Functions Definition and 1000 Threads

Hi there, kinda new here so please let me know if this question has been answered. I am hoping to get a link or two to some good sources of information on Lorentz transforms and distribution functions (as used in physics). I understand DF's in class and I understand the math behind them I just...

Can somebody please explain to me why the integral of, for instance, cos((2*pi*x)/a)*cos((4*pi*x)/a) vanishes over the interval 0 to a? As I understand it, this is generally the case when integrating sines and cosines with different arguments "over the interval of a period." But I'm confused...

Euler mentions in his preface of the book "Foundations of Differential Calculus" (Translated version of Blanton): I don't understand here, who/who all had invented/discovered the study-of-ultimate ratio (differential calculus) for rational functions long before (Newton and Leibniz), without...

Homework Statement Determine all values of the constant a such that the following function is continuous for all real numbers. f(x) = ax/tan(x), x ≥ 0 = a2 - 2, x < 0 Homework EquationsThe Attempt at a Solution I tried so many different ways to get the first part of the function to be...

Homework Statement integrate tan^3(9x) Homework Equations tan^2(x)= sec^2(x)-1 integral of tanxdx= ln|secx| The Attempt at a Solution Integrate tan3(9x)dx Integral (sec2(x)-1)tan(9x)dx so then I distribute the tan(9x) giving me: integral tan(9x)sec2(x)dx - integral tan(9x) dx so then I solve...

Can the general solution to the Schrodinger equation be asymmetric (has neither even or odd solutions)? Question (1): I saw somewhere that you cannot have a solution that is both-- it must be either odd or even, and I was wondering: why? I was working on a problem where the potential function...

Hi all, I have a non-economic background and I am currently interested in utility functions and how they are modeled in economics. Some internet research and I found out that there are obviously different ways of model utility. In my own studies of related topics I encountered the following two...

f(x)=log(1+x)/(1-x) and g(x)=(3x+x2)/(3x2+1) prove that (fοg)(x)=3f(x)

IF f(X)={x2, X>3 ; 3X+4, 0<X<3 ; X3+2 , X<0 } find (f°f°f)(-1) p.s the answer is 49! i don't know how this f(x) includes three terms x2 , 3x+4 and x3+2 And which term i need to use for the (f°f°f)(-1)

Homework Statement Hi, am having difficulty with the Linear algebra in QM. We have been given a problem set and one of the questions am struggling with is as follows: Consider the space of all linear functions ##f(x) = ax + b## (x real) defined over the range ## -1 < x < 1 ##, with the scalar...

Homework Statement In playing a certain game, your ability scores are determined by six independent rolls of three dice. After each set of six rolls, you are given the choice of keeping your scores or starting over. (a) How many times should you expect to start over in order to get a set of...

Homework Statement Consider a zipper of N links, each of which can either be open or closed with associated energy 0 if closed and ##\epsilon## if open. a) Suppose the N links are independent, compute the partition function of the system and the average number of open links b)Now assume that...

Homework Statement I uploaded the question as a picture and attached it. Homework Equations Unit step function - u_c (t) = \begin{cases} 1 & \text{if } t \geq c \\ 0 & \text{if } t < c \end{cases} Impulse function - δ(t) = \displaystyle\lim_{Δ\rightarrow 0} δ_Δ (t) Multiplication Property...

I have an assignment for MATLAB where I am required to create two vectors x and y and then to find the sum in three ways. first, create an extra variable z and find the sum second, use the dot function third, multiply x with the transpose of y here's my code x=linspace(0,1,5)...

Homework Statement I uploaded the problem statements as a picture as well. I have completed these and was wondering if someone could check my work, and let me know if it is correct. Problem 1.3: Find the expression for the transfer function of this linear time-invariant causal system with...

Homework Statement This is a homework problem for my Honors Calculus I class. The problem I'm having is that though I can solve a traditional function composition problem, I'm stumped as to how to do this for multivariate functions. I read that it requires an extension of the notion of...

Hello, I need to create a 2-D electron energy density plot in Mathematica to compare with my STM experimental results in my lab class. This would be done by plotting the superposition of the symmetric and anti-symmetric wave functions, $$\Psi_s(\textbf{r}) =...

According to wikipedia AQFT needs test functions so that the fields are distributions smeared on these functions. I'd want to know what are these test functions. I read in Haag's book that they are fast decreasing functions defined on space time. They belong to the set S of Schwartz functions...

Mod note: Thread moved from Precalc section Homework Statement F(x)=sqrt(-2x^2 +2x+4) 1.discuss variation of f and draw (c) 2.find the equation of tangent line to (c) that passes through point A(-2,0) The Attempt at a Solution I solved first part I found the domain of definition and f'(x) and...

I am learning Fourier series and have come across the sine, cosine, and imaginary exponential expressions. To my knowledge, these individual terms form a basis since they are all orthogonal to each other. I am just wondering: can a Fourier sine series be used to model a purely even function...

I have heard that in my next semester, our quantum mechanics teacher will be giving a great emphasis on difficult integrals with the most of them having to do with gamma functions. Does anybody know a book(or any other source) that I can learn about and practice gamma functions integration...

Homework Statement Here is an imgur link to my assignment: http://imgur.com/N0l2Buk I also uploaded it as a picture and attached it to this post. Homework Equations u_c (t) = \begin{cases} 1 & \text{if } t \geq c \\ 0 & \text{if } t < c \end{cases} The Attempt at a Solution Question 1.1 -...

f(x)=[((x-1)/(x+1))+((x-1)/(x+1))]1/2 What is F-1(x) No matter what I try I am unable to isolate for y after switching x's with y's. Any ideas?

I am writing a paper and I came up with a function that uses a hypothetical relationship to predict the value of one variable at different points in time, I graphed it, and then graphed the actual readings from an experiment. How can quantitatively describe how close the two trends are? In other...

Hi Can anyone point to me a reference where orthogonal properties of confluent hypergeometric functions are discussed? Navaneeth

Homework Statement ∫(t/√(1-t4))dt Homework Equations ∫(du/√(a2 - u2)) = arcsin (u/a) + C ∫(du/(a2 + u2) = (1/a) arctan (u/a) ∫(du/(u√(u2 - a2))) = (1/a) arcsec (|u|/a) The Attempt at a Solution Edit: I meant to write u where t2 is[/B]

This is a helpful document I got from one of my DE's teachers in graduate school, and I've toted it around with me. I will type it up here, as well as attach a pdf you can download. Bessel Functions $$J_{\nu}(x)=\sum_{m=0}^{\infty}\frac{(-1)^{m}x^{\nu+2m}}{2^{\nu+2m} \, m! \,\Gamma(\nu+m+1)}$$...

Homework Statement The functions f and g are given by https://scontent-kul1-1.xx.fbcdn.net/hphotos-xtf1/v/t35.0-12/11993948_10204837479208369_1887096410_o.jpg?oh=b1653a61128c571af8137b1fd00ccb01&oe=55F47BC4 a) without using differentiation, find the range of f b)show that f(x)^2+g(x)^2=1.Hence...

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need someone to help me to...

I have a question inspired by a recent thread that I did not want to hijack (https://www.physicsforums.com/threads/distributions-on-non-test-functions.831144/) I realize that weaker requirements on the space of test functions results in a more restricted set of distributions. For example, if...

Please can you give definitions of increasing, non-increasing, decreasing and non-decreasing functions ? I found something but there is a lot of differents between these definitions...Can you give these definitions ? Thank you so much, Best wishes :)

The definitions of distributions that I have seen (for instance https://en.wikipedia.org/wiki/Distribution_(mathematics)#Distributions ) define a distribution as a map whose domain is a set of test functions. A defining quality of test functions is that they have compact support, which for most...

Let f(x) and g(x) be quadratic functions such as the inequality \left| f(x) \right| \ge \left| g(x) \right| is hold for all real x . Prove that \left| \Delta_f \right| \ge \left| \Delta_g \right|. For quadratic function f(x)=ax^2+bx+c , then \Delta=b^2-4ac. I have no idea how I could...

Homework Statement [/B] Homework Equations Listed under 2.1 in the image above. This is the only relevant equation that I'm aware of, but I'm almost sure that there is something else I need to know before I can solve the problem. The Attempt at a Solution I tried solving for the...

Hello all, Can anyone give me a pointer on how to start this proof?: f:E\rightarrow F we consider f^{-1} as a function from P(F) to P(E). Show f^(-1) is injective iff f is surjective.

Homework Statement question: State two different functions that have same range but different domain. Then tell me what is the range of those two functions. The attempt at a solution Y = x/2 Y= x/2 +1 I don't know if that is correct or not. Any suggestion will help.

Suppose we define the measurement of an observable A by v(A) v being an 'algorithm giving out one of the eigenvalues each time it is called' (we accept the axiom of choice) In this context we have in particular v(A)≠v(A) since when we call the left hand side and then the right handside the...

Can I present the trigonometry functions (such as SinX, CosX, TanX, CotX) by using only- Log, Lan, multiplication, division, addition, subtraction, exponantion, nth root operations?

Is there a way to formally prove that if ##f## and ##g## are multiplicative inverses of each other, then ##f^{-1} (x) = g^{-1} (\frac{1}{x})##?

Homework Statement Can you create a list of which functions increase towards infinity the fastest for limit solving? Homework EquationsThe Attempt at a Solution I'm trying to make a list from least speed, to fastest speed, in approaching infinity. As in, if you have a limit, and it has...

I am confused about the order in which we apply transformations to a input of a parent function to get the corresponding input of the new function. Say for example, we have the function ##y = \sin(-2x + 1)=\sin(-2(x-\frac{1}{2}))##. Intuitively, it would seem as though we would transform a point...

I am reading Joseph J. Rotman's book: A First Course in Abstract Algebra with Applications (Third Edition) ... I am currently focused on Section 3.5 From Numbers to Polynomials ... I need help with an aspect of the proof of Lemma 3.70 ... The relevant text from Rotman's book is as follows:In...

Please help give references on solving the following integral: \int\frac{1}{c_{1}e^{ax}+c_{2}e^{bx}}dx where a\neq b Thanks a lot in advance.

Came across this in a discussion of essential self-adjointedness: Let P be the densely defined operator with Dom(P) = C^{\infty}_c (\mathbb{R}) \subset L^2 ( \mathbb{R} ) and given by Pf = -i df/dx. Then P is essentially self-adjoint. It is the C^{\infty}_c (\mathbb{R}) \subset L^2 (...

#Hi All, Let ## f: \mathbb C \rightarrow \mathbb C ## be entire, i.e., analytic in the whole Complex plane. By one of Picard's theorems, ##f ## must be onto , except possibly for one value, called the lacunary value. Question: say ##0## is the lacunary value of ##f ##. Must ## f ## be of the...

This is picture taken from my textbook. I understood the last two statements "To check whether..". A function is one if its strictly increasing or decreasing. But I am not able to understand the first statement. Polynomials are continuous functions. Also, a continuous function ± discontinuous...

Homework Statement Prove that $$\sum_{r=1}^{b-1}[\frac{ra}{b}]=\frac{(a-1)(b-1)}{2}$$ where [.] denotes greatest integer function and a & b have no common factors. Homework Equations ##n\le [n]<n+1## <x> denotes fractional part of x. 3. The Attempt at a Solution I first added and subtracted...

I read somewhere that mathematical functions can be implemented as sets by making a set of ordered tuples <a,b> where a is a member of A and b is a member of B. That should create a function that goes from the domain A to the range B. But set theory has functions too, could they be sets too...

Hey. Assume you have a signal ##f## with period ##T_f## and a signal ##g## with period ##T_g##. Then the signal ##h= f+g## is periodic iff ##T_f/T_g \in \mathbb{Q}##. So if ##T_f/T_g## is an irrational number, the signal ##h## will not be periodic. Why is this actually the case?

So I've delved into programming, and gotten experienced with the fundamentals. However, the more I learn, the more I question the central object of comp. science, computation, and its foundation. According to Wikipedia, "Computation is any type of calculation that follows a well-defined model...