1. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.1 The MuPad interface in MATLAB ®.

2. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.2 Symbolic variables are identified in the workspace window with a "box" icon.

3. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.3 Unless a variable is explicitly defined, it is not listed in the workspace window.

4. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.4 The variable ideal_gas_law is an equation, not an expression.

5. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 12.1 Functions Used to Manipulate Expressions and Equations continued on next slide

6. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 12.1 (continued) Functions Used to Manipulate Expressions and Equations

7. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 12.2 Using the Solve Function continued on next slide

8. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 12.2 (continued) Using the Solve Function

9. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.5 The range of a projectile depends on the initial velocity and the launch angle.

10. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.6 Symbolic expressions can be plotted with ezplot. In the left-hand graph, the default title is the plotted expression and the default range is -2Π to +2Π. In the right-hand graph, titles, labels, and other annotations are added to ezplot with the use of standard MATLAB ® annotation functions.

11. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.7 The ezplot function can be used to graph both implicit and parametric functions, in addition to functions of a single variable.

12. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.8 Use the interactive plotting tools to adjust line style, color, and markers.

13. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 12.3 Symbolic Plotting Functions

14. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.9 Examples of three-dimensional symbolic surface plots.

15. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.10 A variety of symbolic plots.

16. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.11 Projectile range.

17. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.12 Position of a race car. The car speeds up until it reaches the finish line. Then it slows to a stop. (The dotted line indicating the finish line was added after the graph was created.)

18. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.13 The maximum velocity is reached at the finish line.

19. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.14 The race car is accelerating up to the finish line and then is decelerating. The acceleration at the finish line is zero.

20. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 12.4 Symbolic Differentiation

21. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.15 The projectile range as a function of launch angle.

22. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.16 Pressure profile in a piston–cylinder device. In this example, the pressure is constant.

23. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.17 The work produced in a piston–cylinder device is the area under the curve.

24. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Table 12.5 Symbolic Integration

25. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.18 Internal combustion engine.

26. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.19 For an isothermal system, as the volume increases the pressure decreases.

27. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure 12.20 We can estimate the area under the curve with a triangle.

28. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure P12.9 Pendulum described in Problem 12.9.

29. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure P12.12 Car described in problem 12.12.

30. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure P12.19 Separation process with three components: water, ethanol, and methanol.

31. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure P12.25 Trajectory of a projectile.

32. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure P12.32 Tank-filling problem.

33. MATLAB ® for Engineers, Holly Moore Fourth Edition, Global Edition © Pearson Education Limited 2015 All rights reserved. Figure P12.33 Spring problem described in Problem 12.33.