# Linear Algebra Vs Mathematical Modeling -Importance in relation to physics

1. Aug 2, 2011

### rshalloo

Hey as part of my Physics undergrad in second year I have to take a module in either Mathematical Modelling or Linear Algebra (both course descriptions below) In first year I preferred Linear Algebra ( a very basic intro course) but apparently in second year its just all proof and no calculations.
My question is, which is most useful to a physicist?

Mathematical Modeling: Module Content: Construction, interpretation and application of selected mathematical models arising in chemical kinetics, biology, ecology, epidemiology, medicine, and pharmacokinetics. The mathematical content of the models consists of calculus, linear and non-linear systems of ordinary differential and difference equations. Use of dynamical systems software.
Learning Outcomes: On successful completion of this module, students should be able to:
· Use coupled system of bilinear differential equations in ecological, epidemiological, chemical and other contexts to model competition, predator-pray and cooperation interactions;
· Use coupled system of linear differential equations to model mixing and exchange processes in different contexts;
· Use coupled systems of cubic differential equations to model evolution type phenomena;
· Carry out global analysis of coupled systems of nonlinear differential equations using techniques such as Lyapunov functions and trap regions;
· Solve linear systems of differential equations;
· Linearise and classify systems of nonlinear differential equation at equilibrium.

Linear Algebra: Module Content: Linear equations and matrices; vector spaces; determinants; linear transformations and eigenvalues; norms and inner products; linear operators and normal forms.
Learning Outcomes: On successful completion of this module, students should be able to:
· Verify the linearity of mappings on real and complex vector spaces,
· and the linear independence of sets of vectors;
· Evaluate bases, transition matrices and matrices representing linear transformations;
· Compute eigenvalues and eigenvectors of linear operators;
· Construct orthonormal bases for vector spaces;
· Verify properties of projection mappings, adjoint mappings, self-adjoint operators and isometries.

2. Aug 2, 2011

### xugi

Hmm, i try to give any opinion yah...

When I study about linear algebra,I found that it really helps me to calculate many calculation in Physics easily without doing too many substitution and elimination etc...
For example if u learn 2-4 degree freedom of oscillation, mechanic oscillation with 2-3 dots...

And in relation with Engineering Physics especially in Robotics, when I study Introduction to Robotics lectured by Ousama Khatib for Stanford University (U may download his difficult subject from youtube, here: http://www.youtube.com/watch?v=Mm5Tfm04cKk&feature=relmfu ),
then I found linear algbera is really useful to do transformation from a basis to another basis without using logic calculation anymore, just use matric, transform, etc...

I would like to say that I'm not expert in this robotic subject...
I am still undergraduate second year and much more interested in Modern Physics...

3. Aug 2, 2011

### bp_psy

The stuff in the modeling course is nice but the stuff in the linear algebra course is essential. It is actually a little bit weird they let you chose between the two, since the LA course should be the prerequisite for the modeling course.

4. Aug 2, 2011

### NeoZeon

If you have to take quantum, then u must take LA

5. Aug 2, 2011

### Timo

I almost completely agree with this statement ("essential" is a bit too strong for my taste since I've seen with how little actual physics some interdisciplinary branches of physics get away with). In case you really have to choose, I think the magic sentence for you might be
So if you want to go into the fields of "chemical kinetics, biology, ecology, epidemiology, medicine, or pharmacokinetics" you might consider the modeling course over LA. Otherwise, the course may be of little benefit for you while linear algebra is assumed in a lot of more puristic physics (e.g. quantum mechanics), and a proper mathematical understanding surely won't hurt there.