Mathemathics Definition and 104 Threads

Homework Statement ##\lim_{h \to 0} \frac{f(x - 2h) - f(x + h)}{g(x + 3h) - g(x-h)}## While f(x) = cos x g(x) = sin x Homework EquationsThe Attempt at a Solution Using L Hopital i couldn't make it more simple. I tried to divide it by cos and sin Can you give me clue?

Hello. My problem is that I began with Linear Approximation and I'm terribly stuck. I have problems understanding its very concept and with calculations. (It may sound stupid but I'm autodidact and I'm studying mathematics in english (not my mother tongue) and sometimes it gets hard). It would...

Hi. π is a constant. The purpose of π is to use it to find circumference of a circle or area of a circle. Correct? Can you please elaborate? Can you point out any other two constants and its purpose? Thanks.

Why does max tegmark's and brian greene's levels of multiverses consider as the highest level the mathematical multiverse hypothesis if other authors like David Lewis consider that there could be also universes non described by maths? Why does it stop at level iv (mathematical universes...

I previously made a derivation of Neumann potential. It can be found in the pdf file below. I originally made it in the ##dx## method. It involved equations like ##dm=I dS##. My maths teacher told that such an expression has no meaning, at least in elementary calculus. However I argued that my...

I calculated a simple complex function integration using Mathematica 11. As the screenshot shows, the only difference between the two inputs is that I set a = 1 in the second one. However, the two outputs differ by a factor of 2. What's wrong? Is this a bug?

Here's a math question I've been thinking about lately. We have a stick of length one which is broken in one spot (with that spot chosen randomly and uniformly). Of the two broken pieces we take the one on the right and break it into two pieces in the same manner as before. With our three...

The term 'phase space' is often used in the study of nonlinear dynamics.What is it.

In state space, the coordinates are the state variables of a system.So,each point in state space represents a specific value of state variables.Thus,state space representation represents the changes in a dynamical system. The state variables are the minimum number of variables which uniquely...

Chaos is deterministic behavior.Why is chaos deterministic.Why chaos is not random. Chaos is sensitive dependence on initial conditions,a slight change in initial condition can give rise to totally different trajectories.

I was reading the following article that tries to use some equations originally proposed by Pauli in 1951 to reason from one of two reasonably plausible axions that there are tight constraints on the fundamental particle content and mass spectrum of the Standard Model together with BSM...

Hello All, I am currently a junior in physics and have set sights on Materials Science (Electronic Materials/Nanotechnology) for grad school. My school does not offer MS.Eng as a degree and so the only Materials Science course I can enroll in as the general "Introduction to Materials Science...

Hello. I have an object that I want to talk about. The object above does not seem to have numbers in a definite pattern, so, I think that this object will not have a single equation that describes the object, but instead there will be multiple number of equations of 'y' in 'x'. Correct?

Hi , everyone! This is my first post/thread/anything on this forum so first I apologise if I slip up or make any mistakes. Anyway, my question is about recommendations for textbooks for Undergraduate Number Theory. So far, I have studied Calculus 1-3 (including things like line integrals...

Homework Statement Homework Equations d(y)/d(x) --> max area area of triangle = 1/2 . base . height The Attempt at a Solution for number (2) [/B] x^2 + y^2 = r^2 --> circle equation base = 2R, height = y Area = 1/2 . 2R . y area = 1/2 . 4. √ (r^2 - x^2) area now is half of max = 2, so...

Hello. I am looking for guidance. I have been working in software industry for about eight years now. I see that the trend is moving towards making a machine intelligent. I want to be part of this trend and move forward. My questions is: What skills do I need to become part of this era of...

Hello,I am a mechanical engineering student that loves mathematics and fluid mechanics. My school offers three different analysis courses and I’m not sure which to take. I took honors Fundamental of Mathematics, where we covered Abstract Linear Algebra, Set theory (along with rings and fields)...

The general Ampere force law equation given by Maxwell is: According to Maxwell, all terms containing function ##Q(r)## will vanish after closed integration w.r.t. ##s'## because they will get reduced to functions of ##r## and the upper and lower integration limits will be same since the...

Hi, I am finding it a bit difficult to find a job where pure maths is actually done and looking for some ideas or examples from people who have done this please. I am in my last semester of a Graduate Diploma of Science (Applied Data Science) and am considering what to study for my Masters/pHD...

Homework Statement Let ## f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} (a_n \cos nx + b_n \sin nx) ## What can be said about the coefficients ##a_n## and ##b_n## in the following cases? a) f(x) = f(-x) b) f(x) = - f(-x) c) f(x) = f(π/2+x) d) f(x) = f(π/2-x) e) f(x) = f(2x) f) f(x) = f(-x) =...

Homework Statement Shown in the photo attached. 2. Homework Equations ∫V r2Sinθdθdφdr in spherical coordinates ∫V dxdydz in cartesian coordinates equation of a sphere x2+y2+z2=r2 The Attempt at a Solution In this case y=(y-2): sphere displaced on the y-axis. and since it is bound by all...

Homework Statement I look at the distribution ##(Y_1,Y_2,...,Y_n)## where ##Y_i=μ+(1+φ x_i)+ε_i## where ##-1<φ<1## and ##-1<x_i<1## . x's are known numbers. ε's are independent and normally distributed with mean 0 and variance 1. I need to find the the maximum likelihood estimator for μ and...

I am planning to self-teach myself Trigonometry and all the other required fields before jumping into calculus. I have compiled a list of books that I have researched and would like your opinions and recommendations. Books: Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry...

This is my first post on the forums, Hello! my names Tim, nice to be on here! I will keep this as short as possible. In high school, I hated math and loved science. Its a story I hear often. I was bad at math, or maybe it just wasnt introduced to me correctly. It took a lot of soul searching...

I try to find out how to minimize functions i R by using nlm function: > f<-function(x,y){x^2+y^2+10-5*x-y} > nlm(f,0.1,0.1) That only gives me an estimate for x. How would write the code to get x and y?

I come from totally different field. studied previously business management but I was always fascinated by technologies. I find it really difficult to keep up with all the new terms and mathematical equations to follow up. I have to look after each words in every paragraphs. I have searched for...

Homework Statement If a, b and c are coplanar vectors related by λa+μb+νc=0, where the constants are non-zero, show that the condition for the points with position vectors αa, βb and γc to be collinear is: λ/α + μ/β + ν/γ = 0 Homework Equations Dot product Cross product Tripple product Vector...

Which is more mathematical among The Princeton Companion to Applied Mathematics and Mathematics for Physics by Michael Stone and Paul Goldbart? Both of them are applied mathematics books. What are the main differences between them? Which is more mathematical i.e. mathematically advanced...

Long story short... I have been in community college for quite a while now and I just recently switched my major to Electrical Engineering from Business Administration. I personally just found that career path so boring and so I started hanging out with the science nerds at my community college...

Homework Statement The following equation is to be solved for all x: ## \cos(x) + \cos(3x) = \sin(x) + \sin(3x)## Homework Equations The tripple angle formulas: ## \cos(3x) = 4\cos^3(x) - 3\cos(x) ## ##\sin(3x) = 3\sin(x) - 4\sin^3(x) ## The Pythagorean trig identity: ## \sin^2(x) + \cos^2(x)...

Homework Statement If modulus of z=x+ iy(a complex number) is 1 I.e |z|=1 then find the argument of z/(1+z)^2 Homework Equations argument of z = tan inverse (y/x) where z=x+iy modulus of z is |z|=root(x^2+y^2) The Attempt at a Solution z/(1+2z+z^2) = x+iy / 1+2(x+iy)+( x+iy)2 ...

Hello there :)

Hello, what are some good books to learn group theory for physicists at an undergraduate level? Is Zee's Group Theory in a Nutshell good? Thanks in advance

So I’ve just turned twenty-one years old as of May 2016, and I will be a third year physics major starting in August for the Fall semester. I always hated school growing up, all throughout elementary, middle, and high school; I didn’t find any of the subjects interesting at all. When I was in my...

consider ODE : Show that the solution to this ODE is: Can someone tell what kind of ODE is it?I thought,it's on the form of Bernoulli ODE with P(x)=0.Is it possible to still solve it by using Bernoulli Methodology?I mean by substituting u=y^1-a with a=2? Thanks

What are the mathematics behind multiple dimensions? Does mathematics allow for the existence of more than four dimensions? What allows the ability to possesses more that four dimensions, if there is already proof? I looked around, but I didn't find much by way of the answer I was looking for.

Hello all. Next year, I'm going to attend the university. I really want to study mathematics, since I enjoy doing this. My grades are quite high, but I spend a lot of time understanding what's really happening, although this is not always possible. I also spend time by learning things like...

A common claim that hurricanes and cyclones have geometrical proportions that resemble a logarithmic golden spiral. Knowing that cyclones and hurricanes rotate because of the well-known Coriolis Effect, is it possible that the Golden Ratio is just a natural manifestation of the Coriolis effect?

Homework Statement Homework Equations p.q+p.r The Attempt at a Solution I've expanded p.(q+r) to give p.q+p.r. The magnitude of p is 3, and since ABE is an equilateral triangle, the magnitude of q is also 3, right? So then p.q=9, but the answer scheme states that p.q=4.5. I'm still pretty...

Temperature of a system is defined as $$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$Where Ω is the number of all accessible states (ways) for the system. Ω can only take discrete values. What does this mean from a mathematical perspective? Many people say we...

Hi As I am venturing in graduate level mathematics, I am having a recurring problem; I keep getting stuck in the abstraction of it. Usually it involved set theory; I never get "fluent" in it. However, the main problem is abstraction. For instance, this semester I had topology, and the...

Someone has spray-painted (no idea why) these formulas on the blackboard. I assume they are from the math class that is held before our physics class. I'm guessing it to be calculus or mathematical logic but I don't know. What I'm reading is that pi equals lambda and therefore f equals 1. Does...

Hello world, (or whos reading) My names JJ King, and I am a 1st year under grad at a community college majoring in mechanical engineering (not 100%) and stuck on it, and i'd like to minor in either mathematics or physics- but that's a little bit on me - i'd like to really get a good idea on...

Hi! I know some constitutive models for elastic materials like Neo-Hooke or Mooney-Rivlin, which give a relation between elongation ##\lambda=y/y_o## (where ##y## and ##y_o## are the length of the elastic material in a uniaxial compression test in the direction of the compression at stress ##P##...

I'm a highly determined (and slightly stubborn) high school freshman who wants to learn enough mathematics to conduct mathematics research with a mentor. Looking on the internet, I found a program called MIT Primes, where students can be matched with graduate students/professors at MIT to...

I'll give you my questions first, so you don't have to read the rest of the mess if you don't feel like it. are (non-thesis) master's programs typically less picky than a PhD program? are master's programs typically a good place where I could bolster my GPA with some mathematics courses that I...

Computational Imagination has an interview up with John D. Cook. John is an applied mathematician who I have occasionally corresponded with, and in this interview he talks about his transition from academia to industry, the different careers he has had, and offers some tips on software...

Homework Statement presentation of a component and its mechanical concerns along with some mathematics behind it. Homework EquationsThe Attempt at a Solution I really have no idea how to even start this but I thought of doing the spring in mechanical pens. I would appreciate any help :)

hi my name is Hessam and study mathematics. so i try look at any things behind the skin

Lets begin with the Philosophy of Cantor. Here is a quote from wikipedia:http://en.wikipedia.org/wiki/Georg_Cantor#Philosophy.2C_religion_and_Cantor.27s_mathematics "Philosophy, religion and Cantor's mathematics The concept of the existence of an actual infinity was an important shared...