Won Y. Yang - Applied Numerical Methods Using MATLAB

11 9Table I.1 Some frequently used MATLAB commands.Table I.2 Graphic line specifications used in the plot()command.Table I.3 Functions and variables in MATLAB.

1 Chapter 1 Figure 1.1 Plot of a 5 × 2 matrix data representing the variations of the hi... Figure 1.2 Examples of graphs obtained using the ‘ plot()’ command. (a) Dat... Figure 1.3 Graphs drawn by using various graphic commands. Figure 1.4 3D graphs drawn by using plot3(), mesh(), and contour(). Figure 1.5 Distribution (histogram) of noise generated by the rand()/ ran... Figure 1.6 Process of adding two numbers, 3 and 14, in MATLAB. Figure 1.7 Graphs of sinc functions. Using ‘ sinc1()’ without division‐by‐z... Figure P1.5 Plotting the graph of f ( x ) = tan x . Figure P1.10 The characteristic of an analog‐to‐digital converter (ADC). Figure P1.13 The graph of piece‐wise polynomial functions. Figure P1.20 Process of addition/subtraction with four mantissa bits. Figure P1.28 Graphs for Problem 1.28. (a1) A rectangular pulse function r D( t

2 Chapter 2 Figure 2.1 A minimum‐norm solution.Figure 2.2 Graphs for Eqs. (E2.6.1a,b).

3 Chapter 3Figure 3.1 The graph of a third‐degree Lagrange polynomial.Figure 3.2 Interpolation from the viewpoint of approximation. (a) 4/8/10th‐D...Figure 3.3 Chebyshev nodes (with N = 4). (a) 4/8/10th‐degree polynomial appr...Figure 3.4 Approximation using the Chebyshev polynomial.Figure 3.5 Chebyshev polynomial functions. (a) T 0( x ′) = 1, (b) T 0( x ′) = x ′, ...Figure 3.6 Pade approximation and Taylor series expansion for f ( x ) = e x(Exa...Figure 3.7 Cubic splines for Example 3.3.Figure 3.8 2D interpolation using Zi=interp2()on the grid array gener...Figure 3.9 Two‐dimensional approximation (Example 3.5). (a) True function, (...Figure 3.10 Polynomial curve fitting by the LS method. (a) Approximating pol...Figure 3.11 LS curve fitting and WLS curve fitting for Example 3.7. (a) Fitt...Figure 3.12 Using ‘cftool’ for curve fitting.Figure 3.13 The DFT(FFT) {X(k), k = 0 : N − 1...Figure 3.14 DFT spectra of a two‐tone signal. (a) polar(th, r ), (b) semilog x (Figure 3.15 Interpolation/smoothing using DFS/DFT. (a) Original discrete‐tim...Figure P3.4 Chebyshev nodes.Figure P3.9 Coordinates and path of a robot planned using the cubic spline. ...Figure P3.11 LS fitting curves for data pairs with various relations.Figure P3.15 LS and WLS fitting curves to y = axe bx.Figure P3.17.1 Two rectangular pulses, a triangular pulse, and a dual triang...Figure P3.17.2 Effects of sampling period, zero‐padding, and whole interval ...Figure P3.18 The effect of windowing on DFT spectrum. (a) Rectangular window...

4 Chapter 4Figure 4.1 Chebyshev nodes. (a) . (b) .Figure 4.2 Bisection method for Example 4.2. (a) Graphic description of the ...Figure 4.3 False position method for solving f ( x ) = tan( π − x ) − x .Figure 4.4 Solving nonlinear equations f ( x ) = 0 using the Newton method. (a)...Figure 4.5 Secant method for solving f ( x ) = tan( π − x ) − x .Figure 4.6 Solving nonlinear equations f ( x ) = 0 using the Newton method. (a)...Figure 4.7 Solving nonlinear equations f ( x ) = 0 using the Newton method.Figure 4.8 A BJT circuit and its PSpice schematic with DC (bias point) analy...Figure 4.9 A complementary BJT circuit and its PSpice schematic. (a) A compl...Figure P4.1 Fixed‐point iteration for solving f ( x ) = x 2− 3 x + 1 = 0. (a) ....Figure P4.3 Bisection method for solving f ( x ) = tan( π − x ) − x = 0.Figure P4.10 A BJT circuit and its PSpice simulation results with DC (bias p...Figure P4.11 A BJT circuit (a) and its PSpice schematic with DC (bias point)...Figure P4.12 An NMOS circuit (a) and its PSpice schematic with DC (bias poin...Figure P4.14 Single‐stub impedance matching.Figure P4.15 Two‐port networks in cascade interconnection.

5 Chapter 5Figure 5.1 Forward/central difference approximation error of the first deriv...Figure 5.2 Forward/central difference approximation error of the first deriv...Figure 5.3 Various methods of numerical integration using Newton–Cotes rules...Figure 5.4 Subintervals (segments) and their boundary points (nodes) determi...Figure 5.5 Region for a double integral.Figure 5.6 One‐fourth (1/4) of a unit sphere (with the radius of 1).Figure 5.7 A piecewise linear (PWL) waveform.Figure 5.8 A piecewise linear (PWL) waveform.Figure P5.5 The graph of the integrand function of the integral (P5.5.1)Figure P5.11 Bit error rate (BER) vs. SNR curves for multidimensional (ortho...Figure P5.14 A unit sphere.

6 Chapter 6Figure 6.1 Numerical solutions of the DE y′ ( t ) + y ( t ) = 1 with y (0) = ...Figure 6.2 Numerical solutions of the DE y ′( t ) + y ( t ) = 1 with y (0) = 0.Figure 6.3 Numerical solutions and their errors for the DE y ′( t ) = − y ( t ) + 1...Figure 6.4 Numerical solutions and their errors for the DE y ′( t ) = y ( t ) + 1....Figure 6.5 Numerical/analytical solutions of the state equation (6.5.2)/(6.5...Figure 6.6 Solutions of the discretized state equation (6.5.21).Figure 6.7 Solution graphs for Example 6.1. (a) Numerical solution using o...Figure 6.8 Solution graphs for Example 6.2. (a) Numerical solution using o...Figure 6.9 The solution of the BVP (6.1) obtained by using the shooting meth...Figure 6.10 The solution of the BVP (6.1) obtained by using the finite diffe...Figure P6.1.1 Contours and gradient vectors for a function of two variables Figure P6.1.2 A surface and its normal vectors each plotted using ‘surf()’ a...Figure P6.1.3 Slope/direction fields and possible solutions for differential...Figure P6.4.1 Block diagram of a PLL circuit.Figure P6.4.2 A DC motor system.Figure P6.4.3 A two‐mesh RC circuit.Figure P6.5 A model for vehicle suspension system. (a) The block diagram and...Figure P6.6 The paths of a satellite with the same initial position and diff...Figure P6.7 The output voltages of an RC diode circuit obtained from PSpice ...Figure P6.13 Solutions of eigenvalue BVPs.

7 Chapter 7Figure 7.1 Illustration of the golden search method.Figure 7.2 Illustration of the quadratic approximation method.Figure 7.3 Illustration of the Nelder–Mead method. (a) Notations used in the...Figure 7.4 Illustration of the Newton's method and steepest descent method....Figure 7.5 Illustration of the conjugate gradient method.Figure 7.6 Some illustrative functions used for controlling the randomness –...Figure 7.7 Flowchart of genetic algorithm (GA).Figure 7.8 Reproduction/crossover/mutation in one iteration of genetic algor...Figure 7.9 The objective and constraint functions for Example 7.1. (a) Mesh‐...Figure 7.10 The objective and constraint functions for Example 7.3.Figure 7.11 The objective and constraint functions for Example 7.4. (a) Mesh...Figure 7.12 Minimum points in the admissible region (satisfying the constrai...Figure 7.13 The contours, local minima/maxima, and saddle points of the obje...Figure 7.14 The result of using the MATLAB built‐in function ‘lsqnonlin()’ f...Figure 7.15 Illustration of the Newton's method and steepest descent method....Figure 7.16 The objective function, constraints, and solution of an LP probl...Figure 7.17 The objective function, constraints, and solution of an ILP prob...Figure 7.18 Branch‐and‐bound (BB) search (enumeration) tree for finding the ...Figure 7.19 A neural network (NN) with supervised learning scheme.Figure 7.20 Error reducing as the training process goes on.Figure 7.21 An FIR filter.Figure 7.22 Updating the parameter of an adaptive predictor using the steepe...Figure 7.23 LMS and RLS adaptive parameter estimation. (a) Parameter estimat...Figure P7.2 The contour, extrema, and saddle points of the objective functio...Figure P7.3 The graph of f(x) = sin(1/x)/{(x − 0.2)2 + 0.1}...Figure P7.4 The contour for the objective function (P7.4.1) and lines showin...Figure P7.10 The site of a new warehouse and the locations factories.Figure P7.11 Refraction of a light ray at an air‐glass interface.Figure P7.13 Two objective functions for training a neural network. (a) J a=...