Math Methods for Physicists: Course Topics

[cesaruelas]

What topics should a year-long course in mathematical methods for physicists for which the pre reqs are vector calculus, ode's and linear algebra cover?

 

[Jorriss]

What topics should a year-long course in mathematical methods for physicists for which the pre reqs are vector calculus, ode's and linear algebra cover?

There's a TON of topics the course could cover.

Complex analysis, special functions, asymptotic methods, sturm-liouville theory, calculus of variations, just more linear algebra and vector calculus, WKB analysis, integral transforms, green's function techniques, etc.

 

[jedishrfu]

prof Nearings ebook might be good to look as far as course syllabus on mathematical methods for physicists:

http://www.physics.miami.edu/~nearing/mathmethods/

 

[jtbell]

There's a TON of topics the course could cover.

Yep, and what a specific course covers depends a lot on which gaps in students' mathematical background the professor teaching the course thinks needs to be filled at that particular college/university.

 

[Matrix0]

I believe that a year-long course in mathematical methods for physicists should cover a wide range of topics to prepare students for the complex mathematical challenges they will encounter in their research and studies. Some key topics that should be included in this course are:

1. Multivariable Calculus: This topic builds upon the pre-requisite of vector calculus and covers important concepts such as partial derivatives, multiple integrals, and vector fields. These are essential tools for understanding and solving problems in physics.

2. Differential Equations: ODE's (ordinary differential equations) are a crucial tool for modeling and solving physical systems. This topic should cover techniques for solving various types of ODE's, including separation of variables, power series, and Laplace transforms.

3. Linear Algebra: This is another important pre-requisite for the course, but it should also be covered in more depth. Topics such as vector spaces, linear transformations, eigenvalues and eigenvectors, and matrix operations are essential for understanding advanced mathematical methods used in physics.

4. Complex Analysis: Complex numbers and functions play a significant role in many areas of physics, such as quantum mechanics and electromagnetism. A thorough understanding of complex analysis is crucial for tackling these complex problems.

5. Fourier Analysis: This topic is essential for understanding periodic phenomena in physics. It covers concepts such as Fourier series, Fourier transforms, and the Fourier integral theorem.

6. Partial Differential Equations: Many physical systems are described by partial differential equations, making this topic crucial for physicists. It should cover techniques for solving various types of PDE's, such as separation of variables, method of characteristics, and Green's functions.

7. Numerical Methods: In many cases, analytical solutions to complex problems are not possible, and numerical methods are needed. This topic should cover techniques such as finite differences, finite elements, and Monte Carlo simulations.

Overall, a year-long course in mathematical methods for physicists should provide students with a strong foundation in advanced mathematical concepts and techniques to prepare them for the challenges of their future research and studies. It should also emphasize the application of these methods to real-world problems in physics.