Mathematical Definition and 1000 Threads

Homework Statement Derive the equation of motion of a particle of mass m and charge q moving in three dimensional space under a Coulombic attraction toward a fixed center. I have the answer for a plane but a i need it for the space Homework Equations Mathematical Methods for...

Hello; I wonder which one of the following textbooks is suitable for mathematical physics undergrad course: 1:) Mathematical Methods: For Students of Physics and Related Fields by "Sadri Hassani". 2:) Mathematical Methods in the Physical Sciences by "Mary L. Boas". Thank you in Advance

I was told I lack mathematical rigour. But how do I go on improving on it? Is it only a matter of being very careful? Do I have to always support everything with a clear Euclidean succession of logical steps? Is it only a matter of 'believing' in the validity of the supporting tools? Then it's...

In an Engineering course I was used to being rewarded for proving a good understanding of theory. For example, if I explained a basis of the following solution, it would still give some rewards, even if the solution itself had major computing errors or even if it was partially mathematically...

I'm reading this book now. I like it because it's rigorous and interesting but I have too much difficulty solving the exercises. What's worse, Zorich didn't give the answers. Where can I find the answers? I mean is there a book or something that gives the answers or even just some hints to the...

Mathematical method in electrical potential ?? Hi All, I need mathematical help from the topic electrical potential for lectures on physics by Richard Feynman. Need some help to understand mathematical method used here. question : 1) From electrical potential.png ( how this partial...

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

Hello all, I know that perhaps this question has cropped frequently in a lot of places, but I would like to be quite specific in my case. I've just finished High School with UK A level syllabus. The syllabus inside Math A level is mostly straight solving equation type of questions, such as for...

Hi Please advice me a good book on mathematical statistics.I want it to be oriented in math students or engineering level. Best Regards

I was curious if anyone is aware of anything resembling a mathematical map, or learning tree. By this I mean a diagram that illustrates the sequence in which one must learn particular topics. I ask because I find myself encountering topics (today it was finite element method) and clicking the...

I'm having a gap in understanding the relation between them, and resolving my confusion is really appreciated. For example, the Hamiltonian operator, why do we call its eigenvalues energies? how do we actually measure it in the laboratory, quantum mechanically? And maybe I need a better...

Some students are not convinced that a proof by mathematical induction is a proof. I have given the analogy of dominoes toppling but still some remain unconvinced. Is there very convincing way of introducing mathematical induction? I need something which will have an impact. Are there any real...

Some students are not convinced that a proof by mathematical induction is a proof. I have given the analogy of dominoes toppling but still some remain unconvinced. Is there very convincing way of introducing mathematical induction? I need something which will have an impact. Are there any real...

Hi everyone, I'm having trouble getting a mathematical result in the following paper: http://link.springer.com/chapter/10.1007%2F978-3-540-88853-6_4#page-1 In particular, I can't figure out how they reach equation 7. They use equations (3) and (5), and I think they discard a lot of the...

Greetings! This is my first post and I am hopefully doing it in the right section of the site. Onto the topic: I am searching for the mathematical link between the kinetic force applied on two electro-magnets being forced against each other (assume repelling charges) and the effect that it...

If the ladder operator ##a=\sqrt {\frac{m\omega}{2\hbar}}x+\frac{ip}{\sqrt{2m\hbar \omega}}## and ##a^\dagger=\sqrt {\frac{m\omega}{2\hbar}}x-\frac{ip}{\sqrt{2m\hbar \omega}}## then I get that the number operator N, defined as ##a^\dagger a## is worth ##\frac{m \omega...

What would be an expression for the modulo operation based only on basic arithmetic i.e. addition, subtraction, multiplication and division? For example, if I would like to define 7 mod 3 using only the basic arithmetic operations, how would I write a function for it in a programming language...

I wanted to know if there is a mathematical model to know the force with which a source of a magnetic field attracts or repels another source of magnetic field. For example, the mathematical model for the electrostatic force a charged particle exerts over another charged particle is: F =...

Homework Statement a, b, x, y are rational numbers (ay - bx)² + 4(a - x)(b - y) = 0 implies that x = a and y = b or 1 - ab and 1 - xy are squares of rational numbers 2. The attempt at a solution My attempts are hard to transcribe, is this mandatory for getting help? This is my first post, I...

Stability, Helmholtz free energy mathematical relation "proof" Homework Statement I must show that \left ( \frac{\partial ^2 F}{\partial V ^2} \right ) _T=\frac{\frac{\partial ^2 U}{\partial S^2} \frac{\partial ^2 U}{\partial V ^2} - \left ( \frac{\partial ^2 U}{\partial S \partial V} \right...

Homework Statement (1 1)^n = (1 n) (0 1) (0 1) Prove this through mathematical induction. Homework EquationsThe Attempt at a Solution I've replaced n with 1, so I've done that far. Then I said k = n. Then replaced all n with (k+1). I'm really stuck...

Hi, i’m looking for some mathematical tools for analysis or classification of solutions of optimal control problems/variational. Equations of motions and optimized function depend on some parameters eg. dX1/dt = f(X1,X2, u1, p1) dX2/dt = f(X1,X2, u2, p2) where X1,X2 are state variables, u1,u2...

URGENT ! Mathematical Logic and Structures Hey guys, i need a HUGE favor, i need the resolution for this 5 questions, its a question of end this year my degree or stay one year just with a subject. Please I am begging, who knows the resolution please say me something. Part 1...

URGENT ! Mathematical Logic and Structures Hey guys, i need a HUGE favor, i need the resolution for this 5 questions, its a question of end this year my degree or stay one year just with a subject. Please I am begging, who knows the resolution please say me something. Part 1...

Is there a field of "Mathematical Astrophysics"? Just was wondering (for graduate school purposes), is there a field that does what mathematical physics does but for astrophysics? (e.g., perhaps simplifying or re-expressing the mathematics used in some subdiscipline of astrophysics?) Or perhaps...

Have you ever struggle to do a simple math/physics problem correctly for a long time JUST because of a ridiculous oversight you repeatedly made?

Hey guys, I just recently transferred to the mathematics department at University of Illinois as a junior undergrad and one of the classes I'm required to take this fall is called Mathematical Reasoning and I'm pretty sure it has to do with proofs... Which I know absolutely nothing about! What...

Homework Statement Let ≥ be a binary relation, defined on the set X as follows: for any x,y\inX, x≥y if x-y≥0 and x-y is even. Determine if the following are lattices: X={2,4,8} X={1,4,8,9} Homework Equations Note that ≥ in this case is just the symbol for relation as it relates...

So, energy is simply a mathematical expression of how much work is done in the system? Since energy is not a "physical" object that has mass. It's not matter at all. If so, the laws of conservation makes sense, it can't be created nor destroyed. But I can't imagine how a mathematical...

Verify that 1(1!)+2(2!)+...+n(n!) = (n+1)! - 1 is true using induction This problem has me stumped...

Hi, I have these 2 problem, that I'm not so sure how to handle. 1-Let $$X_1,X_2,...,X_n$$ independant Random variable that all follow a continuous uniform distribution in (0,1) a) Find $$E[Max(X_1,X_2,...,X_n)]$$ b) Find $$E[Min(X_1,X_2,...,X_n)]$$ where E is for the...

Suppose I make an application with a password of max 20 characters -- no special characters and not case-sensitive. So that means there is a 1-to-1 correspondence between the set of all passwords P and the set S = {1, 2, ..., 3720 - 1, 3720}. A simple bijective function f:P-->S could be...

Homework Statement Prove the theorems using mathematical induction. \forall n \in N, n\geq 4 \rightarrown2\leq n! Thanks in advance! Homework Equations The Attempt at a Solution First, check the base case which is n=4. \Rightarrown=4\geq4-True \Rightarrow42\leq4*3*2*1...

definition of "mathematical object" ...And "mathematical existence." Do these phrases have accepted definitions? Back when Dedekind was rejecting Cantor's transfinite ideas, could there have been a definition Cantor would refer to and say definitively "my (infinite) sets have mathematical...

Hi there, I am a long time reader of the Physics Forums, but a first time poster. The problem I am requesting assistance with stems from a problem in Reif's Fundamentals of Statistical and Thermal Physics. 7.16 An aqueous solution at room temperature T contains a small concentration of...

Let A(subn) = {1,2,3,...,n} For any set B, let P(subk)B=the set of all subsets of B with exactly k elements. For example, P(sub2)({1,2,3})={{1,2},{1,3},{2,3}}. A) Find P(sub2)(A(sub1)), P(sub2)(A(sub2)), P(sub2)(A(sub4)), and P(sub2)(A(sub5)) B) Use mathematical induction to prove that the...

Homework Statement Find the minimum and maximum of the given equation, f(x,y,z)=x+y+z, with the constraint 1/x+1/y+1/z=1. Homework Equations f(x,y,z)=x+y+z, with the constraint 1/x+1/y+1/z=1. The Attempt at a Solution I know the solution, which is minimum {(1,1,-1), (1,-1,1), (-1,1,1)} and...

Hi all, I am revising on Proof by mathematical induction and I have came across a question I haven't found a way to work it out. \sum_{r=1}^n r(r!) = (n + 1)! -1 I understand the steps of proving by mathematical induction question. The ! is causing the confusion.

Hi all, I am so sorry I don't know whether to post this. I am revising Proof by mathematical induction Further maths using an Edexcel FP1 book. The following is from chapter 6 example 3. I know how to work Proof by mathematical induction it is part of the example that I don't understand. I...

Hello, I need to minimize {- f (x) | a <=x <= b} where f ( x) is a concave and twice differentiable function. In addition, a and b are positive constants such that a <b. Assume that -f (x) exists in the given interval [a, b] . Show that if the optimal solution is at x*= a , then delta f...

Please refer to the image attached. Where does the > 2 x k come from? Based on the proposition, shouldn't it be > k+1?

Homework Statement Let f : A → B be a function and let S, T \subseteq A and U, V \subseteq B: Prove that if U \subseteq V; then f-1(U) \subseteq f-1(V): Homework Equations Preimage: f-1(U) = {x \in f-1(U) \ni f(x) \subseteq U} The Attempt at a Solution Assume U \subseteq...

Homework Statement Let f: A --> B be a function and let S, T \subseteq A and U, V \subseteq B. Give a counterexample to the statement: If f (S) \subseteq f (T); then S \subseteq T: Homework Equations The Attempt at a Solution PF: Assume f(S) \subseteq f(T). Let x \in...

Greetings everyone, I am posting this question here since I cannot post it in the math and science learning materials section of the forum. My question is that sometimes in physics I get into a lot of involved math particularly linear algebra, Hilbert space, partial differential equations and...

Hi This is a question from my self study of ch.2 of Alfred Tarski's Introduction to Logic Which of the following implications are true from the perspective of mathematical logic? a) If a number x (assuming x is an integer) is divisible by 2 or by 6, then it is divisible by 12 b) if 18 is...

Homework Statement 1-1/2+1/4-1/8+...nth term= [(2^n-(-1)^n)]/3(2^(n-1))] I just can't get the nth term. I realize that the denominator should be 2^(n-1) and that, because the sign constantly changes there needs to be something like -1^n so I came up with the equation -1^n/-2^(n-1) but this...

Hello, everyone. I am currently a junior [physical] chemistry major and am picking out my future upper division electives. I've narrowed them down to a handful of classes and what I'm looking for is just a little background information on them, which ones might be better than others, general...

Hello I'm learning about proofs and in my book there's a sect. On mathematical induction. And I'm trying understand why this makes it true for all values. 1+3+5...2n-1=n^2 Suppose that the formula is known to be true for n=1, and suppose that as a result of assuming that it is true for n=k...

Can someone explain to me the mathematical intuition that motivates the embedding of quantum operators between the conjugate wave function and the (non-conjugated) wave function? That is, we write: \Psi^{*}\hat{H}\Psi, that is: \Psi^{*}(\hat{H}\Psi), so that \hat{H} operates on \Psi (not...

LQG, strink theory and Penrose's spinor theory, or maybe it's twistor theory, I don't know, all I know is that all three theories achieve mathematical miracles in their attempts to go beyond the Standard Model - how can all three theories do this but be mutually exclusive at the same time. Or...