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

• Shinaolord
In summary, the conversation is discussing the choice between two classes for a degree in applied physics: applied vector and tensor mathematics and nonlinear dynamics and chaos. The speaker suggests taking the applied vector and tensor mathematics course because it would be more immediately useful in terms of its applications in later coursework. They also mention that nonlinear dynamics and chaos could be useful in physics when studying processes that involve nonlinearity and sensitive dependence on initial conditions. The speaker recommends looking at textbooks on the subject to determine if the course would be interesting.
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!

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.

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

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.

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!

## 1. What is the difference between Vector & Tensor and Nonlinear Dynamics?

Vector & Tensor and Nonlinear Dynamics are two different branches of mathematics that are used for applied physics. Vector & Tensor focuses on the manipulation and analysis of vectors and tensors, which are mathematical objects that have both magnitude and direction. Nonlinear Dynamics, on the other hand, deals with the study of systems that have nonlinear behavior, such as chaotic systems.

## 2. Which math class is more applicable to real-world physics problems?

This ultimately depends on the specific problem at hand. Vector & Tensor is often used in mechanics and fluid dynamics, while Nonlinear Dynamics is useful for studying complex systems in fields like optics and electromagnetism. Both classes have their own strengths and applications in the field of applied physics.

## 3. Do I need a strong background in mathematics to take these classes?

Yes, a strong foundation in mathematics is necessary for both Vector & Tensor and Nonlinear Dynamics. These classes involve advanced topics in calculus, linear algebra, and differential equations. It is recommended to have a solid understanding of these subjects before taking these classes.

## 4. Can I take both Vector & Tensor and Nonlinear Dynamics at the same time?

This may vary depending on the institution and its course offerings. Some universities may offer both classes in the same semester, while others may have them scheduled for different semesters. It is best to consult with your academic advisor to determine the best course of action.

## 5. How will taking these classes benefit me in my career as a physicist?

Both Vector & Tensor and Nonlinear Dynamics are essential tools in the field of applied physics. These classes will provide you with the mathematical tools and techniques necessary to analyze and solve complex real-world problems. They will also help develop your critical thinking and problem-solving skills, which are highly valued in the field of physics.

Replies
4
Views
1K
Replies
10
Views
1K
Replies
18
Views
2K
Replies
9
Views
2K
Replies
16
Views
2K
Replies
2
Views
4K
Replies
4
Views
1K
Replies
13
Views
2K