis
6.6 Phasors
6.6.1 Phasor of Two Added Signals
6.7 Interference and Diffraction of ElectromagneticWaves
6.7.1 The ElectromagneticWave
6.7.2 Addition of ElectromagneticWaves
6.7.3 Generalization to N-waves
6.8 Solving ac Circuits with Phasors: The Impedance
Method
6.8.1 RLC Circuit Phasor Analysis
6.8.2 The Infinite LC Ladder
6.9 Transfer Function for a Difference Equation with
Constant Coefficients*
6.10 MATLAB Commands Review
7. Vectors
7.1 Vectors in Two Dimensions (2-D)
7.1.1 Addition
7.1.2 Multiplication of a Vector by a Real Number
7.1.3 Cartesian Representation
7.1.4 MATLAB Representation of the Above Results
7.2 Dot (or Scalar) Product
7.2.1 MATLAB Representation of the Dot Product
7.3 Components, Direction Cosines, and Projections
7.3.1 Components
© 2001 by CRC Press LLC
7.3.2 Direction Cosines
7.3.3 Projections
7.4 The Dirac Notation and Some General Theorems*
7.4.1 Cauchy-Schwartz Inequality
7.4.2 Triangle Inequality
7.5 Cross Product and Scalar Triple Product*
7.5.1 Cross Product
7.5.2 Geometric Interpretation of the Cross Product
7.5.3 Scalar Triple Product
7.6 Vector Valued Functions
7.7 Line Integral
7.8 Infinite Dimensional Vector Spaces*
7.9 MATLAB Commands Review
8. Matrices
8.1 Setting up Matrices
8.1.1 Creating Matrices in MATLAB
8.2 Adding Matrices
8.3 Multiplying a Matrix by a Scalar
8.4 Multiplying Matrices
8.5 Inverse of a Matrix
8.6 Solving a System of Linear Equations
8.7 Application of Matrix Methods
8.7.1 dc Circuit Analysis
8.7.2 dc Circuit Design
8.7.3 ac Circuit Analysis
8.7.4 Accuracy of a Truncated Taylor Series
8.7.5 Reconstructing a Function from Its Fourier
Components
8.7.6 Interpolating the Coefficients of an (n – 1)-degree
Polynomial from n Points
8.7.7 Least-Square Fit of Data
8.8 Eigenvalues and Eigenvectors*
8.8.1 Finding the Eigenvalues of a Matrix
8.8.2 Finding the Eigenvalues and Eigenvectors Using
MATLAB
8.9 The Cayley-Hamilton and Other Analytical Techniques*
8.9.1 Cayley-Hamilton Theorem
8.9.2 Solution of Equations of the Form
8.9.3 Solution of Equations of the Form
8.9.4 Pauli Spinors
8.10 Special Classes of Matrices*
8.10.1 Hermitian Matrices
dX
dt
= AX
dX
dt
=AX+B(t)
© 2001 by CRC Press LLC
8.10.2 Unitary Matrices
8.10.3 Unimodular Matrices
8.11 MATLAB Commands Review
9. Transformations
9.1 Two-dimensional (2-D) Geometric Transformations
9.1.1 Polygonal Figures Construction
9.1.2 Inversion about the Origin and Reflection about the
Coordinate Axes
9.1.3 Rotation around the Origin
9.1.4 Scaling
9.1.5 Translation
9.2 Homogeneous Coordinates
9.3 Manipulation of 2-D Images
9.3.1 Geometrical Manipulation of Images
9.3.2 Digital Image Processing
9.3.3 Encrypting an Image
9.4 Lorentz Transformation*
9.4.1 Space-Time Coordinates
9.4.2 Addition Theorem for Velocities
9.5 MATLAB Commands Review
10. A Taste of Probability Theory*
10.1 Introduction
10.2 Basics
10.3 Addition Laws for Probabilities
10.4 Conditional Probability
10.4.1 Total Probability and Bayes Theorems
10.5 Repeated Trials
10.5.1 Generalization of Bernoulli Trials
10.6 The Poisson and the Normal Distributions
10.6.1 The Poisson Distribution
10.6.2 The Normal Distribution
Supplement: Review of Elementary Functions
S.1 Affine Functions
S.2 Quadratic Functions
S.3 Polynomial Functions
S.4 Trigonometric Functions
S.5 Inverse Trigonometric Functions
S.6 The Natural Logarithmic Function
S.7 The Exponential Function
S.8 The Hyperbolic Functions
S.9 The Inverse Hyperbolic Functions
Appendix: Some Useful Formulae