# What is Mathematical methods: Definition and 76 Discussions

Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".

View More On Wikipedia.org
1. G

### [Sturm-Liouville eigenvalues and eigenfunctions problem]

I have found that w(x) should be e^-x to make L self-adjoint. and insert back get xL''+(x+1)L' +lambda L = 0 now it needs to assume a monic polynomial function, so I assume Ln = x^n+ sum from k=0 to n-1 (a_k*x^k) get the 1st and 2nd order differential and insert back I get lambda_n =...
2. G

### A Upper indices and lower indices in Einstein notation

I have read some text about defining the cross product. It can be defined by both a x b = epsilon_(ijk) a^j b^k e-hat^i and a x b = epsilon^(ijk) a_i b_j e-hat^k why the a and b have opposite indice positions with the epsilon? How to understand that physically?
3. ### Other Math Physics Resource Request: Mary L Boas Book

I have been reading Mathematical Physics from Marl L. Boas' Mathematical Methods in the Physics Sciences and it's ok. But, I feel like for someone who hasn't been exposed to topics like Fourier Series, I need greater context. I feel like I should have chosen a different book, but that's...
4. ### Mathematical Methods Book That Uses SI Units

I'm looking for an undergraduate-level 'mathematical methods' or 'engineering mathematics' book that uses SI units for the purpose of self-study. I've had my eyes on Zill's Advanced Engineering Mathematics, but it seems to use US customary units. So ideally I'm looking for a book that covers...
5. ### Finding analyticity of a complex function involving ln(iz)

Hey everyone! I got stuck with one of my homework questions. I don't 100% understand the question, let alone how I should get started with the problem. The picture shows the whole problem, but I think I managed doing the a and b parts, just got stuck with c. How do I find the largest region in...
6. ### I Rodrigues' Formula for Laguerre equation

This is exercise 12.1.2 a from Arfken's Mathematical Methods for Physicists 7th edition :Starting from the Laguerre ODE, $$xy''+(1-x)y'+\lambda y =0$$ obtain the Rodrigues formula for its polynomial solutions $$L_n (x)$$ According to Arfken (equation 12.9 ,chapter 12) the Rodrigues formula...
7. ### Mathematical methods: logarithms question

I know that sinhx = 1/2(e^x-e^-x) and that e^2x-1 = e^x(e^x-e^-x) and similar identities but don't know how to get any further. Any hints at where to go with this would be appreciated.
8. ### Mathematical methods for physics and engineering-Reviews/Suggestions

Hi, I was told by someone to go for the above mentioned book (authored by Riley and a couple of other authors). I need a definitive tour de mathematica- something that I could use for the beginning of my Physics UG until the end of it (or even further if such a book exists!). Also, something...
9. ### Unknown mathematical methods in Physics?

What are streams of mathematics that are generally not used by Physicists but you think can be used successfully provided they become more developed? I want to know about such things cause it is quite interesting. Also, can Projective Geo be used in physics?
10. ### Error in Mathematical Methods for Physicist by Arfken, et al

Mathematical Methods for Physicist: A Comprehensice Guide (Seventh Edition) by George Brown Arfken, Hans Jürgen Weber, Frank E. Harris I am studying it. Up to now I read to page 35 and have found 3 errors. Chapter 1 Mathematical Preliminaries 1.1 Infinite Series More Sensitive Tests Equation...
11. ### Possible Error in Vladimir Arnold Mathematical Methods C

I'm reviewing differential forms again and I believe there is an error in Vladimir Arnold's Mathematical Methods of Classical Mechanics. On page 176 of the hardcover edition of it, in chapter 7, on the section of differential forms, problem 4 he says that dr^2(r^2=x^2+y^2) acting on the 2nd...
12. ### Mathematical Methods for Physics and Engineering

I’m thinking about getting this monster of a book because I heard it was incredibly awesome and useful, but I have one question. I want to be both a physicist and a mathematician in the future, so can aspiring pure mathematicians learn many useful things from this book, or does this book only...
13. ### General question about vector addition -- using graphical versus mathematical methods

Homework Statement I have an exam on vectors and 2 dimensional motion today. I NEED to know if it is possible to solve any GRAPHICAL VECTOR PROBLEM using only INTEGRATION AND MATH WITHOUT ADDING VECTORS TOGETHER GRAPHICALLY. So given any word problem that is supposed to be solved using that...
14. ### Mathematical methods for students of physics and related fields

This book is too expensive for me to buy. Can someone share ebook/ pdf?
15. ### Mathematical methods for physicists by Arfken and Weber

I'm searching for a good online lecture series to go with the book Mathematical methods for physicists by arfken and Weber . Tell me If you know about such series . Other general tips on starting rigourous mathematical physics are also welcome.
16. ### Mathematical methods for physicists

I'm currently doing mechanical engineering undergraduate degree but I don't want to continue with this field for further education. I'm more interested in physics. That's why I have started studying on my own. I'm really confused how to start. I have purchased several classic textbooks on...
17. C

### Difficulty with Mathematical Methods of Classical Mechanics

Homework Statement A friend and I are going through Vladimir Arnold's Mathematical Methods of Classical Mechanics, but I think my lack of a background in pure math / proofs is seriously hampering my ability to do any of the problems in the first chapter. For example: PROBLEM. Show that if a...
18. ### Other Question on math methods book

Hi everyone, which text on methods is better between the following two : 1) https://www.amazon.com/dp/0486691934/?tag=pfamazon01-20 2) https://www.amazon.com/dp/3319011944/?tag=pfamazon01-20
19. ### Alternative to Mathematical Methods books

I have a background in Calculus (Simmons and Lang), Linear Algebra (Lang), and Differential Equations (Simmons). I want to read a book in Mathematical Methods but I find that the treatment is just too superficial. Examples are, Mathematical Methods by Boas, Hassani, and Hobson. I want to know...
20. ### After Boas's Mathematical Methods?

Hi all, Is there a more advanced version of Mary Boas's Mathematical Methods? Specifically, these are some topics I would like to learn more about and work through problems on: 1. Uniqueness and Existence theorems boundary value problems with 2nd order PDEs of elliptic, parabolic, and...
21. ### Applied Mathematics for physicists books (poll)

Hello, i want to get a mathematics book for physicists, and i have stumbled across some good books, but as i have not read them yet, i can't really decide which one to buy. So, which one do you prefer and why? Also, do you have any other book to recommend? Thanks!
22. ### Deriving Properties of Inner Products for Complex Vector Spaces

(Not an assigned problem...) 1. Homework Statement pg 244 of "Mathematical Methods for Physics and Engineering" by Riley and Hobson says that given the following two properties of the inner product It follows that: 2. Attempt at a solution. I think that both of these solutions are...
23. ### Difference Between "Engineering Math" and "Mathematical Methods"

What really is the difference between a book for Engineering Math and a Math methods book for, say, Physics? They all look very similar to me. Also, a math method book may significantly differ from another math method book depending on the level covered and a math method book may be very similar...
24. ### Mathematical Methods in the Physical Sciences (alternative?)

Is there any alternative books that teach you how to just do the problems rather than emphasizing why, and is there any books that emphasize why in an easier format? Something like a "mathematical methods for dummies" book? This is the book I'm referring to (...
25. ### Understanding the method of Green's function

I'm trying to understand the derivation for methods of Greens functions for PDEs but I can't get my head around some parts. I'm starting to feel comfortable with the method itself but I want to understand why it works. The thing I have problem with is quite crucial and it is the following: I...
26. ### Bessel functions and the dirac delta

Homework Statement Find the scalar product of diracs delta function ##\delta(\bar{x})## and the bessel function ##J_0## in polar coordinates. I need to do this since I want the orthogonal projection of some function onto the Bessel function and this is a key step towards that solution. I only...
27. ### Mathematical Methods book

Hello, i am currently enrolled in a Mathematics course which covers these subjects: -Calculus of Variations -Laplace Transform -Fourier Analysis -Special Functions -Integral Equations And as an introduction to the subject it has several things from calculus like maxima/minima of functions of...
28. ### How to prove that H_a and H_b are orthogonal?

1. Okay, so I am going to prove that \int H_a\cdot H_bdv=0 Hint: Use vector Identities H is the Magnetic Field and v is the volume. Homework Equations this this[/B] k_bH_b=\nabla \times E_b k_aH_a=\nabla \times E_a k is the wave vector and E is the electric field The Attempt at a...
29. ### Boas - Mathematical Methods - Solutions to problems in book?

I started with Mary Boas' book "Mathematical Methods in the Physical Sciences". Now it is stressed in the introduction to make homework and do the problems. However, I would very much like to know if I got the answers right, and I even prefer if the problems are worked-out. So I guess my...
30. ### What units will this equation have?

Let u be density of something (heat, smell, etc.). Assume the something only diffuses; there’s no convection or ballistic transport. Let’s work in one spatial dimension (x). Then u satisfies the diffusion equation, ∂u/∂t = D ((∂^2)u/(dx^2))
31. ### Legendre Second Kind: $Q_n(x)$ Functions

Legendre functions $Q_n(x)$ of the second kind \begin{equation*} Q_n(x)=P_n(x) \int \frac{1}{(1-x^2)\cdot P_n^2(x)}\, \mathrm{d}x \end{equation*} what to do after this step? how can I complete ? I need to reach this formula \begin{equation*} Q_n(x)=\frac{1}{2} P_n(x)\ln\left( \frac{...
32. ### Is Intro to Mathematical Physics as Challenging as It Sounds?

I am transfer student and this going to be my first year in university. My major is electrical engineering and one of my requirements is to take an upper level physics course. I chose mathematical methods however the title of the class is intro to mathematical physics and i am worried that...
33. ### Prerequisites to Mathematical methods Mary Boas

Hello! I'm looking to study Mary Boas' Book on mathematical methods and i'd like to know if the prerequisites can be covered in ocw mit courses or any other open courses. Please do suggest if any. Also are there any parallels that can be drawn with the ocw mit courses for the various topics...
34. ### Mathematical Methods in the Physical Sciences by Boas

I study in high school, but I know a fair amount of math (differential, integral, and vector calc., differential equations, linear algebra, etc.) Would you recommend this book if I want to pursue higher levels of math such as PDE's and Tensors and so on? Does this book explain things clearly...
35. ### Failed first mathematical methods test

I got a 61% on my first mathematical methods for physics and engineering test. I thought I would at least get a solid C on that test :( If I were to receive a 100% on everything thing else ( 1 test , 1 final, 5 homeworks) I could end up with a 92.5% in the class. After that test I currently...
36. ### Carl M. Bender (Advanced Mathematical Methods )

Hello all, I just bought the book "Advanced Mathematical Methods for Scientists and Engineers - Asymptotic Methods and Perturbation Theory". I was wondering if anyone know about a solutions manual for the book? I would like to work through some of the problems while I go through the book, but...
37. ### Answers to Hassani "Mathematical Methods "?

This book "Hassani - Mathematical Methods For Students of Physics and Related Fields 2nd Ed." doesn't have any answers to end-of-chapter problems. I feel like I'm shooting in the dark. Can anyone guide me regarding how I can acquire answers to some problems, let's say odd numbered ones? Or...
38. ### Where should I go after Boas' Mathematical Methods in Physics?

I'm currently a rising sophomore (undergrad), and I'm trying to fill in some gaps in my applied math background this summer. So far, I've taken linear algebra and multi/intro analysis, but they were both theory-only and had very few applications (ex: I finished LA without knowing the various...
39. ### Boas: Mathematical Methods for Phys Sci Pr.1.13.25

Mclaurin Series with Division by Zero? Boas: Mathematical Methods for Phys Sci Pr.1.13.25 Homework Statement Using the methods of this section: (a) Find the first few terms of the Maclaurin series for each of the following functions. (b) Find the general term and write the series in...
40. ### Mary Boas: Mathematical Methods Problem 1.13.8

Homework Statement Using the methods of this section: (a) Find the first few terms of the Maclaurin series for each of the following functions. (b) Find the general term and write the series in summation form. (c) Check your results in (a) by computer. (d) Use a computer to plot the...
41. ### Not understanding textbook solution: Mary Boas mathematical methods

Homework Statement 4. Write the Maclaurin series for 1/√(1 + x) in ∑ form using the binomial coefficient notation. Then find a formula for the binomial coefficients in terms of n as we did in Example 2 above.Homework Equations { \left( 1+x \right) }^{ P }=\sum _{ n=0 }^{ \infty }{ \left(...
42. ### Good books on Mathematical methods

Hello, I'm a first year Physics student. I've decided to take on mathematical methods and be as thorough with it as I possibly can. I am looking for books that cover vector calculus, Orthogonal transformations, tensors, curvilinear co-ordinates, index notations and the dirac-delta function in...
43. ### Mathematical methods for physics and engineering

Hi everybody. I am studying Biotechnology (B.Sc.) and we only have one course of Calculus and one of General Physics. I would like to continue my study with am M.Sc. in Computational Science or something similar so i need to study more math and physics (so first of all math!). I found the book...
44. ### Mathematical methods in physical scince

I don't know where to post this thread. Where could i download the book on mathematical methods in physical science by Mary?
45. ### Mathematical Methods or Complex Analysis?

Hi, Physics Forums. I just have a quick question regarding which two math-type electives I should take as a physical chemistry major. Right now I am enrolled in Linear Algebra (Math 115A) and Mathematical Methods for Physicists (Physics 131) and plan on taking the second MM (Physics 132) next...

Homework Statement Derive the equation of motion of a particle of mass m and charge q moving in three dimensional space under a Coulombic attraction toward a fixed center. I have the answer for a plane but a i need it for the space Homework Equations Mathematical Methods for...
47. ### Mathematical Methods book for Undergraduate

Greetings everyone, I am posting this question here since I cannot post it in the math and science learning materials section of the forum. My question is that sometimes in physics I get into a lot of involved math particularly linear algebra, Hilbert space, partial differential equations and...
48. ### Physical Chemistry Electives: ODE, Mechanics, or Mathematical Methods?

Hello, everyone. I am currently a junior [physical] chemistry major and am picking out my future upper division electives. I've narrowed them down to a handful of classes and what I'm looking for is just a little background information on them, which ones might be better than others, general...
49. ### Mathematical Methods for Physicists by Arfken and Weber

Author: George B. Arfken (Author), Hans J. Weber (Author), Frank E. Harris (Author) Title: Mathematical Methods for Physicists Amazon Link: https://www.amazon.com/dp/0123846544/?tag=pfamazon01-20 Prerequisities: Calculus 1,2,3 Table of Contents: Preface Vector Analysis Definitions...
50. ### Mathematical Methods of Classical Mechanics by V.I. Arnol'd

Author: V.I. Arnol'd (Author), K. Vogtmann (Translator), A. Weinstein (Translator) Title: Mathematical Methods of Classical Mechanics Amazon Link: https://www.amazon.com/dp/1441930876/?tag=pfamazon01-20 Prerequisities: Contents: