Math 396 / Math 395

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Ron Buckmire: 
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Course Schedule

Syllabus

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.

Introduction to Perturbations on Algebraic Equations 

 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
(5-10 minutes each). One written solution per group

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

Boundary Layer Theory Continued: Asymptotic Matching.
 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)
 εy''+2y'+y=0, y(0)=0, y(1)=1.

Logan, p. 121, #1(b)
 εy''+y'+y2=0, y(0)=1/4, y(1)=1/2.

Logan, p. 121, #1(b)
 εy''+*1+x)y'=1, y(0)=0, y(1)=1+ln(2).

 

 

Party!

 

Last Updated April 21, 2009