Mathematical Definition and 1000 Threads

I want to have a simple and intuitive explanation of why the sin and cos waves have such a simple repetitive values for their derivatives at a specific point. Their derivative values are also periodic in respect to the derivative order. For example, e^-x is also periodic, but its derivatives are...

As I understand it, the usual method for proving uniqueness of a mathematical object (for example the identity element of a group) is to use a proof by contradiction. Now, for example, if we have ##a## such that ##ax=b## and we want to prove this is unique, we start by assuming the contrary...

Hi, my Calculus book (Elementary Calculus an Infinitesimal approach) uses a mathematical argument, and I'm not sure if it's correct so i thought i wuold check with you guys :) When the book want's to find the derivative of f(x)=x^2 the books starts like this y=x2 Δy +y = (x + Δx)2 So my...

Why is/are an electron/electrons a sphere/spheres ? Need the mathematical proof...

Hey everyone, I just got my admission from the following programs: MSc Mathematical Physics --Edinburgh MSc Theoretical Physics -- Durham MSc Quantum Fields and Fundamental Forces -- IC I have a BSc in Mathematical Science, and I wish to continue a Phd study in particle physics and cosmology...

In order for me to be able to run a simulation I need to write an equation which calculates the distance from a point inside a circle of radius 'r' to any point along the circle's circumference using a point a distance 0<=d<=r from its center. The ultimate system to be simulated is a radially...

Which mathematical software(s) can you recommend for 1. As a substitute for a calculator (TI89): making basic graphs, regressions (linear, exponential), vectors, solving equations, showing graphs in 2d and 3d? 2. Writing an ebook with lot's of math. I'm thinking Mathml or Mathtype might be...

Okay, so I'm currently sitting my final exams before I'll be attending university come September. Here in Ireland if you wish to attend any third level institute then you must apply to CAO (Central Applications Office) on your CAO application you put a numbered list of courses you are interested...

Homework Statement Sorry to disappoint the math fanatics but no this is not a question that integrates all three topics at once but individual ones. I still need assistance though with the following more so in the reasoning behind them as I feel my logic is flawed...

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...

Hi there, Once again I find myself twiddling around with some quantum mechanics, and I bumped into something I find strange. I can't see what the error of my thinking is, so I hope someone could be able to point it out. I'm looking at solutions to the infinite square well, and arrive at the...

I have a master's in physics. I'm looking at PhD programs, but I really don't want to take the same courses over and take comprehensive exams (or the damn GRE). I managed to squeeze in a few math classes before I finished. I would like to do research in physics, but from a more math-heavy...

Hi everybody! I was just curious if there are any good or recommended mathematical pod cast, as I was recently bitten by the math bug, just going back to college after getting out of the military and would like to have something interesting to listen to while driving to and from school. I am...

ZapperZ submitted a new PF Insights post Mathematical Preparations Continue reading the Original PF Insights Post.

I always have some interesting on the photon. after I read the oscillator expansion of the electromagnetic field in a finite volume, I find photon is more a mathematical concept in theoretical physics than real particle. not like electrons, number of photon is a representation of the energy...

Homework Statement Prove that (n2+3)(n2+15) is divisible by 32 for all odd positive integers n. Homework Equations I suppose we are supposed to use mathematical induction since it is in that chapter, but the following questions specifically state that we should use induction but this question...

how can we relate innermost stable circular orbits, keplerian, epicyclic, frame dragging precession frequency with dipole moment.

Please, I've been unable to comprehend how the mathematical wave equation was derived.. Please can anyone explain it to me...

Anyone else use mathematical textbooks from around 1950? I do... by accident... Tend to pick them up in thrift stores where they just get dropped, discarded... But, I find them engaging! Many of them are around 1950. It is also a little fun to see how mathematics has progressed. For example...

Hello PF, pardon me if this isn't the wrong place but I just had a quick question. So I have always wanted to do Theoretical Physics (particular interests are Quantum Gravity, Cosmology, QFT and Quantum Optics, but those are subject to change), but recently I have started to look into...

how can i find this book?? ( Isaac Newton - The Mathematical Principles of Natural Philosophy)

probably, I am a home-utored student(self-teaching!) and I'm seeking a little help. While I am drawn to MANY forms of physics or mathematics, the mathematical physicist seems to be the ticket. But I am not sure. I was just wondering if this would be a good way to go, and what exactly is the...

Hello I recently noticed that mathematical logic is related to computer science. I haven't studied math in university yet I'm not good at math and Since I'm not a native English speaker some English is hard to me. Is there any good and easy book which describes mathematical logic used in...

Where exactly does this area of study reside? Is it within the math department or the physics department? More specifically, do you need to get accepted into a math or physics graduate program? The undergraduate mathematical physics program here is listed under both the math and physics degrees...

Homework Statement A step in this process of proving Sn: 1+4+7+...+(3n-2) = n(3n-1)/2 confuses me. I hope someone can clarify this for me. I do not require the work done, I need clarification on a step only. Thanks! Homework Equations After assuming n=k, we say Sk: 1+4+7+...+(3k-2) =...

Hi i am working on a research paper for which i need very good citation for the analytic analysis coupling Electric - Thermal-Structural physics(via Joule Thomson effect & Thermal stress/strain). Please provide any good source of mathematical relations describing the above complete or in part...

Many books in QM (eg: Sakurai) mention that the stern-gerlach experiment provides enough motivation for the mathematical structure of QM, Sakurai even mentions Gottfried's book. Point is, i didnt find Gottfried's book, so i am looking for other books that develop the math of quantum mechanics...

Homework Statement I am just learning the joys of mathematical induction, and this problem is giving me fits.Homework Equations I am trying to prove that 2 + 4 + 6 + … + 2n = [2n(n+1)]/2The Attempt at a Solution The base case is to prove P(1) is correct. Simple enough -- 2 = [2 x 1 (1+1)]/2...

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...

Learned this identity a year ago randomly studying for adv biomechanics and was wondering if there were real-world applications for this outside of mathematicians appreciating the formula.

This is from from Sakurai and Napolitano HW Prob #2.6. I've done the HW problem and can fit all the pieces together with the mathematical formalism, but even afterwards I'm still scratching my head wondering what I'm looking at. I start with the commutator [[H,x],x]. If I take...

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...

I don't know is this good place to put this topic anyway I am on the first year of physics and I am struggling with mathematical analysis. I can't understand a lot of thngs that we are doing actually I can't even follow our lectures. I would be really grateful if someone recommend me a book that...

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...

$$ T(n) = \begin{cases} 2 & \text{if } n = 2 \\ 2T(\frac{n}{2})+n & \text{if } n = 2^k \text{, for } k > 1 \end{cases}\\ \text{ } \\ \text{ } \\ \text{ } \\ \text{Prove } T(n) = n\lg(n) \text{ if } n = 2^k\text{, for } k > 1.$$ I am crawling through the "Introduction to Algorithms" textbook...

I'm a graduate mathematics student and I did my undergrad in applied math. I also took the normal 10 hrs of physics foundations and then a semester of modern physics (basic quantum intro, special relativity, orbit states etc.). I was thinking about pursuing study in areas that would be...

Hi! I'm interested in mathematical analysis of Full-Wave Bridge rectifier with smoothing capacitor. I tried to find it on web but without success. I read how smoothing capacitor affect output voltage, but I never saw some mathematical description. Can one mathematically prove it? How can one...

Hi all, Wasn't sure whether this fits best in the maths or engineering forums, either way I'm hoping that a mathematical solution exists for my problem which I'll now explain. My problem is one of biomechanics. One of the primary exercises I use is the barbell squat. Holding a loaded bar on...

So I've just recently started learning path integral methods in QFT and string theory, and I've heard from numerous sources that the path integral (specifically fermionic path integrals, perhaps?) are objects which are not at all on solid mathematical ground. The feeling I get is that perhaps...

Are there any QFT books written from a mathematical perspective? Something in the same vain as V. Arnolds Mechanics and Takhtajan's QM. Thanks.

I am confused on a math problem. I am supposed to use mathematical induction to show that (Summation with n on top and i=1 on the bottom) (2i-1) = 1+3+5+...+(2n-1)= n^2

Homework Statement Consider the continuous-time processing system in figure 1, which has two inputs and one output. The linear sub-system H is characterised by the impulse response h(t) = e −2t , where t denotes time. Block diagram is the product of x1(t) and x2(t) going through a block step...

Homework Statement There exists a number m, which is an element of the positive integers, that for all positive integers n, n+m can be divided by 3. Prove whether this statement is true or false. Homework EquationsThe Attempt at a Solution I ran into a similar question earlier on, which just...

If there were an infinite number of universes will it be true to say that every conceivable (imagination) life form exists somewhere? Example, somewhere in a universe a 3 headed dragon exists - or does mathematical limit apply in this case?

In the last semester I was taking a microcontroller programming course. For the programming assignments, our professor would hold an extra credit competition where we competed for the smallest, fastest, and most energy-efficient code for the same application. It got me thinking. What I'm...

Can you explain me mathematically one particle in many places. Thanks

I am majoring in Physics and Math at Purdue University. For the physics requirements, I need to take two Mathematical Methods of Physics courses. Below are the catalog entries for the two courses. Mathematical Methods of Physics I Discussion of wide-ranging physics problems from mechanics...

I participated in a recent thread where it was obvious the poster was confused about what physical theories are. Of course they are mathematical models, but they say the mathematics can't be the reality etc etc. I am sure regular posters here have seen the arguments - they appear with...

How do people here feel about Max Tegmark's Mathematical Universe Hypothesis (http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis). I see it as an extreme form of reification (http://en.wikipedia.org/wiki/Reification_%28fallacy%29). In this sense, it is taking to the extreme a common...

Hey guys First real thread besides my introductory thread. I'm a Danish student in what is somewhat equivalent to my junior/senior year in the american school system. That was a small attempt at school system conversion. I'm writing a project about the black hole Sgr. A* in the centre of our...