Recommend math topics for physics?

[Fizex]

I'll be taking calc III, diff. eq. and linear algebra this semester and I want to learn 6-10 additional topics so I can purchase some books to read during the semester. What topics would be most useful to physics?

I think differential geometry would be one. PDE's and analysis are another.

 

[sponsoredwalk]

Why don't you get https://www.amazon.com/dp/0130414085/?tag=pfamazon01-20? Do a bit of research into this book & into Forms in general, they would be a great precursor to Diff Geom. As for analysis, all I can say is type real analysis or mathematical analysis into amazon search & read the contents pages of every book & the reviews of every book, also read old PF discussions about analysis books & you'll find a book that suits you

 

[deluks917]

A very good book on DE's is Arnold Ordinary differential equations.

 

[sponsoredwalk]

A very good book on DE's is Arnold Ordinary differential equations.

Yeah but aren't the prerequisites for that book familiarity with analysis & linear algebra as
the book says? Even one person on amazon says topology, abstract algebra & diff geom
(which is probably a bit of an exaggeration). The OP is only learning LA & thinking of
analysis so a Differential equations book like Tenenbaum & Pollards one would be more apt.

 

[rezeew]

I would recommend the following math topics for physics:

1. Vector Calculus: This is a crucial mathematical tool for understanding and solving problems in physics, especially in the fields of electromagnetism and fluid mechanics.

2. Complex Analysis: This branch of mathematics deals with functions of complex numbers and has many applications in theoretical physics, such as quantum mechanics and electromagnetism.

3. Group Theory: Group theory is the study of symmetry and is essential for understanding the fundamental laws of nature. It has applications in particle physics, condensed matter physics, and quantum mechanics.

4. Partial Differential Equations (PDEs): PDEs are used to describe the behavior of physical systems and phenomena, such as heat transfer and wave propagation. They are essential in many areas of physics, including quantum mechanics and fluid dynamics.

5. Numerical Methods: In many cases, exact solutions to physical problems are not feasible, and numerical methods are needed. This includes techniques such as finite element analysis, Monte Carlo simulations, and numerical optimization.

6. Tensor Analysis: Tensors are mathematical objects that describe the properties of physical systems in multiple dimensions. They are widely used in general relativity, electromagnetism, and fluid mechanics.

7. Fourier Analysis: This mathematical technique is used to decompose complex functions into simpler components and has applications in many areas of physics, including signal processing and quantum mechanics.

8. Differential Geometry: This branch of mathematics deals with the geometry of curves and surfaces and is essential for understanding the concepts of space and time in physics, especially in general relativity.

9. Probability and Statistics: These are crucial tools for analyzing and interpreting experimental data in physics, as well as for modeling and predicting physical systems.

10. Linear Algebra: This is a fundamental mathematical subject that is used extensively in physics, from solving systems of equations to understanding quantum mechanics and electromagnetism.

I would also recommend exploring additional topics such as chaos theory, information theory, and optimization, as they have applications in various areas of physics and can provide a deeper understanding of complex systems. I wish you all the best in your studies and hope these recommendations will help you in your pursuit of learning physics.