Certain lessons in this syllabus are marked CP under the page heading. For these lessons, your instructor may ask you to use SAGE or Maple or the TI92 or another software package to solve and plot, by numerical means, the indicated problem. Many problems need to be solved and plotted by numerical means since these problems may not have an explicit solution written as elementary functions. These problems may help you understand the usefulness of the numerical approach.
| LESSON/PAGES | TOPICS | PROBLEMS |
| 1. | Introduction to Diff. Eqs | p.7: 1,3,11,15-20 |
| 2. | Initial Value Problems | p.15: 1,5,9,17, p.24: 1-8, 15-18 |
| 3. | Review of separable and | |
| 1st order linear | p39, 1,7,16,21; p 47, 1,2,8,21,25 | |
| 4. | App's (falling body/cooling/circuits) | p.64: 23,28 |
| 5. | Numerical Solutions | p 108, 1 (all parts) |
| 6 | Existence and uniqueness | p117, 1-3 |
| 7 | Review | |
| 8. | IVPs and BVPs. | p.142: 1,9,10,20 |
| . | p151 1,3,5,7,8 | |
| 9,10. | Homogeneous w/const. coeffs | p.164: 1,3,5,7,9,17,18 |
| p.172: 1,3,11,12,17 | ||
| p230, 1,3,5,7,8,12,29 | ||
| 11., 12. | Undeter. Coeffs. or Annihilators | p.184: 1,2,13,17 |
| 13. | Variation of Parameters | p.190: 1,3,5 |
| 14. | review | |
| 15. | Test 1 (no calculator) |
| LESSON/PAGES | TOPICS | PROBLEMS |
| 16., 17. | Springs (Free) | p.203: 1,3,5,6 |
| 18. | Springs (Forced), Circuits | p.214: 5,11 |
| 20. | Circuits | p203, 8, 12 |
| 21. | Series solns, I | p 249, 1, 3, 9,17,18,19,21,22 |
| 22. | Series solns II | p259, 1, 2, 3 |
| 23. | Laplace Transform | p.312: 1,3,6-8 |
| 24 | Inverse Laplace/Derivatives | p.322: 1-4,11,12,24,25 |
| 25. | First Translation Theorem | p.329: 1,3,7,13,14,24,25 |
| 26. | and Unit step functions | |
| 27. | Review | |
| 28. 328-333 | 7.3 Unit Step | p.337: 1,2,12 |
| 29. 305-313 | Dirac delta fcn, | p344, 1,2,3,14 |
| 30. | Convolution thrm, | p351, 4,5,8,9,13 |
| 31. | Review | |
| 32. | Test 2 | |
| 33. | Intro to systems of DEs | p360, 1,2,5,20,21 |
| Lanchester's eqns | ||
| 34. | Intro to matrices | p372, 1,3,6,8,10,12,22,23 |
| 35. | row reduction | |
| 36. | row reduction, inverses, | |
| determinants | ||
| 37. | Cramer's rule, eigenvalues, | |
| eigenvectors | p183, 1, 2, 6, 7, 15-17 | |
| 37. | review | |
| 38. | Systems of DEs ( | p.398: 1,2, 15 |
| 39. | Systems of DEs | p.410: 1,2,9 |
| 40 | 7.6 Non-homog systems of DEs | |
| (by Laplace transforms) | p. 439, 1, 2 | |
| 42. 319-322 | 7.6 Electrical networks | |
| (using Laplace transforms) | p.411, 25, 26, p 439, 13 | |
| 43. 381-385 | 9.4 Euler's Method for higher | |
| order DEs and systems | p.481: 1(a), 8 (by | |
| Euler's method) | ||
| 44. | review | |
| 45. | Test 3 |
| LESSON/PAGES | TOPICS | PROBLEMS |
| 46. 465-468 | Separation of Variables | p.575: 1,2, p610, 1, 2 |
| Transport equation (optional) | class notes | |
| 47. | Orthogonality+FS | p. 585: 14,19, 20 |
| 48 | Fourier Series | p.592, 1, 2, 9 |
| 49. | Fourier Sine and Cosine Series | p.600: 1,3,5,7,9,15,16 |
| 50. | Fourier Sine and Cosine Series | |
| 51. | Heat Equation | p.610, 7, 8, 9 |
| 52. 475-477 | 12.3 Wave Equation | p.632. 1,4 |
| 53. | review | |
| 54 | Schrödinger's eqn | class notes |
| 55. | Review | |
| 56. | Test 4 | |
| 57. | final exam review | |
| 58. | final exam review | |
Class web page:
http://cadigweb.ew.usna.edu/~wdj/teach/sm212/
You will find the policy statement, some lecture notes, and
old hourly and final exams there.
For hints on using the TI92, see
http://cadigweb.ew.usna.edu/~wdj/teach/sm212_ti92.html
Some instructors may allow for extra credit computer projects using the free program SAGE (www.sagemath.org). Please ask your individual instructor about this.