Instructors: Peter J. Mucha
Course on canvas.dartmouth.edu.⇗
Schedule
| Week |
Topics |
|
1
MTWF
|
Chapter 6: Dimensional Analysis and Scaling
- Monday 3/25: Section 1.1 "On the Nature of Applied Mathematics" & Section 6.2
- Tuesday 3/26: Finish Section 6.2, and Section 6.1
- Wednesday 3/27: Section 6.3
- Friday 3/29: Introduction to Perturbation Theory. See these instructions for obtaining Maple on your computer.
For additional references for dimensional analysis and scaling, look at almost any book by G. I. Barenblatt.
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|
2
MTW
|
Chapter 7: Regular Perturbation Theory
- Monday 4/1: Section 7.1
- Tuesday 4/2: Section 7.2 (office hours 2:15–2:45)
- Wednesday 4/3: Detailed walk through Maple notebooks
- Friday 4/5: No class meeting.
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3
WF
|
Series solutions and an application of perturbations
- No class meetings or office hours on Monday 4/8 or Tuesday 4/9
- Wednesday 4/10: Local behavior near ordinary points of homogeneous linear equations
- Friday 4/12: Network dynamical importance from perturbations (if interested, see also Perturbation Methods by E. J. Hinch for more details about eigenvalues and eigenvectors)
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4
MWF
|
Chapter 9: Singular Perturbation & Initial Layers
- Monday 4/15: Dominant balance and singular perturbation for algebraic equations (Section 9.1)
- Tuesday 4/16: No class meeting (office hours 12:00–12:50)
- Wednesday 4/17: Continue Section 9.1
- Friday 4/19: Initial layer example
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5
MWF
|
Boundary Layers & Chapter 10: Biochemical Kinetics
- Monday 4/22: Section 9.2
- Tuesday 4/23: Extra office hours (12:15–1:05 & 1:30–2:30)
- Wednesday 4/24: Section 9.2 to higher order in Maple
- Friday 4/26: Section 10.1
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6
MWF
|
Model Problems & Midterm
- Monday 4/29: Section 10.2
- Tuesday 4/23: Extra office hours (12:15–1:05 & 1:30–2:30)
- Wednesday 5/1: Midterm Exam In Class
- Friday 5/3: Finish Section 10.2
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|
7
MTW
|
Chapter 11: Return of the Simple Pendulum
- Monday 5/6: Stability of Equilibria (Section 11.1) and Conservation of Energy
- Tuesday 5/7: Poincaré–Lindstedt Method (Section 2.2 and Logan Section 3.1.3)
- Wednesday 5/8: Method of Multiple Scales (Section 11.2)
- Friday 5/10: No class meeting
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8
MTWF
|
Chapter 3: Random Processes and Asymptotic Expansion of Integrals
- Monday 5/13: Section 3.1
- Tuesday 5/14: Laplace's Method (Section 3.2)
- Wednesday 5/15: Stirling Series (Section 3.2) and Optimal Asymptotic Truncation
- Friday 5/17: (buffer)
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9
MWF
|
Chapter 3: Random Processes and PDEs
- Monday 5/20: Section 3.3
- Tuesday 5/21: No class meeting
- Wednesday 5/23: Section 3.3 and 3.4
- Friday 5/26: Section 3.4
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10
W only
|
- Monday 5/27: No class (reading day)
- Tuesday 5/28: No class meeting (office hours 1–2)
- Wednesday 5/29 (LDOC): Perturbations in multilayer networks (research paper)
- Sunday 6/2: Final Exam at 11:30am
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