Order of Magnitude Estimation and Approximate Astrophysics
Lecture Time/ Credits: 30/2
Pre-requisite : English
Instructors : Stephen Justham
To develop skills in solving general problems, even when minimal information is available, especially through thoughtful estimation, physical insight and appropriate approximations.
This course will try to develop skills in estimation and physical insight. This will be done mainly through practice on examples, but we will emphasise strategies such as dimensional analysis and use of symmetry or limiting cases.
Topics and Schedule:
(This assumes 15 two-hour classes. Several topics are likely to be combined in each week, i.e., the weekly example problems will often involve the use of more than one approach
1. Estimation and basic Fermi problems: becoming comfortable with the unknown.(2课时)
2. Analogies and abstraction.(2课时)
3.Dimensionless quantities: how big is big?(2课时)
4.Taking advantage of symmetry and simplifications.(2课时)
5.Conserved quantities and the assumption of equilibrium. (2课时)
6.Scaling relations and self-similar solutions. (4课时)
7. Dimensional analysis (4课时)
8. Limiting cases.(4课时)
9. Event rates, astrophysical timescales, and rates of change. (2课时)
10.Further applications of physics to the real world (4课时).
11. Exam. (2课时)
This course will mostly be taught in English. However, unlike the literature reading course, the main work in the course should not significantly rely on English language ability.
Much of the class time will be spent on small-group solutions and discussion of example problems, intended to illustrate approaches to problem solving. Some of the examples will be astrophysical, others will be drawn from questions which will hopefully be interesting to consider and fun to solve. The course is intended to be enjoyable, but not to be easy; the class time should be spent actively thinking, and so class attendance is not optional.
“The Art of Insight in Science and Engineering” by Sanjoy Mahajan. Which is available to download for free in PDF from here:https://mitpress.mit.edu/books/art-insight-science-and-engineering.
Students may also optionally enjoy reading: The Feynman Lectures on Physics
(see http://www.feynmanlectures.caltech.edu )“Street-Fighting Mathematics” by Sanjoy Mahajan, which is available to download for free in PDF from here: https://mitpress.mit.edu/books/street-fighting-mathematics .