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 =...
8 Chapter 8Figure 8.1 Three basis vectors obtained using the Gram‐Schmidt orthogonaliza...Figure 8.2 Eigenvectors and eigenvalues of a covariance matrix.Figure 8.3 Eigenvectors and eigenvalues of a covariance matrix.Figure 8.4 An undamped mass–spring system.Figure 8.5 Solutions for Example 8.6 (results obtained by running the script...Figure 8.6 An N e = 4‐element UCA receiving two signals s 1(n) and s 2(n).Figure 8.7 Spatial spectra and reconstructed signals. (a1) Spatial spectrum Figure P8.5 Householder reflection.
9 Chapter 9Figure 9.1 Grid for an elliptic PDE with Dirichlet/Neumann boundary conditio...Figure 9.2 Temperature distribution over a rectangular plate for Example 9.1...Figure 9.3 Results of various algorithms for a 1D parabolic PDE – heat equat...Figure 9.4 Temperature distribution over a plate for Example 9.3.Figure 9.5 Solution to the 1D hyperbolic PDE for Example 9.4. (a) The soluti...Figure 9.6 Solution to the 2D hyperbolic PDE – vibration of a square membran...Figure 9.7 A region (domain) divided into four triangular subregions.Figure 9.8 The basis (shape) functions for nodes in Figure 9.7 and a composi...Figure 9.9 An example of triangular subregions for FEM.Figure 9.10 FEM solutions for Example 9.6. (a) 31‐point FEM (finite element ...Figure 9.11 The GUI (graphical user interface) window of the MATLAB PDEtool....Figure 9.12 Pull‐down menus from the top menu and its submenu of the MATLAB ...Figure 9.13 Using PDEtool Example 9.1/9.7. (a) Specifying the BCs for the do...Figure 9.14 Using PDEtool Example 9.3/9.8. (a) PDE Specification dialog box....Figure 9.15 Using PDEtool Example 9.5/9.9. (a) PDE Specification dialog box....Figure 9.16 Using PDEtool Example 9.6/9.10. (a) PDE Specification dialog box...Figure P9.7 Refined triangular meshes for Problem 9.7.
10 1Figure A.1 Mean value theorem.
11 9Figure I.1 The MATLAB desktop with Command/Editor/Current folder/Workspace w...Figure I.2 The MATLAB desktop with Command/Editor/Current folder/Workspace w...
Guide
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