Instructors: Peter J. Mucha

Course on canvas.dartmouth.edu.⇗

Syllabus

Schedule
Week Topics
1

Dimensional Analysis and Scaling

  • Tuesday 3/28: Section 1.1
  • Thursday 3/30: Section 1.2
  • Friday 3/31: Self-Similarity

See also Lin & Segel (available online), especially Chapter 1, "What is Applied Mathematics?", and Chapter 6 on dimensional analysis and scaling. For additional references for dimensional analysis and scaling, look at almost any book by G. I. Barenblatt.
2

Regular Perturbation Methods

  • Tuesday 4/4: No class meeting. This is a great time to review Section 1.3 "Differential Equations" at your own speed.
  • Thursday 4/6: Section 3.1
  • Friday 4/7: Section 3.1 continued

See also Perturbation Methods by E. J. Hinch.

See these instructions for obtaining Maple on your computer.
3

Examples

  • Tuesday 4/4: No class meeting.
  • Thursday 4/13: Approximations in Selected Scientific Papers
  • Friday 4/14: No class meeting
4

Perturbation of Eigenvectors & Singular Perturbation

  • Tuesday 4/18: Eigenvector example from Hinch Chapter 1. Dominant balance and singular perturbation for algebraic equations (see Logan Section 3.2, Lin & Segel 9.1)
  • Thursday 4/20: Regular and singular perturbations of ODEs. Conservation of energy. Damped oscillator.
  • Friday 4/21: Initial layer of the damped oscillator (see Logan 3.4)
5

Boundary Layers

  • Tuesday 4/25: Midterm Reading Selections Due (136)
  • Tuesday 4/25: Lin & Segel Section 9.2
  • Thursday 4/27: Re-do Section 9.2 to higher order in Maple
  • Friday 4/28: Lin & Segel Exercise #2a from Section 9.2
6

Multiple Scales

  • Tuesday 5/2: Midterm Exam In Class (46) - In Kemeny 242 & 307
  • Thursday 5/4: Poincaré–Lindstedt Method (Section 3.1.3)
  • Friday 5/5: Multiple scale expansions (Lin & Segel 11.2)
7

Optimal Asymptotic Truncation
8

Asymptotic Expansion of Integrals

  • Tuesday 5/16: No class meeting
  • Thursday 5/18: Laplace's Method (Logan Section 3.6, Lin & Segel 3.2)
  • Friday 5/19: No class meeting
9

Continue approximations of integrals and more examples from the literature

  • Tuesday 5/23:  Laplace's Method with Interior Points and Stirling's Approximation (from Lin & Segel 3.2)
  • Thursday 5/25:  Random Processes (in part from Lin & Segel 3.1 & 3.3)
  • Friday 5/26:  Perturbations in Networks (research papers)
  • Friday 5/26: Final Reading Selections Due (136)
10
  • Tuesday 5/30 (LDOC):  Graduate student presentations of interesting papers and chapters
  • Sunday 6/4: Final Exam at 11:30am (46)