Math 396: SCHEDULE |
Week 1: Tue Jan 20 | Introduction to applied math: dimensional analysis Logan (1-8) |
Week 2: Tue Jan 27 | Practicum: Students present solutions to HW problems (5-10 mins each) Alexander & Sfregola (1.1.1)McCalla & Bennett (1.1.2), Spahn & Hoewisch (1.1.4) The Buckmigham Pi Theorem: Statement, Proof & Application |
Week 3: Tue Feb 3 | Practicum: Students present oral solutions to HW problems from page 17 (5-10 minutes each) Sfregola, Wade & Miller (#4) Wong, McCalla & Bennett (#1), Alexander, Spahn & Hoewisch (#2) Introduction to scaling. Section 1.2 |
Week 4: Tue Feb 10 | Practicum: Students present oral solutions to HW problems from page 30 (5-10 minutes each). One written solution per group. #1: Hoewisch, Wade & Sfregola #2: Wong, Bennett & McCalla #3: Spahn, Alexander & Miller Scaling continued. Section 1.2 |
Week 5: Tue Feb 17 | NO CLASS! (Buckmire out of town) |
Week 6: Tue Feb 24 | Practicum: Students present oral solutions to homework problems (5-10 minutes each). One written solution per group. Group 1: Bennett, Alexander & Hoewish: Use scaling "Choice #2" from Week #4 worksheet to rescale the Projectile Problem and explain why Choice #2 is NOT a good scaling choice by showing it has non-physical solutions for very small epsilon. Discuss how to estimate solutions if epsilon were NOT very very small also. calculate how big V would have to be for epsilon to be greater than 0.1. Group 2: Wong, McCalla & Miller: Use scaling "Choice #3" from Week #4 worksheet to rescale the Projectile Problem and explain why Choice #3 is a good scaling by solving the problem. Go back into unscaled variables as well and show the solution is h(t)=0.5gt^2+Vt. Group 3: Spahn, Wade and Sfregola. Prepare solutions to Page 33,
#11. |
Week 7: Tue Mar 3 | Practicum: Students present oral solutions to homework problems (5-10 minutes each). One written solution per group. GROUP 1: (Spahn, Wong, Mccalla) Logan, p. 111 #1(b) GROUP 2: (Bennett, Miller, Alexander) Logan, p. 101 #6. GROUP 3: (Sfregola, Wade, Hoewisch) Logan, p. 101, #7. Completion of (Regular and Singular) Perturbation of Algebraic Equations |
SPRING BREAK | |
Week 8: Tue Mar 17 | Practicum: Students present oral solutions to homework problems (5-10 minutes each). One written solution per group. GROUP 1: (Spahn, Wong, Mccalla) Logan, p. 111 #1(b) GROUP 2: (Bennett, Miller, Alexander) Logan, p. 101 #6. GROUP 3: (Sfregola, Wade, Hoewisch) Logan, p. 101, #7. Introduction of Regular and Singular Perturbations of Ordinary Differential Equations. |
Week 9: Tue Mar 24 | Practicum: Students present oral solutions to homework problems (5-10 minutes each). One written solution per group. Continuation of Regular and Singular Perturbations of Ordinary Differential Equations. |
Week 10: Tue Mar 31 | Practicum: Students present oral solutions to homework problems (5-10 minutes each). One written solution per group. GROUP 1: (Bennett, Wong, Wade) Logan, p. 100, #2. GROUP 2: (Hoewisch, Miller, Alexander) Logan, p. 103, #14. GROUP 3: (Sfregola, McCalla, Spahn) Logan, p. 103, #16.
How Regular Perturbation Methods can Fail with certain ODEs. |
Week 11: Tue Apr 7 | Practicum. Students present oral solutions to homework problems GROUP 1: (Sfregola, Wade, Wong ) Logan, p. 100, #8(a). GROUP 2: (Miller, Hoewisch, Spahn ) Logan, p. 101, #8(b). GROUP 3: ( McCalla, Alexander, Bennett) Logan, p. 101, #8(c).
Poincare'-Lindstedt Method applied to Duffing's Equation |
Week 12: Tue Apr 14 | No Practicum. QUIZ on Non-dimensionalization and (TAKE-HOME QUIZ) on regular and singular perturbation! Introduction to Boundary Layer Theory. |
Week 13: Tue Apr 21 | |
Week 14: Tue Apr 28 | Individual Practicum. Students select their
own problem and have 5 minutes to present the solution in oral form. You
may also submit a written solution of the problem. All students get to
select their own problem! Suggested problems: Logan, p. 121, #1(a) Logan, p. 121, #1(b) Logan, p. 121, #1(b)
Party! |
Last Updated April 21, 2009