Estimation and Approximation in Physics
Instructor
Roman Grigoriev
Office: Howey W304
Phone: 404-385-1130
E-mail: roman.grigoriev at physics.gatech.edu
Office hours: TBD
Place and Times
Textbook
An appropriate textbook does not exist, but there are several good sources of relevant information:
We will rely primarily on the lecture notes. In addition, you should print out a list of useful physical constants and values that come up often in order-of-magnitude calculation.
Course Description
The aim of this course is to help you transition from taking classes
to doing research by developing your problem-solving skills and
integrating the knowledge from your undergraduate (as well as
graduate) studies. We will focus on approximations (from very coarse
to very accurate) as a tool both to explore unfamiliar problems by
identifying the important physical phenomena and to check the results
of detailed (analytical or numerical) calculations. Order-of-magnitude
estimates, dimensional analysis, scaling arguments, and perturbation
theory will be used to analyze problems in classical and quantum
mechanics, thermodynamics and statistical physics, fluid dynamics,
biophysics, and astrophysics. However, the main emphasis will be on
methods rather than phenomenology.
Pre-requisites
You are expected to be familiar with classical and quantum mechanics and electricity and magnetism at the level of PHYS 3201, PHYS 3123, and PHYS 3143.
Course Goals and Learning Outcomes
Upon successful completion of this course, you should be able to
- Research an unfamiliar problem and identify the relevant physics
- Formulate a mathematical description of the problem
- Construct a simplified description that enables an analytical solution
- Obtain an approximate closed form solution that captures the essential physics
Grading
The class will be highly interactive, with all students expected to actively participate in the discussion. The grades will be based on class participation (10%) as well as homework (60%) and a final project (30%). You can discuss problems
with each other, but the solutions have to be executed and submitted individually.
Some problem sets will include more challenging problems (marked by an asterisk) that are required for graduate students and optional (for extra credit) for undergraduates.
The expected level of the project will also differ for the undergraduate and graduate students.
Grading scale:
A = 80-100%,
B = 70-80%,
C = 60-70%,
D = 50-60%,
F = 0-50%
Course Content
1. Counting and estimation
2. Scaling
3. Dimensional analysis
4. Differential equations and scales
5. Perturbation theory
6. (Self)similarity
7. Atomic and molecular properties
8. Biomechanics
- Physical size:
- Skeletons of a
mouse and an
elephant. A paper with a more elaborate analysis of bone scaling.
- Paper on overall size of different types of animals.
- Distribution networks:
- Locomotion:
- Water striders walking (and resting) on water:
[movie],
[movie]
- "Jesus Christ" lizard running on water:
[movie],
[movie],
[movie]
9. Nuclear physics and astrophysics
10. Multi-physics problems
- Freezing boiling water: [movie]
- Shape and size of falling droplets and rising bubbles.
- Paper with detailed analysis of droplet breakup.
Homework Assignments
Final project
- Please type up the project in the form of a scientific report or paper with a short introduction and conclusions. If figures/illustrations are essential, please include these as well. You can send the report to me electronically as a PDF (this is my preference). If you want to submit a printed version and I am not in my office, please slide it under the door. The project is due Thursday, May 3 at 3pm.
Academic Integrity
Georgia Tech aims to cultivate a community based on trust, academic integrity, and honor. Students are expected to act according to the highest ethical standards. For information on Georgia Tech's Academic Honor Code, please visit http://www.catalog.gatech.edu/policies/honor-code/ or http://www.catalog.gatech.edu/rules/18/.
Any student suspected of cheating or plagiarizing on a quiz, exam, or assignment will be reported to the Office of Student Integrity, who will investigate the incident and identify the appropriate penalty for violations.
Accommodations for Students with Disabilities
If you are a student with learning needs that require special accommodation, contact the Office of Disability Services at (404) 894-2563 or http://disabilityservices.gatech.edu/, as soon as possible, to make an appointment to discuss your special needs and to obtain an accommodations letter. Please also e-mail me as soon as possible in order to set up a time to discuss your learning needs.