1. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.1 A continuous and discontinuous function at the origin. (a) f(t) is continuous at the origin. (b) f(t) is discontinuous at the origin.

2. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.2 The step function.

3. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.3 The linear approximation to the step function.

4. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.4 A step function occurring at t = a when a > 0.

5. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.5 A step function Ku(a - t) for a > 0.

6. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.6 The function for Example 12.1.

7. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.7 Definition of the three line segments turned on and off with step functions to form the function shown in Fig. 12.6.

8. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.8 A magnified view of the discontinuity in Fig. 12.1(b), assuming a linear transition between −  and + .

9. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.9 The derivative of the function shown in Fig. 12.8.

10. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.10 A variable-parameter function used to generate an impulse function.

11. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.11 A graphic representation of the impulse K  (t) and K  (t - a).

12. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.12 The first derivative of the impulse function. (a) The impulse-generating function used to define the first derivative of the impulse. (b) The first derivative of the impulse-generating function that approaches  ۱ (t) as  → 0.

13. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.13 The impulse function as the derivative of the step function: (a) f(t)→u(t) as  → 0 ; and (b) f’(t) →  (t) as  → 0.

14. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.14 A decaying exponential function.

15. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.15 A sinusoidal function for t > 0.

16. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel

17. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel

18. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel

19. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.16 A parallel RLC circuit.

20. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel

21. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.17 Plotting poles and zeros on the s plane.

22. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.18 A series RLC circuit with a 60 Hz sinusoidal source.

23. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure 12.19 Plot of the inductor current for the circuit in Fig. 12.18.

24. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure P12.2

25. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure P12.3

26. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure P12.6

27. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure P12.21

28. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure P12.27

29. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure P12.28.

30. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure P12.29

31. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure P12.30

32. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure P12.31

33. Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Figure P12.32