## 2007-12-30

### MIT Lecture summary

I didn't realize that we can see a MIT Lecture on the Internet for free...

Goal
The goal of English II-FS is to be able to listen to English lectures. In order to find out how much this goal has been reached, you will listen to a real 40-to-50 minute long lecture, a science class from MIT (Massachusetts Institute of Technology). It is not required that you understand the lecture completely, but it is hoped that you will be able to gain some understanding of the content through your note taking.

Procedure
l. Select the lecture that you are most interested in. There are five to choose from:
・Physics (Newton’s Laws)

・Chemistry (The Structure of the Atom)

・Mathematics (Linear Algebra)

・Mathematics (Calculus)

・Biology (DNA)

2. Watch the lecture and take notes using what you have learned in class.

3. Use the notes to write a summary of the lecture in English. (If you are not sure how to write a summary, please see the example provided on the CELESE website.)

Requirements
You must hand in to your English II-FS teacher by the in-class final test day:
l. The notes you took
2. A 250 to 350 word summary

Scoring Procedure
Notes 5 points
Summary 15 points

under Calculus summary
【words】
ODE = ordinary differential equation
= ODE is solved exactly, whenever possible, and approximately using a variational method.
Differential [Noun] = 微分、差、格差、差動
Equation = 方程式、平均化、均衡　【略称】→eq.
GEOM = geometry = 幾何学 cf. geometric = 幾何学の
Derivative = 導関数、微分係数
Integral curve = 積分曲線
Elementary = 初歩的な、基本の、簡単な、単純な
Numerical = 数に関する、数値の、数の、数で示される
Analytic = 解析の、分析の、分析に使う
Direction field = 方向場
Slope = 傾き
Isocline = アイソクライン、等斜褶曲
Cf.アイソクライン法 ＝ 変化がどちらの方向であるかを矢印で表す方法。

Principle = 法則、公理
Exist = to be real; to be present in a place or situation
[~ on sth] = to live, especially in a difficult situation or with very little money.
[Noun] = existence
Uniqueness = 一意性<数学>,　独自性, 唯一性
Indicate = to show that sth is true or exists = to mention sth, especially in an indirect way
= to represent information without using word = to give information in writing
Subscript = [adj] 下付の = [Noun] 下付き文字
Variable = 変数、変量、可変
Slant = 傾き、傾斜
Corridor = 重要な交通ルート、廊下、回廊地帯
Tangent = タンジェント、接線、接面、正接

Course: Differential Equations
Professor Arthur Mattuck
1. FIRST-OREDER ODE’S
2. geometric, view of ODE’s

3. What is a geometric view of ODE’s?
Analytic Geometric
~~~ 　⇔ ~~~

4. What is the direction field?

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Sample:Fraction summary
This lecture begins with explaining the theory of friction and then introduces two methods to measure friction. The third part of the lecture provides several calculated examples and a visual example. Finally examples of reduced friction are given in the end.

Friction is not a simple force. The reason why is if a force is applied to a stationary object, the friction will increase in value in a direction opposite to the applied force, until some threshold is met. This threshold is known as μs, the static friction. That is the amount of friction threshold required to start an object moving. The kinetic friction μk, is the friction force while the object is moving. The static friction is always greater than the kinetic friction.

Measurement of Friction
There are two methods to measure friction. The first is to use a slope. We need to increase the angle of the slope until the object begins moving. At the instant the object begins to move we can measure the angle of the slope and calculate the friction coefficient from Newton’s second law, F = ma.

The equation can be derived as μs = tan α.
μs is the static friction. α is the angle that the object begins moving.

There are two interesting points from this equation. That first is that the mass of the object has no effect on frictional force and the second is that the surface area of contact has no effect on frictional force.

The second method of measurement involves the use of a pulley. Here a weight is added to a string through a pulley to provide a force in the opposite direction to that provided by gravity. Here we can calculate the friction by either increasing the angle, or increasing the weigh attached to the pulley.

Examples and experiments
Two worked examples were provided in the lecture. The first demonstrated acceleration uphill, the second no acceleration. This demonstrated that friction is a complicated and a very reactive force depending on which direction the force is coming from. Next two experiments were carried out to demonstrate the two measurement methods.

This was followed by examples of reduced friction. They were hydroplaning in a car where a little bit of water mixes with dirt and grease on the road. A hydroplane example was also provided by adding lubricant (water) between a lid and a pot. Finally, gas was demonstrated as being a very good lubricant. This was demonstrated by both an air-track and a container of carbon dioxide.