Calculate solutions to physics problems
All physics problems can be formulated
Many strategies for solving equations.
Display solutions in a way that helps us
interpret the physics
Division of Labor
Most of the work in solving a problem is still done in
the physicist’s head
Derive the equations that represent the system of interest
Understand all the approximations and limitations
(conditions for validity)
Determine how to instruct the computer to solve the
The computer does what it is told to do.
The physicist has to interpret the computer’s output
Computational solutions are theoretical predictions
(based on the equations). They must eventually be
compared to measurements.
Many types of equations:
You may have a set of equations that must
be solved simultaneously
Matrix manipulations, linear algebra
Your equations may depend on initial
conditions or boundary conditions
Some special equations have an analytical, or
“closed-form,” solution, which is a certain known
function or combination of functions.
Most equations (or sets of equations) must be
solved numerically, using a computer. The
resulting solution is approximate, and consists only
of a set of numbers
In most cases, you will want to make a plot
of the solution, in order to visualize how
certain quantities depend on others.
This is something that a computer is
especially good at.
Programs such as Mathematica and MATLAB can help
you work with equations analytically
Might help you obtain analytical solution
Most physics problems (that are not highly simplified)
involve equations that must be solved numerically.
Smooth funtions must be discretized
Derivatives become differences
Integrals become sums
Errors of approximation must be carefully tracked
Can be done with Mathematica or MATLAB
Actual solving strategies are built in
Need to understand limitations
Can use a scientific programming language
such as FORTAN or C
Many basic strategies have already been written
Use library of routines - customize to your problem
Solution must be plotted to be useful
Special graphics programs are available
Mathematica & MATLAB do this well, too