Textbooks for various topics in math for scientists

In summary, the conversation is about two math courses for scientists offered at the speaker's school. The speaker, who is pursuing an interdepartmental degree in microelectronics and solid state physics, is interested in the topics covered in these courses but does not have the time to take them. They are looking for recommendations for textbooks or online resources that cover the topics, which include Bessel functions, Legendre polynomials, tensors, vectors, vector analysis, numerical methods, and complex space. A suggestion is made for the book "Mathematical Methods for Physicists" by Arfken & Weber, but the speaker also mentions that there is no required textbook for the course.
  • #1
pjcircle
15
0
There are two courses specifically called math methods for scientists (grad level) that are offered in my school. I am doing a interdepartmental degree in microelectronics/solid state physics (Electrical Engineering/Materials Engineering/Physics) focused more on the physics side of it. I eventually do plan on getting a PhD in physics and would like to know the topics in these courses (I literally do not have the time to take these courses). I am going to list the topics below and would like to know any good textbooks/online resources that thoroughly go through these topics so I can go through it during my free time. I have a good background in linear algebra, calculus, Differential equations and a very good understanding of math that has to do with signal processing (fourier/z/laplace transforms/systems theory and a lot of background with complex numbers). I am taking multivariable calculus next term so if anything I list is covered in a typical multi class let me know please. Here are the topics from the course descriptions.

Bessel functions, and Legendre polynomials as involved in the solution of vibrating systems; tensors and vectors in the theory of elasticity; applications of vector analysis to electrodynamics; vector operations in curvilinear coordinates; numerical methods of interpolation and of integration of functions and differential equations.
Vector and Tensor Fields: transformation properties, algebraic and differential operators and identities, geometric interpretation of tensors, integral theorems. Dirac delta-function and Green's function technique for solving linear inhomogeneous equations. N-dimensional complex space: rotations, unitary and hermitian operators, matrix-dyadic-Dirac notation, similarity transformations and diagonalization, Schmidt orthogonalization.

Sorry for the wall of text!
 
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  • #2
I think Mathematical Methods for Physicists by Arfken & Weber might suit your needs, but why don't you just see what the textbook for the course is?
 
  • #3
Theres no textbook for the course (i wish there was lol)
 

1. What are the benefits of using textbooks for various topics in math for scientists?

Textbooks provide a comprehensive and structured approach to learning mathematical concepts. They also include a variety of practice problems and examples to reinforce understanding. Additionally, textbooks are written by experts in the field, ensuring accuracy and reliability of information.

2. How do I choose the right textbook for a specific topic in math?

When choosing a textbook, consider the level of difficulty, the author's expertise, and the specific topics covered. You may also want to read reviews and compare multiple textbooks to find one that best suits your learning style.

3. Are there online resources available for textbooks on math for scientists?

Yes, many textbooks now have online resources such as practice quizzes, interactive simulations, and supplementary materials. These can be accessed through the publisher's website or through a code included with the textbook.

4. Can I use textbooks from other fields of science for studying math?

While some concepts may overlap, it is best to use textbooks specifically designed for math topics in science. These will provide a more focused and relevant approach to understanding mathematical concepts in the context of scientific disciplines.

5. How can I make the most out of using a textbook for learning math as a scientist?

To make the most of using a textbook, it is important to actively engage with the material. This can include taking notes, practicing problems, and seeking clarification when needed. It may also be helpful to supplement textbook learning with other resources such as online tutorials or study groups.

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