SM212    Differential Equations    Fall 2000-2001
Syllabus

Link to Website

Textbook: Differential Equations with Boundary Value Problems, 3rd ed., by Dennis G. Zill and Michael R. Cullen.

Below are the topics that will be covered in SM212 this semester. Most lessons have both a reading assignment and a problem assignment. As the course progresses you will see that the process of solving differential equations can be algebraically complicated and therefore a computer algebra system such as Maple is a useful tool in the solution process, especially as the problems approach ''real world'' complexity. In addition to the daily problem assignments your instructor may assign computer problems to be done with the aid of Maple. These problems are found on the Mathematics Department web page under Math Courses-Differential Equations-SM212.

Lesson/Pages

Topic

Problems

1. p. 1-10

Basic definitions and Terminology

p. 10: 1,3,7,9,11,15,18,38,41

2. p. 12-16. 
Examples 1,2,3

Mathematical models of physical problems

p. 26: 1,2,3,4,12,13,16

3. p. 38-44

Separable DE’s

p. 44: 3,5,13,17,31,43,49,57

4. p. 53-59

Exact DE's

p. 60: 3,9,11,15,25,29,35

5. p. 62-69

Linear DE's

p. 69: 5,9,15,23,47,49,55

6. p. 98-99. Example 4 Computer Project 1

Newton cooling/ falling object

p. 103: 12,13,14,27

7. p. 101-102

Mixing

p. 103: 21,22,23,25

8. p. 488-492

Direction fields/ Euler's method

p. 492: 1,3; p. 502: 1(see Prob. 57, p.46),2,9(a)

9. p. 499-502

Improved Euler method

p. 502: 13(d) (h = 0.1 only)

10. Review

   

11. Test I

   

12. p. 130-132; 134-136; 139-141

Higher order DE's

p. 149: 1,4,11,15,18,31

13. p. 159-164

Second order homogeneous DE's

p. 167: 1,3,5,7,9,17,39,41,61

14. p. 164-166

Higher order homogeneous DE's

p. 167: 19,21,23,27,33,49

15. p. 145-149; 181-186

Differential operators

p. 186: 11, 15, 19, 21, 23, 27, 29, 31

16. p. 187-193

Undetermined coefficients

p. 193: 5,9,13,17,39

17. p. 212-218

Simple harmonic motion

p. 219: 1,3,9,11,13,21,25

18. p. 222-229

Damped motion

p. 229: 1,3,7,9,11,13,

17,19

19. Review

   

20. p. 232-236

Forced motion, pure resonance

p. 239: 1,3,5,15

21. p. 236-239
Computer Project 2

Resonance for damped springs

p. 239:10,11,13

22. Review

   

23. p. 18-19; 242-245

Electrical circuits

p. 246: 1,3,7,9,13

24. p. 523-524

Euler's method for higher order DE's and systems

p. 527: 1,7 (use Euler, not Runge-Kutta)

25. Review

   

26. Hour Test II

   

27. p. 324-333

Laplace transforms

p. 333: 3,5,7,13,21,29,31,37,39

28. p. 335-338

Inverse LT's

p. 341: 1,3,5,9,15,21

29. p. 338-341

Inverse LT's

p. 341: 25,29,31,33

30. p. 343-345; 351-352

Translation and derivative theorems

p. 352: 1,5,9,11,13,15,17,19,21,37,41

31. p. 355-356; 363-367

Solving DE's with LT's

p. 374: 7,9,13,17,49

32. p. 345-350

Unit step function

p. 352: 23,25,27,31,33,35,45,47,53,57

33. p. 367-368

DE's involving unit step function

p. 374: 21,23,25,43,52

34. p. 356-359

Convolution

p. 361: 9,19,21,25,27; p. 374: 11

35. p. 359-361; 371-372 Computer Project 3

LT's of periodic functions

p. 361: 31,33; p. 374: 46,47

36. p. 379-383

Dirac delta function

p. 383: 1,3,5,11

37. p. 398-403

Systems of DE's by Laplace transforms

p. 405: 1,7,13,14

38. p. 403-405

Electrical networks

p. 405: 15,21

39. Review

   

40. Hour Test III

   

41. p. 413-422

Matrices

p. 432: 1,3,11,13,15,23

42. p. 423-427

Reduced row echelon form

p. 432: 31,33,37,39

43. p. 427-432

Eigenvalues and eigenvectors

p. 432: 41,43,45,49,50

44. p. 453-456

Homogeneous linear systems: real eigenvalues

p. 450: 1,7; p. 466: 1,3,9,13,14

45. p. 457-461

Homogeneous linear systems: complex eigenvalues

p. 466: 15,17,23

46. p. 473-476

Nonhomogeneous systems

p. 476: 1,11,19,25

47. p. 598-603

Orthogonal functions

p. 603: 3,5,7,11,17, Expand the function f(x) = x in terms of the orthogonal set given in Problem 11.

48. p. 604-609

Fourier series

p. 609: 1,3,5,11, (in each case sketch the function to which the series converges over three periods) 17

49. p. 611-617

Sine and cosine series

p. 619: 1,3,5,13,25,29,33

50. p. 644-647

PDE's and separation of variables

p. 648: 3,5,9,11

51. p. 650-651; 657-659

Heat equation, zero ends case

p. 660: 1,2

52.

Heat equation, insulated ends case

p. 660: 3,4

53.

Heat equation, heat transfer from lateral surface

p. 660: 5,6

54. Review

   

55. Hour Test IV