Choose Math Class for Applied Physics: Vector & Tensor or Nonlinear Dynamics?

[Shinaolord]

Hello, for my degree I have to choose one of the two following classes. I am planning to pursue applied physics, specifically atomic, condensed matter or chemical physics.
So, which should I take?

1) applied vector and tensor mathematics

Introduction to vector and tensor mathematics with applications.
Topics include vectors; vector differential calculus, space curves; dyadic products and matrices; gradients, divergence, curl, Laplacians; Stokes' integral theorem, Gauss theorem, conservation laws; curvilinear coordinates; tensors, material derivatives; applications of potential theory in electricity and magnetism, heat transfer, solid and fluid mechanics.

2. Nonlinear dynamics and chaos
Ordinary differential equations and dynamical systems via a modern geometric approach, including physical and engineering applications. May include chaotic phenomena and fractals.
Much appreciated!

 

[deskswirl]

Hmm.. Having taken a course in Nonlinear Dynamics and Chaos myself I vote for the Applied Vector and Tensor Mathematics course. In my personal opinion it would be more immediately useful in the sense of its applications. And the fact that your are more likely to need it it in your later coursework (E&M especially). That is not to say that Nonlinear Dynamics will not show up in physics though.

 

[Shinaolord]

Hmm I see. What are some of the applications of nonlinear dynamics to physics? I am not really sure of any.

 

[deskswirl]

When I took the class we focused on biological models due to the lecturer having done research in that area. Broad answer: Whenever the processes/models which you are observing involves a nonlinearity and displays sensitive dependence to initial conditions quite interesting short and long term behavior happens.

Go by your university library and look for a copy of Strogatz's Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering OR Chaos: An Introduction to Dynamical Systems by Alligood, Sauer, and Yorke. Flipping through the table of contents and browsing should tell you if the course will be interesting or not.

 

[Matrix0]

Both classes have their own benefits and applications in the field of applied physics. It ultimately depends on your personal interests and career goals.

If you are more interested in theoretical and mathematical aspects of applied physics, then the vector and tensor mathematics class would be a better fit. This class will provide a strong foundation in mathematical tools such as vector calculus, tensors, and differential equations, which are essential for understanding and analyzing physical systems in atomic, condensed matter, and chemical physics. These mathematical concepts are also widely used in various other fields, so it will be a valuable skill to have.

On the other hand, if you are interested in the practical applications of applied physics, such as studying chaotic phenomena and nonlinear systems, then the nonlinear dynamics and chaos class would be more suitable. This class will provide a deeper understanding of how complex systems behave and how to model and analyze them. This knowledge can be applied in fields such as materials science, fluid dynamics, and chemical reactions, which are all relevant to applied physics.

In summary, both classes have their own merits and relevance to applied physics. It is important to consider your interests and future career goals in making your decision. Whichever class you choose, make sure to fully engage in the material and take advantage of any opportunities for hands-on experience and practical applications. Good luck with your studies!