Mathematical Definition and 1000 Threads

Homework Statement (5^2) + (11^2) + (17^2) +...+ (18n-1)^2 a)Write the sum in sigma notation b)Using the sigma identities solve the sum (easy to do)Homework Equations ∑i = .5*k*(k+1) etc The Attempt at a Solution The problem I'm having is with the 25 and 121. I thought it was ∑ (6n-1)^2...

hi i have this homework question and I am not sure if my thought process is valid. The Question: let a, b and c be roots of the polynomial equation: x^3+px+q=0 and S(n)=(a^n)+(b^n)+(c^n) now prove: that for S(n)= -p(S(n-2))-q(S(n-3)) for n>3my attempt: ------------- first off...

Hi I have a problem about Inequality. Let's suppose we have a inequality like this: axb≥d and cxd≥d so I want to find connection between a and d its possible to do something like that Thanks

can anyone give me the detailed mathematical deduction(proof) of kirchhoff's law?

Recall that the fibonacci sequence is defined as { f0=0; f1 = 1 and {fn = f n - 1 + fn -2 for n 2 Prove by generalized mathematical induction that fn = 1/sqrt(5)[ϕn - (-ϕ)-n] where ϕ = [1+sqrt(5)]/2 is the golden ratio.. (This is known as de Moivre's formula.) So...

I want to discuss about Chapter 8, equation 43 for any real number α(alpha) The author tells "The continuity and monotonocity of E and L show that this definition leads to the same result as the previously suggested one".(i.e.,Equ 33) But I think properties of L is not required for the...

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...

What are your favorite small numbers? Why? Anyone can post in this thread, but the rules are: 1. The numbers must be single digit (you can cheat if you use hexadecimal, hint, hint). 2. 1 doesn't count (it's not prime, so go away). 3. If a closed form is not available, you can only use 20...

I am reading Principles Of Mathematical Analysis by Walter Rudin. Chapter 8, Equation 28 needs some clarification. We are taking a lim as h->0 on a series. Value of series is lim as n->INF on the squence of partial sums. So first we take lim as n->INF on a sequence of partial sums and then...

I am not too used to reading mathematical text using symbols. I need some help confirming what I have in my textbook. The book is describing a point in 3D space using the definition R x R x R = {(x,y,z) | x,y,z \in R} and R is all real numbers Using this source describing the...

Hi All, Have the following given and would like some help with the 3 questions below. Any help will be greatly appreciated :) City 1 TOTAL POPULATION CITY 1 100,000 Avg Age of Population 27.8 Median Age (Male) 20.5 Median Age (Female) 27.8 % Male Population 46.43% % Female Population 53.57%...

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...

OK, so the word "addiction" has obvious negative connotations, but am I alone - methinks not - in being far more than just "interested" in maths, and actually more of a border-line addict, always looking for that next discovery/fix...? Bad mammal! lol (Heidy)(Heidy)(Heidy)

Homework Statement A wave is represented by y = A sin (kx + ωt). Draw two cycles of the wave from x = 0 to x = 2λ at a) t = 0; b) t = T/4, where T = 1/f = 2∏/ω Homework Equations y = A sin (kx+ωt) k = 2∏/λ (number of wave peaks) The Attempt at a Solution I had a really hard...

Hey! I've just started to learn some mathematical induction and it's proving quite tricky. Hopefully someone could help me out a little with my questions! I don't know how to format question on this forum but I'll try my best to accurately represent it: n $$sigma$$ i * 2^i = (n-1) * (2^n+1) +...

I have a difficult problem on my research exploration for math. I am modeling the convection currents of boiling water in a pot, which is heated by an electric stove. There is a constant supply of energy at 8000 watts (the average for a stove) that heats the pot from the bottom of the pot...

I have a difficult problem on my research exploration for math. I am modeling the convection currents of boiling water in a pot, which is heated by an electric stove. There is a constant supply of energy at 8000 watts (the average for a stove) that heats the pot from the bottom of the pot...

Here is the question: I have posted a link there to this thread so the OP can see my work.

In the attached equation from structural analysis, I don't understand the transition between the second and third equal signs. I think that u_{j,l}da_l = u_{j,1}da_1+u_{j,2}da_2+u_{j,3}da_3 , so doesn't equating da_j\delta_{lj} = da_l assume that l=j . can anyone help me see why this...

if the greater of two numbers is one more than twice the smaller and the smaller is x, what is the bigger? if the bigger is x, what is the smaller number? my answer to the first part is 2x+1. but i don't know how to represent the second condition in a mathematical form. and can you also give...

1. a.if john finished the job in 8 days, what was the part he finished in n days? b. by how much 4k greater than 4h? c. represent the amount of salt in x gallons of a 25% by volume of salt in solution water. d. represent 3 consecutive integers if the smallest is n. answers a. n/8 b. 4h+4k c. i...

Right now I'm a 2nd year biology major, focusing on neurobiology. During my first year I noticed that biology outside neuroscience and some physiology doesn't really interest me that much. So I started taking some maths and programming already during my 1st year. Now I'm taking mostly maths and...

Homework Statement if A' = BxC/(A.BxC) B' = CxA/(A.BxC) C' = AxB/(A.BxC) prove that A = B'xC'/(A'.B'xC') B = C'xA'/(A'.B'xC') C=(A'xB')/(A'.B'xC')Homework Equations The Attempt at a Solution I was sort of lost on how to do this. First I tried to simplify a', b', and c' and plug those into a...

Hi guys, I studied mechanical engineering and I am currently a graduate student (turbulence modeling). I am interested in the more formal/mathematical aspects of fluid dynamics, which are mainly worked in mathematical faculties and I would like to know if someone knows/have an idea about...

I'm a computer science major, computational biology in particular, that's looking to delve deeper into mathematics without actually double majoring. I've taken up to calculus 2, last topic covered was Taylor series. I've scoured numerous sources but to no avail. I've read that intro to logic and...

I'm working on a project on Logic and as part of it I want to write a selection of sentences in mathematical/logical syntax. I've consulted a mathemagician for the the first sentence but need confirmation on the other five, would someone be able to tell me if my maths lingo is correct? What I...

I've always wondered do mathematical physicists tend to normally have a rigorous training in physics? I know (at least at most universities) mathematical physics is grouped under the math department rather than the physics department. So what training in physics do these individuals actually...

I've just started working through Rudin's Principles of Mathematical analysis. In my opinion, the choice of symbols doesn't promote "rigour" and encourages us to make needless assumptions. For example, when defining an ordered field, the fourth axiom for addition states: To every x...

I don't know where to post this thread. Where could i download the book on mathematical methods in physical science by Mary?

With mathematical induction i should prove that is true for all natural numbers:http://img.tapatalk.com/d/13/10/18/u6epesu5.jpg Im sorry beacuse i have inserted an image,but I am still not used to write it in $$ here...

I ran into some formula: ^{a}_{0}∫J_{o}(kr) rdr= a/k J_{1}(ka) How can this be true? What property was used?

Hello! I am on my last year of study for my bachelor degree in Mechatronics. Looking back at my courses I can say that what I want to do with my life is mathematical modelling of systems (Be they technical, financial, whatever). My favorite courses so far were the mathematical ones and the...

I want to address this post primarily to people who have already studied mathematical logic, or are currently studying it. Since a while I've immersed myself in studying some math, and I must say that I started to enjoy pure mathematics. However, sometimes I don't really feel comfortable...

Not really sure where this question belongs, but it is based on a school assignment so I'll put it here. I'm a Physics major and math minor, and I am about halfway through my first group of advanced physics courses (namely intro classes for analytical mechanics, modern physics, and theoretical...

Homework Statement Not really sure where this question belongs, but it is based on a school assignment so I'll put it here. I'm a Physics major and math minor, and I am about halfway through my first group of advanced physics courses (namely intro classes for analytical mechanics, modern...

I have been studying topology and abstract algebra for some years, and for a lot of time I have been having a hard time trying to understand the definition and concept of "preservation of mathematical structures". For instance for binary operators a Homomorphism is said to preserve...

Hello everybody Two questions concerning the notion of wave function. 1. Every quantum mechanics book describes the space of wave functions (or more generally of quantum states) of a given system as a Hilbert space. But correct me if I'm wrong QM also says that two elements of such a...

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...

Hello^^ (I'm new here) I want to know the mathematical tools i need to study continuum mechanics. It would be great if someone give me a link that contains video lectures. Thanks for help .

Homework Statement Prove; n^2 > n+1 for n = 2,3,4 by Induction Homework Equations The Attempt at a Solution p(n)= P(2) 2^2> 2+1 --> 4>3 Induction step: P(n+1): (n+1)^2 > (n+1) +1 (n+1)^2> n+2 n^2 + 2n + 1 > n+2 | -n n^2 +n + 1> 2 | -1 n^2 +n > 1 Is this correct, and how...

Is this anything to get excited about? I have no idea what it's about. https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/ https://www.simonsfoundation.org/wp-content/uploads/2013/09/amplutihedron_span.jpg

Hello, I was an electrical engineering student and knew how to utilize the necessary mathematical tools to solve anything that came my way. I always had a deep latent predilection for mathematics but due to some constraints I was unable to spare much time on improving my knowledge of the subject...

Homework Statement Let u be an arbitrary fixed unit vector and show that an vector b satisfies b^2 = (\vec{u} \cdot \vec{b}) + (\vec{u} \times \vec{b})^2 Explain this result in words, with the help of a picture. Homework Equations The Attempt at a Solution I understand that the equations says...

How would you relate computer science to analysis ( real and complex ) ?

Assuming a mathematical plane, does it have a top and a bottom or does defining them make the plane three dimensional? Example: Given a flat, transparent plastic sheet. One draws a picture on it with a marker. If one turns the sheet over, in other words looking at the bottom of the sheet...

[FONT="Arial"]Is there a formula that shows the relationship between AC power and DC power? Something on the lines of, for example: Power of AC ... = Power of DC ... ? Thank you.

This is not a homework question but I project I am working on and need someone with more mathematical prowess than myself. I am using a computer program to draw random numbers from two independent distributions, x1 and x2, for two different cases and I want to establish a theoretical...

If the holographic principle says that the the observable universe could be represented as a two dimensional surface, and we accept the idea that the universe is itself a mathematical object, and cantor showed that we could in some cases represent higher dimensional sets within lower dimensional...

Homework Statement Find all natural numbers such that 2n ≥ (1+n)2, and prove your answer. 2. The attempt at a solution I can see this is true for n=0 and n>5. I try to prove this using induction as follows 20 =1≥ 1=(1+0)2 base case: 26 =64≥ 49=(1+6)2 so it is true for n=6 and suppose 2n...

Re: Are my answers correct? Quadratic and logarithmic modeling I actually have a few more things that i'd like you to check for me please. Answers: Appetizer: {0<=x<=10 y=7 x>10 y=2(x-10)+7 or y=2x-13 Quest: {0<=x<=40 y=40 x>40 y=1(x-40)+40 or y=x) Voyager: {0<=x<=60 y=60 x>60...