Problem 1 - Modelling with functions and equations
This is a hand-in written by Group 60 (FIRE) for the weekly module #1 in the mathematical modelling course (DAT026) at Chalmers University of Technology.
Group 60 consists of:
Time spent: 24 hours 23 minutes
Time spent: 19 hours 22 minutes
We hereby declare that we have both actively participated in solving every exercise, and all solutions are entirely our own work.
A number of mathematical equations are listed below. Their justification (why they are true or reasonable), how well they model reality and a categorization of them are done for each equation.
The equation describes the relationship between the catheti (\(a, b\)) and the hypotenuse (\(c\)) for a right angled triangle. It can easily be proved by considering a square with a smaller rotated square in it - which results in there being 4 right angled triangles as well it.
It has been a well known relationship for a few thousand years. And it is very easy to prove mathematically.
The solution is exact.
The equation models how the stock index grows linearly over time. It is an inexact, approximative solution that has probably been derived from empirical studies from data points. Perhaps it has been derived using regression analysis.