MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 13.1 Interpolation between.

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MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 13.1 Interpolation between data points.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 13.2 Linear interpolation: Connect the points with a straight line to find y.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. 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.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. 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.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 13.1 Interpolation Options in the Interp1 Function

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 13.2 Internal Energy of Superheated Steam at 0.1 MPa, as a Function of Temperature

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 13.5 Geysers spray high-temperature and high-pressure water and steam.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 13.3 Properties of Superheated Steam at 0.1 MPa (Approximately 1 atm)

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 13.6 Power plants use steam as a "working fluid."

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 13.7 A linear model; the line was "eyeballed."

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 13.4 Difference between Actual and Calculated Values

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 13.8 Data and best-fit line using linear regression.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 13.9 Left-division can be used to force a first-order data fit through zero.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Second- and third-order polynomial fits.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Fourth- and fifth-order model of six data points.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Culverts do not necessarily have a uniform cross section.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Hand fit of water flow.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Different curve-fitting approaches.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 13.5 Heat Capacity of Carbon Dioxide

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Heat capacity of carbon dioxide as a function of temperature.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure A comparison of different polynomials used to model the heat-capacity data of carbon dioxide.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Interactive basic fitting window.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Plot generated with the basic fitting window.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Residuals are the difference between the actual and calculated data points.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Basic fitting window.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure Data statistics window.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure The derivative of a data set can be approximated by finding the slope of a straight line connecting each data point.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure The calculated slopes are discontinuous if they are based on data. The appearance of this graph was adjusted with the interactive plotting tools.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure The slope of a function is approximated more accurately when more points are used to model the function.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure A comparison of the derivative approximation of sin(x), based on the number of points used.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure A superior approximation of the derivative is obtained using the centered difference approach, implemented in the gradient function.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 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.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure The area under a curve can be approximated with the trapezoid rule.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure The area of a trapezoid can be modeled with a rectangle.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure The integral of a function can be estimated with the trapezoid rule.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 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.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure A piston–cylinder device.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 13.6 MATLAB ® ’s Differential Equation Solvers continued on next slide

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 13.6 (continued) MATLAB ® ’s Differential Equation Solvers continued on next slide

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 13.6 (continued) MATLAB ® ’s Differential Equation Solvers

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure This figure was generated automatically by the ode45 function. The title and labels were added in the usual way.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure This system of equations was solved with ode45. The title, labels, and legend were added in the usual way.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 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 graphical output, one for y, and one for dy/dt.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure A boundary value problem solved using bvp4c.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure P13.9 An electrical circuit.

MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure P13.19 A gas turbine used to produce power.