# Math 22a Fall 2018

## 22a Linear Algebra and Vector Analysis

# Linearization

The chain rule and the Taylor approximation have lead to linear and quadratic approximations. These approximations are very important in all of sciences as most laws we know in physics, engineering, chemistry or economics are just approximations of more complicated laws. Linear laws are especially appealing. Here are examples:Physics: Hooke's law Force is proportional to the displacement | Engineering: Ohm's law Potential is proportional to current | Chemistry: Ideal gas law Temperature is proportional to pressure | Economics: Cobb-Douglas law log(consumption) is proportional to the logs of labor or the log of capital | Biology: Malthusian population growth is proportional to population size |

F = k X | V = I R | P V = n R T | Y = L^{a}K^{b} |
X' = k X |

Hooke | Ohm | Clausius | Douglas | Malthus |

By the way if you look at the guys above, you wonder whether it is really fun to discover a law. Cheer up guys! You are famous pop stars of science, for heavens sake!