Mathematical Definition and 1000 Threads

In Boas' book I can read that the definition of center of mass of a body has coordinates x_{CM}= \int x_{CM}dM= \int x dM. Shouldn't it be this same integral but divided by M?! Also, I didn't find the definition of center of mass for particles or any non continuous bodies. I'd be grateful if...

I want to be able to follow basic books for quantum physics to get a taste of some of the underlying principles. The problem is: I don't even know half of the symbols. So basically, what mathematical knowledge is needed to be able to follow the formulas and principles in a quite basic quantum...

This is a very philosophical question, so i understand the answer is going to be very arbitrary and subject to opinion. I am interested in both Pure mathematics and Theoretical Physics. The time is soon approaching, where i must decide upon which path to take. I love proofs, and i love...

I just have a few quick questions on mathematical neuroscience. What are the branches of mathematics that are used frequently in neuroscience? And finally, is it common for math majors to enter neuroscience in graduate school? Yes, I'm thinking about it micro, now don't pester me!

Hi, I'm a physics major working an internship for an engineering company at present. I have been trying to model the energy consumption and/or power for an elevator system. The goal is to be able to input different variables (cab weight, capacity, counterweight percentages, motor types...

Hello. I'm a college undergrad who has developed a mathematical perspective technique for drawing that I am convinced is original enough to be meaningful. Without going into too much detail, I think I have the mathematics background to formalize it, and I have the visual arts background to make...

I need to understand physics (and other) concepts but I'm having trouble visualizing what the equations mean. One example would be an applied math thing - I want to understand what about electromagnetism exactly the Maxwell equations are describing exactly so I can gain insight into what math...

Hi! I started to look into freq response analysis of a cantilever beam using COMSOL. Luckily COMSOL already has an example model "Model Library>> Structural mechanics module>>Dynamics and Vibrations>>rotating blade". While not changing anything in the model and with Omega=0 and Cloris =0, I get...

\vec{E}=f_1(z-ct)\hat{x}+f_2(z-ct)\hat{y}+0\hat{z} f_1(u) and f_2(u) are functions of "u" u=z-ct i have the formula \nabla \times \vec{E}=-\frac{db}{dt } \nabla\times\vec{E}=|\begin{array}{ccc} \hat{x} & \hat{y} & \hat{z}\\ \frac{{d}}{dx} & {\frac{{d}}{dy}} & \frac{{d}}{dz}|=\\...

I do not know if this is the correct forum to post this, but I have always wondered if the ability to play chess and mathematical ability go hand-in-hand with each other. A lot of people around me always tell me that. I like playing chess, I don't know if I'm good, but I like playing it. I also...

"Mathematical Logic" by Cori and Lascar: Incomplete proof of Lemma 1.9? I have a question on the book "Mathematical Logic: Propositional calculus, Boolean Algebras, predicate calculus" by Rene Cori and Daniel Lascar. Proof of Lemma 1.9 given on...

I have a question on the textbook "Mathematical Logic: Propositional calculus, Boolean Algebras, predicate calculus" by Rene Cori and Daniel Lascar. This is not about an exercise but about the conceptual content of the book. So I did not post this in the "Coursework and Homework questions"...

I pasted a paragraph from http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-845-quantum-complexity-theory-fall-2010/lecture-notes/MIT6_845F10_lec02.pdf" below. ------------------------------ Consider the following matrix which represents a 45◦ counter clock wise...

In electromagnetism J denotes the oriented charge-current density, J=d*F. Conservation of charge immediately follows. J=d2*F=0(identically). All exact forms are closed. We can identify scalar mass as the norm of the one-form, μ=(E/c2,-p/c). *μ is then spatial mass density. Like...

"100% Mathematical Proof" vs Vellmen's "How to Prove it" Hello, I'm looking for books that teach proof methods and techniques. I know Vellemen's book is a popular choice but a few dissenting reviews among unanimous praise, on its amazon page, caught my attention. Like this one: And here are...

Homework Statement Prove that 11^n - 4^n is a multiple of 7 Homework Equations N/AThe Attempt at a Solution I substituted k+1 in for n and simplified to get 11(11^k)-4(4^k) but after this point I get stuck. Any help would be appreciated.

Homework Statement Summation of i(i + 1) (with i going from i = 2 to i = n-1) = n(n-1)(n=1) / 3 a. Write P(2). Is P(2) true? b. Write P(k) c. Write P(k+1) d. Prove by mathematical induction that the formula holds true for all integers n \geq 2 Homework Equations...

My system is a compound pendulum hinged at some distance from one end and have a propeller mounted dc motor at the other end. I wish to position the pendulum with the help of motor propeller system. I tried but i am unable to get a mathematical model for it. I am getting a non linear model...

I have a problem. The amount of units I have taken up until now (this coming semester I'll be starting my Junior year) and the amount of time I have left is restricting my options for math courses. I do want to become a physics major and I intend on going to grad school. I have a strong...

Hi, So I'm with a real dilemma and I only have a few days to make a choice. My situation is the following: I'm 18 years old and next year I'm going to start university in Canada (Montreal). I have already applied in engineering physics and got accepted. However, the problem is that I'm really...

In the introduction to their book 'The Theory of Games and Economic Behaviour' von Neumann and Morgenstern consider the arguments against the use of mathematics in economics. One of the reasons they believe that previous applications of mathematics to economics had been unsuccessful was that...

How are the tensors of General Relativity simplified and operated? And can someone give me a mathematical example of General Relativity being done with just some basic values being plugged in for G=kT?

I feel like I have gone pretty far in math now, but I keep finding myself asking the same question. Say I had a series of data points from like a randomly collected survey or stock stock price graph over time etc. Is there a way to take this seemingly random and scattered data and turn it into...

I was working on my homework and I did two of the mathematical induction problems before this one and they were super easy but I must be forgetting something because I just can't seem to solve this one. 2+7+12+17...+(5n-3) = (n/2)(5n-1) So I know that step 1 is to prove that it works with...

I was watching one of Susskind's videos and I had some questions: Briefly summarizing from the video: E = hf (Planck's constant times frequency) E = cp (speed of light times momentum) or p = E/c = hf/c And we know that if we have wavelength lambda, then if t = 1/f and vel = dist/time...

Trying to translate a mathematical term from Hebrew to English ("regression rule") If I translate it word by word in Hebrew, it's the "regression rule" Such as, I am told that "a series is defined for every natural n by the regression rule"...

Good morning, what is the mathematical formalism used for a rigorous formulation of the Kaluza-Klein theory? Is there any reference? Thanks!

so the problem is 3+7+11+15+...+(4n-1) = n(2n+1) so I know that step 1 is to plug in 1 for the right side and check that it equals three... 3=1(2(1)+1) and yes it equals 3 Then I know that you assume that 3+7+11+15+...+(4n-1) = n(2n+1) The next step is where I get confused I know that...

I recently read about the unexpected hanging problem and I was so surprised that logic actually failed in determining the solution!:( Is this just an isolated exception, or are there more paradoxes like this? And more importantly, why does logic fail? Isn't there any way around this? I just...

Homework Statement For each n\,\in\,\mathbb{N}, let p_n(x)\,\in\,\mathbb{Z}_2[x] be the polynomial 1\,+\,x\,+\,\cdots\,x^{n\,-\,1}\,+\,x^n Use mathematical induction to prove that p_n(x)\,\cdot\,p_n(x)\,=\,1\,+\,x^2\,+\,\cdots\,+x^{2n\,-\,2}\,+\,x^{2n}Homework Equations Induction steps...

Homework Statement Prove that (n + 1)n - 1 < nn for n ∈ Z+. [Hint: Induction is suggested. Write out the induction statement explicitly. Make one side of the inequality look like your induction hypothesis.] Homework Equations The Attempt at a Solution ^ That's what I have so far. I'm good...

What course did you or do you typically learn about mathematical splines?

Hi, I am new to this forum, so forgive me if this is a really obvious question. I am a high school student interested in doing a project involving differential equations, and vector analysis (basically calc 1 - III, linear algebra, and a bit of differential equations). I will use this program...

Does Time have a mathematical equation or Law? Thanks!

Homework Statement Prove: 1+2(2+3+4+···+n)+(n+1)=(n+1)2-1 for all n within NHomework Equations PMI The Attempt at a Solution I tried applying PMI starting with the basis step, allowing n=1, assuming the equation would be true. However 1+2(1)+(1+1)=?=(1+1)2-1 yields 5=?=3 which is false. The...

I'm curious as to the highest level of mathematical skill required for adequate understanding of Einstein's theories. For example, how deep into PDE's do the field equations require?

Background Next year I am going to be a final year student - Msci Physics. I am fairly mathematically competent even though I don't "take" any theoretical/math options (my confidence in this area is another question). In first year we had a standard introduction to all the topics we were...

I have some problems. Number 1) Two people are playing, they take a three digit number, at this number, we add its inverse, and wins the number before arrives a sum > 1900, what sum or sums are these? What number is that? Number 2) A person receives 1 euro if He arrive on...

So, do you think you are a mathematician? Prove it and calculate your MPQ (Mathematical Purity Quotient) Here are 125 questions to determine how much of a mathematician you really are. Answer each question with YES/NO and add up the number of times you answered YES. Then divide this score by...

[b]1. Assume that f : A -> B and g : B -> C and that f is not one to one. Prove that g(f) is not one to one. [b]2. one-to-one: x1 != x2 and f(x1) != f(x2) not one-to-one: f(x1)=f(x2) and x1 != x2 [b]3. The start of the proof should go as follows: Assume f: A->B, g: B -> C, f is not...

So, right now I'm in the middle of my third year of being a math/financial economics major, and academically I have been strong but now am really taking a hard hit. The main thing that I feel is that the deeper into math I've gone, the less interesting its become. Reading math on a lower-level...

Homework Statement Use mathematical induction to prove the following statement. n \geq 2,~ \sum_{k=1}^{n} \frac{1}{k^2}~<~1-\frac{1}{n} Homework Equations The Attempt at a Solution This is the third problem I've done of this type, so I am by no means an expert. So this attempt may be...

I have a severe learning disability solely in mathematical comprehension, possibly dyscalculia. I was given a lot of special assistance in high school to help me graduate. I was able to graduate with a diploma with only basic arithmetic. Most of the algebra, geometry, trigonometry and so forth...

Greetings everyone, I'd like to continue my physics and mathematics education but I'll have to do that on my own since I'm heading into engineering. I'm looking for a book that would cover a lot of the mathematics that are needed at the undergrad physics level. I'll have Calc 1,2,3, Linear...

In the context of Set theory and Relations why do we use mathematical induction. Is there any deep relation between all these concepts or mathematical induction is only a separate concepts introduced in the textbooks after Sets and Relation ; Functions ; and then Mathematical induction.

Someone posted this on another forum, and, not knowing enough about it to supply a satisfying answer, I figured I'd ask you guys.

Richard Feynman once remarked during a lecture that the invention of analytical methods such as calculus allowed people to "be more stupid", in reference to solving problems. I think he was on to something with that remark. Often when faced with a problem which requires me to set up some...

Homework Statement The sequence a0 -> n is defined by ai = b+i*c. Prove by induction on n that the sum of the terms in the sequence is (n+1)(a0 + an)/2.Homework Equations The Attempt at a Solution I defined predicate P(n) as (n+1)(a0+an)/2. My goal is P(n+1), which is (n+2)(a0+an+1)/2. I...

Hi. I am from Greece and I am an undergraduate student at the University of Patra and I study pure Mathematics. I am interested in mathematical competitions a lot, but I have never gone before in a mathematical competition. I want to study so I can be able to take part in competitions for...

A mathematical model may show that there are two possible states for something in the real world, let's say a coin, that may be either heads or tails; make a computer program to simulate coin flipping and you soon discover that the odds of heads or tails is 50/50. In the real world however...