I have a particular colleague who, when he was out socially, would occasionally tell people who asked what he did for a living “I work with models”. I’m pretty sure he was doing it as a funny ice breaker rather than any serious attempt to impress people (I always found that just saying I design bridges worked for me). What he was actually referring to was mathematical modeling, the way most detailed engineering design is done now that computers are advanced enough to handle it.

The easiest understanding of mathematical modeling is just a literal interpretation of the phrase. Mathematical modeling is building a model of a thing or a process through the use of math. A mathematical equation or process is used to determine what happens when you put something into a system.

Let’s start with a simple example. The model for distance traveled is:

Distance = Travel time x Average speed

Say your grandmother is driving through the woods and over the river to visit you. Grandmother doesn’t see so good anymore so you worry about her when she drives. You could just call herr on her cellphone every 20 minutes, but she gets annoyed when you do that too often. Besides, distracted driving is dangerous driving and finding anything in grandmother’s purse IS distracting. You can maybe call maybe once without ticking off the old lady, so you should probably do it right after she makes the turn onto Old Hickory Boulevard, because even people who’ve lived in Nashville for 50 years get a little confused about Old Hickory Boulevard. So how do you know when she gets to that spot? Well, you put together a little mathematical model. You know she drives 40 mph no matter how many honks she gets from the people behind her on I-40 so you use our equation above.

Grandmother’s driving distance so far = Time on the road x 40mph

or D = T x 40

Grandmother tells you she’s going to leave at 7 AM, which really means 6:30 AM because great-grandmother didn’t raise no Late Louise. So at 8 AM she has been on the road for 1.5 hours and she has traveled:

D = 1.5 hours x 40 miles per hour = 60 miles

Not quite to the turn at Old Hickory Boulevard yet. So we have to wait a little longer. If you prefer, we can rearrange our model a little. We know that the important turn is 80 miles from grandmother’s house and we really need to know what time to call her. So we can use a little algebra (did everyone quit when I typed ‘algebra’?) to rearrange the equation how we want it.

T = D/40 or T = 80/40 = 2 hours

Now add grandmother’s starting time and our model is complete and we know what time to set the alarm to wake up and call grandmother.

T = Start time + (Distance/Average Speed)

T = 6:30 AM + (80 miles/ 40 mph) –> T = 6:30 AM + 2 hours

So set that alarm and call grandmother at 8:30 AM, just to make sure she turned left on Old Hickory Boulevard.

This is getting long, and I’m sure I lost a lot of you at ‘algebra’ so we’ll wrap it up for now. Next time I’m going to talk some more about modeling complexity and variables, so get a good nights sleep. Now, please excuse me while I work on the model for reader loss whenever I say ‘algebra’.

on March 16, 2012 at 11:41 AMMathematical Modeling 201 – Adding Complexity « Because I Can[…] Comments « Mathematical Modeling 101 […]

on May 1, 2012 at 8:29 PMHydrology for Engineers « Because I Can[…] much water am I going to have to drain off my project?”. There are countless different mathematical models available to figure this out. They vary from extremely simple to eye numbingly […]