Mathematical Definition and 1000 Threads

Ever since Newton, determinism - i.e. the concept that the prior state of a system determines the next state of the system - has become an integral part of science, in particular of physics. This is particularly because Newton invented a mathematization of the concept of change: the calculus; in...

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking? If yes, which ones?

I found the formula but I can't understand how to interpret the 3 cases. Case 3 make sense. d > 0 if a > 0 because Vo^2 > 0 and Δx > 0 by default (can't have negative length). In this case t2 is negative because the numerator is a sum of two negative values and the denominator a > 0 so we...

Ok this should be just an observation solution .. But isn't the equation for chord length $$2r\sin{\frac{\theta}{2}}= \textit{chord length}$$ Don't see any of the options Derived from that..

On the outside rim of a circular disk the integers from 1 through 30 are painted in random order. Show that no matter what this order is, there must be three successive integers whose sum is at least 45.

How do I guarantee that that the friction in the movement of a simple mathematical pendulum is negligible?

How much mathematical rigor do you need to have good understanding of physics? My professor for multivar calc this year isn't really that good(that or I'm not good enough to keep up) so I've resorted to reading and working through Stewart on my own and I'm wondering if that's enough since...

A coil is modeled as Z = jwL or Z = sL or V = L dI/dt What are the equations for an induction motor? Single-phase one.

Consider a circle with a chordal line dividing the area into two unequal parts. It seems to be accepted practice to call the smaller of these parts a circular segment. Is there a generally accepted name for the larger area? I've been writing some material where this geometry arises, and I've...

Dear all I am trying to prove by induction the following: I checked it for n=1, it is valid. Then I assume it is correct for some k, and wish to prove it for k+1, got stuck with the algebra. Can you kindly assist ? Thank you.

I don't know how to type mathematical symbols and equations and stuff. Like if I want to ask something here in physics forum, I need to type mathematical expressions like everyone here does. How can I do that? Do I need any software?

Salutations, I have been trying to approach a modelling case about organism propagation which reproducing with velocity $$\alpha$$ spreading randomly according these equations: $$\frac{du(x,t)}{dt}=k\frac{d^2u}{dx^2} +\alpha u(x,t)\\\ \\ u(x,0)=\delta(x)\\\ \lim\limits_{x \to \pm\infty}...

Sorry if that title doesn't match up well with my question. I think it captures roughly what I'm wondering about. My uncertainty is to do with how much of mathematics is certainly true. Like, if I picked up any undergrad or grad textbook in mathematics, would everything in it be true based on...

I am currently an undergrad in pure Math. Until now, the courses I found the most fun/interesting were Probability 1&2, Geometry and Group Theory. I still have 3 semesters to go. Prior to math I did some university courses in physics which were Classical Mecanics1, Optics and Intro to modern...

I am looking for good references / clarifications on the subject. First of all, my question is concerned only with mathematical formulation of something that sort of plays the role of the Feynman path integral of the "standard" QFT. It is not concerned with the physical or philosophical...

Homework Statement Prove that 1\cdot1!+2\cdot2!+...+n\cdot n! = (n+1)!-1 whenever n is a positive integer. Homework EquationsThe Attempt at a Solution I'm having trouble simplifying towards the end of the proof. Proof: Let P(n) be the statement 1\cdot1!+2\cdot2!+...+n\cdot n! = (n+1)!-1...

Hi, Before I post my question, let me admit that my foundation on mathematics is poor. I am trying to work on it, specifically on the application part. When I came through the following image, I was stuck to understand why I will need one like Taylor's series in a simple case like "F+ΔF = F...

I'm in need of assistance for the following attachement.

This is probably a stupid question but I have Neumann BC boundary : ## \nabla u . \vec{n} =0## (same for ##v##)conditions for the following reaction-diffusion system on a [0,L_1]x[0,L_2]x...x...[0,L_n] n times in n dimensional space so ##u=u(x_1,...,x_n,t)## is a scalar I believe? so that ##...

I know to calculate a combination with n options and r selections while repetition is allowed you are supposed to do (n+r-1)! / r!(n-r)! and the purpose of r! as a denominator is to act as a ratio to eliminate same outcomes but of different orders and is what makes us calculate the combination...

Homework Statement Use mathematical induction to prove that (8n − 7n − 1) is divisible by 49 for any n ∈ N. Correction by mentor for better readability: ##49\,|\,(8^n-7n-1)## The Attempt at a Solution We can see that the base case is satisfied here: n = 1, 8^1-7*1-1 = 0 and 49 | 0 is true...

Anyone completed IA Maron Mathematical Analysis? Anyone like it?

This doesn't really fit in any other place. I'm interested in alternatives to the Gini coefficient for studying inequality, such as were discussed in this thread and this one. What do I see as the shortcomings of Gini? By example: in Lower Slobovia, everyone has nothing. It's a perfectly...

Homework Statement 1. Show that for all real numbers x and y: a) |x-y| ≤ |x| + |y| Homework Equations Possibly -|x| ≤ x ≤ |x|, and -|y| ≤ y ≤ |y|? The Attempt at a Solution I tried using a direct proof here, but I keep getting stuck, especially since this is my first time ever coming...

In everyday language, beauty is an emotional concept. How would you mix that with quantum physics and the mathematics behind it? Or is what he refers to as "beauty" is more like simplicity? I mean, I agree with the man, the Standard Model feels redundantly complex, but I feel like there is...

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...

Hi everyone, I came upon a simple mathematical conundrum a few decades ago that has irked me for a while now and for which I don't have a reasonable mathematical explanation. The only reasonable "explanation" I currently have is that 'certain mysterious things happen when tending towards...

What is the difference between mathematical singularity and black hole singularity[emoji780]

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...

Hi all, I am making a decision regarding the mathematics courses I should take before graduating so that I can leave Uni with a "decent enough" mathematical foundation. Some courses I had in mind were Linear Algebra, Group Theory, and Probability & Statistics, however I have little knowledge...

From another forum I once learned the English expression pet peeve. More and more I realize that in fact I host a whole animal shelter of mathematical (in the broad sense) pet peeves and, maybe worse, sometimes I am causing them to others. In this thread I would like to hear about yours. To...

I just like to read and know, and still, I realize that there have been so many works in mathematics and so much to study which I don't even know of. Is there any way I can keep a track of different mathematical works so that I can read them. For example, it was not very late when I came to know...

Hi. I am trying to understand the images that I have posted below. Each layer of Mathematical Structure Hierarchy in the image in this post and Mathematical Space Hierarchy in the image in this post are: statements. 1. What do these statements of each layer of these hierarchies in the...

Homework Statement Attached Homework Equations Below The Attempt at a Solution To be honest I was going to differentiate one equation to get a 2nd order ODE and plug in the other equation, since to me ##v(0)=0## is not strong enough to do as below, am I completely mis-interpreted...

Hello everyone and I hope you had a happy Easter if you celebrate it and even if you don't, I hope you had happy day at least! I was wondering if anyone knew of any interesting or "fun" mathematical conjecture, equations or whatever that an inexperienced high schooler (me or anyone else curious)...

I'm aware that there are definitions of how reference frames translates to mathematics. But I've came to the following. How incomplete would be to say that, mathematically speaking, two Lorentz (or whatever) inertial frames are two subspaces of a given vector space whose span is the same vector...

Prove by mathematical induction that n sigma r^3 = n^2(n+1)^2/4 r = 1 so far I have 1 sigma r^3 = 1^2(1+1)^2/2 r=1 1 = 1(4)/2 1 = 4/2 1 = 2 I'm not sure what to do after this for the k+1 case.

Hi, First of all, I'm not sure what section to put this in, so if this is in the wrong section, please accept my most sincere apologies. I'm trying to solve this puzzle I've come against, and I'm not quite sure what the best way to go about it is. Here's the question. So, it seems to me...

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...

Why mathematicians do not solve mathematical theories in different fields, name quantum mechanics that tries to describe gravity or any other theory such as multiverse/lqg/branes etc. It's just pure mathematics, only this language can fully describe universe, so why is it still just a theory...

I would like to know where it would be possible to download a 3d simulation software tha twould operate according mathematical pharameters

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...

Hello, I have an problem with mathematical modelling of a special kind of articulated trailer (please have a look at the images: 1st image is the yaw plane and the second is the ZX plane). I have two methods of deriving equations of motion namely Lagrange and Newton-euler to analyse their...

I am a working professional trying to get back to some physics that I used to enjoy a couple of decades ago. I still do remember the basic calculus (integrals, partial derivatives, basic ODE) and am interested in studying General Relativity. I have a decent understanding and memory of Special...

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Renormalization Continue reading the Original PF Insights Post.

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Interacting Quantum Fields Continue reading the Original PF Insights Post.

<Moderator's note: Moved from a technical forum and thus no template.> A^n = 1 2^n 0 1 Prove your formula by mathematical induction. I began by taking A to successive powers but not sure of what my formula should be. A^0 = 1 0 , A^1 = 1 2 , A^2 = 1 4 , A^3 = 1 6 ...

When I asked this question in another forum, some people argued that scientific and mathematical discoveries are born out of curiosity and a way to explain unknown elements that surrounds us. Others say it comes from originality. In my opinion, I think it does come from curiosity, but you have...

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Free Quantum Fields Continue reading the Original PF Insights Post.

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Quantization Continue reading the Original PF Insights Post.