If I can get a total of 10 people interested I will teach a course on Elementary Mathematical Methods for Science. This will consist of units on algebra, estimation and dimensions, geometry, trigonometry, analytic geometry, calculus, linear algebra, multivariable calculus, differential equations, and probability and statistics. Possibly other topics as well.
I have 4 people interested already.
Here is how the course will be conducted:
1) Each Friday I will place material on a web site for the course. This will be in the form of a cdf file, a format created by Wolfram Research. Many of these documents will contain interactive material for you to play with. There will be a number of challenges: 2-3 will be done in complete detail, 1-2 will be done in less detail, 1-2 will be done in little detail, and 1-2 will have no detail.
2) Discussions of the work will continue on the blog until the students are done with them. If this takes 2 months, then I know that I have done something wrong.
3) Throughout the week I will monitor the blog to see what responses I get. This will determine the new material I put up on Friday of that week. I will also put up a record of the discussion formatted for the mathematics
4) Upon completion of an assignment by all participants I will post a transcription of the discussion formatted in Mathematica and converted into a cdf.
5) If people are interested, I will have a live session on Saturday evenings beginning at 8PM central time and going until 10 PM central time. This will be via Skype and will use TeamViewer as the desktop sharing software so that I can answer questions directly.
6) If I can figure out a way to do it efficiently I will produce audio lectures keyed to the material, so you can follow along.
Showing posts with label Dimensional Analysis. Show all posts
Showing posts with label Dimensional Analysis. Show all posts
Friday, February 8, 2013
Monday, September 20, 2010
Secret Weapons of The Theoretical Physicist
Tonight I am thinking about a set of the most powerful techniques of the theoretist, classically called back-of-the-envelope calculations. These consitute two broad categories of methods.
The first is the method of estimation, where you use some basic reasoning abilities to determine a rough estimate of the quantities you are considering. For example, you want to estimate the number of hairs on someone's head. You think about it and decide that if you knew the area of the part of the head covered by hair, then knew the average area of a hair, you could figure it out. Then you make the necessary assumptions about the quantities (either by looking up the information, or by figuring it out for yourself).
The second is the ability to check the correctness of equations and to derive new equations by studying the relevant units of the quantities. All terms of any equation must have the same units. When you chaeck the terms, any that do not have the correct units are just wrong. By including powers of each quantity in each term and making sure all of the units come out the same, you invent a system of algebraic equations that can be solved. This gives you the necessary powers of each variable and shows you the structure of each term within a factor of a constant of proportionality. In this way you can learn what each term must look like. This allows you to invent new equations if you know the units involved. This is called dimensional analysis.
I will be writing about these ideas in my column in the coming weeks. I will also be discussing this in the Classical Mechanics book I am writing with Leonard Susskind.
The first is the method of estimation, where you use some basic reasoning abilities to determine a rough estimate of the quantities you are considering. For example, you want to estimate the number of hairs on someone's head. You think about it and decide that if you knew the area of the part of the head covered by hair, then knew the average area of a hair, you could figure it out. Then you make the necessary assumptions about the quantities (either by looking up the information, or by figuring it out for yourself).
The second is the ability to check the correctness of equations and to derive new equations by studying the relevant units of the quantities. All terms of any equation must have the same units. When you chaeck the terms, any that do not have the correct units are just wrong. By including powers of each quantity in each term and making sure all of the units come out the same, you invent a system of algebraic equations that can be solved. This gives you the necessary powers of each variable and shows you the structure of each term within a factor of a constant of proportionality. In this way you can learn what each term must look like. This allows you to invent new equations if you know the units involved. This is called dimensional analysis.
I will be writing about these ideas in my column in the coming weeks. I will also be discussing this in the Classical Mechanics book I am writing with Leonard Susskind.
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