figure 13.1 interpolation between data points.ssjarng.chosun.ac.kr/matlab/chapter11.pdftitle:...

Figure 13.1 Interpolation between data points.

MATLAB® for Engineers, Fourth EditionHolly Moore

Copyright ©2015, 2012, 2009 by Pearson Education, Inc.All rights reserved.

Figure 13.2 Linear interpolation: Connect the points with a straight line to find y.



Figure 13.3 Both measured data points and interpolated data were plotted on the same graph. The original points were modified in the interactive plotting function to make them solid circles.points were modified in the interactive plotting function to make them solid circles.



Figure 13.4 Cubic spline interpolation. The data points on the smooth curve were calculated. The data points on the straight-line segments were measured. Note that every measured point also falls on the curved line.on the straight line segments were measured. Note that every measured point also falls on the curved line.



Table 13.1 Interpolation Options in the Interp1 Function



Table 13.2 Internal Energy of Superheated Steam at 0.1 MPa,as a Function of Temperature



Figure 13.5 Geysers spray high-temperature and high-pressure water and steam.



Table 13.3 Properties of Superheated Steam at 0.1 MPa (Approximately 1 atm)



Figure 13.6 Power plants use steam as a "working fluid."



Figure 13.7 A linear model; the line was "eyeballed."



Table 13.4 Difference between Actual and Calculated Values



Figure 13.8 Data and best-fit line using linear regression.



Figure 13.9 Left-division can be used to force a first-order data fit through zero.



Figure 13.10 Second- and third-order polynomial fits.



Figure 13.11 Fourth- and fifth-order model of six data points.



Figure 13.12 Culverts do not necessarily have a uniform cross section.



Figure 13.13 Hand fit of water flow.



Figure 13.14 Different curve-fitting approaches.



Table 13.5 Heat Capacity of Carbon Dioxide



Figure 13.15 Heat capacity of carbon dioxide as a function of temperature.



Figure 13.16 A comparison of different polynomials used to model the heat-capacity data of carbon dioxide.



Figure 13.17 Interactive basic fitting window.



Figure 13.18 Plot generated with the basic fitting window.



Figure 13.19 Residuals are the difference between the actual and calculated data points.



Figure 13.20 Basic fitting window.



Figure 13.21 Data statistics window.



Figure 13.22 The derivative of a data set can be approximated by finding the slope of a straight line connecting each data point.connecting each data point.



Figure 13.23 The calculated slopes are discontinuous if they are based on data. The appearance of this graph was adjusted with the interactive plotting tools.was adjusted with the interactive plotting tools.



Figure 13.24 The slope of a function is approximated more accurately when more points are used to model the function.function.



Figure 13.25 A comparison of the derivative approximation of sin(x), based on the number of points used.



Figure 13.26 A superior approximation of the derivative is obtained using the centered difference approach, implemented in the gradient function.p g



Figure 13.27 a) Three-dimensional data, such as peaks, are conveniently visualized with a surface plot. b) A combination contour and quiver plot illustrates the magnitude of the partial derivatives.combination contour and quiver plot illustrates the magnitude of the partial derivatives.



Figure 13.28 The area under a curve can be approximated with the trapezoid rule.



Figure 13.29 The area of a trapezoid can be modeled with a rectangle.



Figure 13.30 The integral of a function can be estimated with the trapezoid rule.



Figure 13.31 The integral of a function between two points can be thought of as the area under the curve. These graphs were created using fplot with a function handle representing a third-order polynomial.g p g p p g p y



Figure 13.32 A piston–cylinder device.



Table 13.6 MATLAB®’s Differential Equation Solvers



continued on next slide

Table 13.6 (continued) MATLAB®’s Differential Equation Solvers



continued on next slide

Table 13.6 (continued) MATLAB®’s Differential Equation Solvers



Figure 13.33 This figure was generated automatically by the ode45 function. The title and labels were added in the usual way.in the usual way.



Figure 13.34 This system of equations was solved with ode45. The title, labels, and legend were added in the usual way.usual way.



Figure 13.35 A higher-order differential equation is solved by creating a system of equations that represents the same information. A second-order ODE requires two equations, resulting in two lines represented in the

hi l t t f d f d /dtgraphical output, one for y, and one for dy/dt.



Figure 13.36 A boundary value problem solved using bvp4c.



Figure P13.9 An electrical circuit.



Figure P13.19 A gas turbine used to produce power.



figure 13.1 interpolation between data points.ssjarng.chosun.ac.kr/matlab/chapter11.pdftitle:...

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