Math Skills
In the beginning there was math,
and He saw that it was good.
Pourqoui?
• In order to do physics, which is the study of how the world works, we need a universal language
• Enter MATHEMATICS
• Physics is the rosetta stone between mathematics and the real world
Significantly Figuring it Out
• There’s a big difference between 10 and 10.0034505 – at least conceptually
• Each one we know to a different precision
Easy does it
• There are very simple rules for figuring sig fig’s (sf’s):
1. Draw a map of the United States2. Put the number in Nebraska
1. If the number has a decimal, start in the Pacific Ocean
2. If the number does not have a decimal, start in the Atlantic Ocean
3. Cross out zeros until you hit something that is not zero.
That’s It?
PAC ATL
110 0.111.1 .011
1101.10.11.011
Bonus
PAC ATL
110.0 .110 1.010
A Small Notation
• Scientific notation is way of expressing big numbers and small numbers in a more elegant fashion.
• General rules– leading number must be at least 1 and less
than 10– must have same number of sig fig’s as the
original number
• Remember basic identities
Bigger Smaller
• In order to put a number in scienfic notation, if you make the leading number smaller, the exponent must get bigger.– Count the number of decimal places you move; this
how much bigger the exponent gets– Move the decimal place four times, the exponent
increases by 4
• If the leading number gets bigger, the exponent must get smaller
Practice
.000560 5.6 x 10-4
56000 5.6 x 104
5.6 x 10-6
5.6 x 101
560 x 10-4
.0056 x 104
5.60 x 10-4
5.6 x 10-2
A Little Ridiculous
• Nobody writes 5.6 x 101, they just put 56.
• Because of this, we use the
“physics rule”– Any number greater than 9999 must be in
scientific notation– Any number less than .0001 must be in
scientific notation– All others can be left alone
Exponentially Easy
• There are two basic situations:– Adding and Subtracting
• Get the exponents the same• add/subtract the leading numbers• exponent of the result is the same as the exponent before
– Multiplying and Dividing• Don’t worry about getting the exponents the same• Multiply/divide the leading numbers• If multiplying, the exponents are added• If dividing, the exponents are subtracted
I Get Around
• The length around a firgure is its perimeter– rectangle– square– triangle
• Circles have a special name for their perimeter– Diff b/t radius and diameter
Area 51
• You should know the areas for all the above geometric figures.– Rectangle– Square– Triangle– Circle
Why?
• You’ll see trig in problems, especially concerning vectors
• Handy knowledge
• Helpful in– construction
• To use the KISS method, we’ll only concern ourselves with right triangles
Basics
• Any right triangle has two smaller sides
• The longest side is called the
• The sum of all angles in a triangle is
Pythagorean Theorem
• The sum of the square of the sides of a right triangle is equal to the square of the hypotenuse
• c2 = a2 + b2
b
a
c
