Computational Mechanics 01 - Getting Started#
Working with Python and Numerical Methods#
Welcome to Computational Mechanics Module #1 - Getting Started!
There are three modules and one final project. The modules will get us started on our exploration of computational mechanics using Python, listed below each module are the learning objectives.
Using the
print()function. The concept of function.Using Python as a calculator.
Concepts of variable, type, assignment.
Special variables:
True,False,None.Supported operations, logical operations.
Reading error messages.
Good coding habits and file naming
How to define a function and return outputs
How to import libraries
Multidimensional arrays using NumPy
Accessing values and slicing in NumPy arrays
%%timemagic to time cell execution.Performance comparison: lists vs NumPy arrays
Basic plotting with
pyplot.
Numerical integration with the Euler approximation
The source of truncation errors
The source of roundoff errors
How to time a numerical solution or a function
How to compare solutions
The definition of absolute error and relative error
How a numerical solution converges
Computational Mechanics Project #01 - Heat Transfer in Forensic Science#
We can use our current skillset for a macabre application. We can predict the time of death based upon the current temperature and change in temperature of a corpse.
Forensic scientists use Newton’s law of cooling to determine the time elapsed since the loss of life,
\(\frac{dT}{dt} = -K(T-T_a)\),
where \(T\) is the current temperature, \(T_a\) is the ambient temperature, \(t\) is the elapsed time in hours, and \(K\) is an empirical constant.
Suppose the temperature of the corpse is 85\(^o\)F at 11:00 am. Then, 2 hours later the temperature is 74\(^{o}\)F.
Assume ambient temperature is a constant 65\(^{o}\)F.