Methods of theoretical physics vs normal math classes

In summary, a methods of theoretical physics course can fulfill math requirements for a physics degree and covers a wide range of mathematical methods used in mechanics, electromagnetism, and thermodynamics. It includes topics such as multiple integration, vector calculus, Fourier series, differential equations, and complex analysis. While a logic course may be interesting, a mathematical methods course would be more beneficial in pursuing a degree in physics. In addition, advanced calculus is generally not necessary for an intermediate level E&M course, but knowledge of vector calculus is essential. However, the level of mathematical background needed may vary depending on the university and the specific course. For those interested in modern physics, courses in group theory and tensor calculus or differential geometry may also be helpful. Overall,
  • #1
marmot
55
1
"methods of theoretical physics" vs "normal math classes"

Hey.

I am in a dilemma. Originally, I was going to go the math minor route but I think I am deciding against it mainly because of the structure. I wanted to take an advanced calculus class to prepare myself for EM, but I really want to take an advanced forrmal logic class and that fills the place available for advanced calculus. There is a class called "methods of theoretical physics" which can count for my math reqs and the description is this:

"Mathematical methods applied to physical problems in mechanics, electromagnetism, and thermodynamics. Multiple integration, vector calculus, Fourier series, ordinary and partial differential equations, eigenvector problems, coordinate transformations, and complex analysis. Newtonian mechanics, rigid body dynamics, heat flow, electrostatics, harmonic motion, and waves."

Would this class be useful? Do I need to know mad vector calculus for electromagnetism or there are just some things that I need to dominate?
 
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  • #2


A mathematical methods course is usually required for any degree program in physics and would be much more helpful than a logic course.
 
  • #3


marmot said:
Do I need to know mad vector calculus for electromagnetism

You sure do! However, the vector calculus you get in a typical Calculus III course should be enough. Also, undergraduate E&M courses often spend a significant amount of time reviewing vector calculus. The first chapter of Griffiths (a popular E&M textbook) is devoted to vector calculus.

Disclaimers:

1. I assume you're in the USA.

2. I assume you're dealing with an intermediate / upper-level E&M course, not the second semester of freshman physics.

3. The situation can vary from one college / university to another. Check your course catalog for the official prerequisites for your E&M course.
 
  • #4


i am sorry. what i meant is that if a mathematical method class would be enough for EM. i was taking before analysis, but i am going to drop it for that class. i am not going to drop logic because its a class i wanted to take before forever and i am willing to make a lil sacrifice fr it.
 
  • #5


marmot said:
i am sorry. what i meant is that if a mathematical method class would be enough for EM. i was taking before analysis, but i am going to drop it for that class. i am not going to drop logic because its a class i wanted to take before forever and i am willing to make a lil sacrifice fr it.

you don't need advanced calc for em - you need vector calc.

why are you taking advanced formal logic? that will help you with nothing except logic - it won't even help you write mathematical proofs.
 
  • #6


marmot said:
what i meant is that if a mathematical method class would be enough for EM.

At most colleges and universities in the US, you don't even need a mathematical methods class for an intermediate level E&M course. All you usually need is the vector calculus that you learn in (usually) in the third semester of a standard calculus sequence.

However, even in the US, there are probably exceptions to this. If you're at a university outside the US, then I would not want to give advice without seeing detailed descriptions of the E&M course and the math courses that you've already taken, and the mathematical methods course.
 
  • #7


Well I did my major in math and physics and I can say that the methods course is enough for an introduction to electrodynamics, but I think that is better to do the minor in math, in the case of an Advance ED course it can be really helpful, because the real difference for example between of a intermediate course book and the Jackson is the math. Also the majority of the courses for methods in theoretical physics don't include modern methods like group theory and tensor. Group theory is important in QM, QF and depending of the approach for classical dynamics and ED. The tensor for GR, but for example the tensors are important in ED, because you can have all the Maxwell equations in one tensor equation, and also the multipole moments description should be more easy to understand too. my advices is that if you are interested in modern physics, is not enough with the calculus, DOE, DPE, Linear Algebra and complex analysis courses, you need group theory (abstract algebra) and tensor calculus or differential geometry, also maybe topology.

Also in physics some books use tricks that you will not understand unless you have a good background in analysis and logic. Also there are some tricks that are used in physics that any math can help you to understand, like the delta function that make a lot of sense in QM to help to the normalization of the improper vectors, but it is not well defined from the mathematical point of view.

Also the good part about taking the math course is that you learn the theory and it can be helpful to reduce problems with a lot of helpful theorems. For calculation, programs like mathematica and mathlab are better than any course.
 

1. What is the difference between methods of theoretical physics and normal math classes?

The methods of theoretical physics and normal math classes differ in their approach and applications. Theoretical physics focuses on understanding the fundamental laws and principles of nature through mathematical models and theoretical frameworks. It often involves complex mathematical concepts and is used to explain natural phenomena. Normal math classes, on the other hand, focus on teaching mathematical concepts and techniques for real-world applications.

2. How are methods of theoretical physics beneficial for scientific research?

Methods of theoretical physics are essential for scientific research as they provide a way to understand complex natural phenomena and make predictions about the behavior of physical systems. These methods also help in developing new theories and models to explain and interpret experimental data. Theoretical physics plays a crucial role in advancing scientific knowledge and technologies.

3. Can someone with a background in normal math classes understand methods of theoretical physics?

While a background in normal math classes can be helpful in understanding methods of theoretical physics, it is not a prerequisite. Theoretical physics involves advanced mathematical concepts, and a strong foundation in calculus, linear algebra, and differential equations is necessary. However, with dedication and effort, anyone with a passion for physics can learn and understand these methods.

4. How do methods of theoretical physics contribute to other fields of science?

Methods of theoretical physics have a significant impact on other fields of science, such as chemistry, biology, and engineering. Theoretical physics provides a framework for understanding the underlying principles and mechanisms of these fields and helps in developing new theories and models. It also allows for the prediction and explanation of complex phenomena, making it a valuable tool for scientific research.

5. Are there any practical applications of methods of theoretical physics?

Yes, methods of theoretical physics have numerous practical applications in fields such as technology, medicine, and energy. For example, the principles of quantum mechanics, a branch of theoretical physics, are used in developing computer chips and transistors. Theoretical physics also plays a crucial role in medical imaging technologies such as MRI and in developing renewable energy sources like solar panels.

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