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.

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.

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)

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

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

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

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

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 Approximation (Section 3.2)
  • Friday 5/17: Finish Stirling Approximation and an example of term-by-term integration

9

MWF

Chapter 3: Random Processes and PDEs

  • Monday 5/20: Watson's Lemma, Asymptotics, and Optimal Asymptotic Truncation (finishing and extending Section 3.2)
  • Tuesday 5/21: No class meeting
  • Wednesday 5/23:  Section 3.3
  • Friday 5/26:  Finish Section 3.3 and 3.4

10

W only
  • Monday 5/27: No class or office hours (reading day)
  • Tuesday 5/28: No class meeting (office hours 1–2)
  • Wednesday 5/29 (LDOC): Personal reflections using such methods (with links to research papers)
  • Sunday 6/2: Final Exam at 11:30am