Linear Algebra Vs Mathematical Modeling -Importance in relation to physics

In summary, the conversation discusses the options of taking either Mathematical Modeling or Linear Algebra as a module for a Physics undergrad in second year. While the first year Linear Algebra course was preferred, second year focuses more on proofs than calculations. The question is raised on which course would be more useful for a physicist. The content and learning outcomes for both courses are outlined, with the suggestion that Linear Algebra may be more essential for physics and a potential recommendation to take the Modeling course if interested in certain fields.
  • #1
rshalloo
52
0
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.
 
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  • #2
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
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
If you have to take quantum, then u must take LA
 
  • #5
bp_psy said:
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.
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
Construction, interpretation and application of selected mathematical models arising in chemical kinetics, biology, ecology, epidemiology, medicine, and pharmacokinetics.
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.
 

1. What is the difference between linear algebra and mathematical modeling?

Linear algebra is a branch of mathematics that focuses on studying linear equations and their properties, while mathematical modeling is the process of creating mathematical representations of real-world systems or phenomena.

2. How are linear algebra and mathematical modeling important in relation to physics?

Linear algebra is a fundamental tool in physics as it provides a mathematical framework for understanding and solving physical problems. On the other hand, mathematical modeling allows physicists to create mathematical models of complex physical systems, making it easier to analyze and predict their behavior.

3. Can linear algebra be used for mathematical modeling in physics?

Yes, linear algebra can be used for mathematical modeling in physics. Many physical systems can be described using linear equations, and linear algebra techniques can be used to model these systems and solve for unknown variables.

4. What are some examples of how linear algebra and mathematical modeling are used in physics?

Linear algebra is used in physics to study quantum mechanics, electromagnetism, and fluid dynamics, among other areas. Mathematical modeling is used to create models of physical systems such as the motion of a pendulum, the behavior of a gas in thermodynamics, and the spread of diseases in populations.

5. How do linear algebra and mathematical modeling work together in physics?

Linear algebra and mathematical modeling work together in physics to help physicists understand, analyze, and solve complex physical problems. Linear algebra provides the mathematical framework and tools, while mathematical modeling helps create simplified representations of real-world systems, making it easier to apply linear algebra techniques and make predictions about the behavior of physical systems.

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