Functions Definition and 1000 Threads

Hi! I was wondering how I could find the equations for the bottom two functions. I understand that the amplitude is not constant like that in the circular sine function--could someone please help me out? Thanks!

Homework Statement Given a Uniform Distribution (0,1) and Z = X/Y Find F(z) and f(z) Homework EquationsThe Attempt at a Solution So I'm just trying to make sure i have the range correct on this one... I'm honestly lost from beginning to end with it. R(z) = {0,∞} because as y is very small, Z...

Homework Statement Prove that there do not exist functions ##f## and ##g## with the following property: $$(\forall x)(\forall y)(f(x+y) = g(x) - y)$$ Homework Equations NA The Attempt at a Solution Here is some information I have found out about ##f## and ##g## if we suppose they exist: ##f(x...

How do you memorize the even and odd function?

I'm realizing now how much I need to know the exact values of various trigonometric functions, as shown in various trig tables. Memorizing is pretty arduous, and I'd prefer to understand it, so how can I learn all of these?

Hi all Just to start with I should highlight my general ineptitude with programming, so I apologize if my question is totally basic. I have a program written (by someone else) in fortran 77. Contained within it is a call to a function which acts on a number of variables. My curiosity is about...

Hi, I know that when you take this limit it is equal to e^-wo, but I was just wondering how you got there when taking the limit? lim w-->wo ((exp(w)-exp(wo))/(w-wo))^-1 = 1/e^wo w and wo are both two points within the same plane.

How do you know when to use exponentials and trig functions when solving for the wave function in a finite square well? I know you can do both, but is there some way to tell before hand which method will make the problem easier? Does it have something to do with parity?

As I understand it a Green's function ##G(x,y)## for a translationally invariant differential equation satisfies $$G(x+a,y+a)=G(x,y)\qquad\Rightarrow\qquad G(x,y)=G(x-y)$$ (where ##a## is an arbitrary constant shift.) My question is, given such a translationally invariant system, how does one...

Homework Statement Homework Equations n/a The Attempt at a Solution ##y'=f(x.y)## is a function of two variables. ##y=y(x)## is a function of only one variable. How can they be related? Clearly ##y(x) = f(x) \neq f(x,y)## Thanks

Homework Statement Hi i have an assignment that is asking me to convert 3 temperatures in fahrenheit to celcius and vice versa. I am very new to programming only 2 weeks in(and i learn by playing with the program) so I do not know all of the terminology / principles. I am not allowed to use...

Homework Statement First, I'd like to say that this question is from an Introductory Linear Algebra course so my knowledge of vector space and subspace is limited. Now onto the question. Q: Which of the following are subspaces of F(-∞,∞)? (a) All functions f in F(-∞,∞) for which f(0) = 0...

Hello! (Wave) I want to find all the continuous functions $f: [0,1] \to \mathbb{R}$ for which it holds that:$$\int_0^1 f(t) \phi''(t) dt=0, \forall \phi \in C_0^{\infty}(0,1)$$ If we knew that $f$ was twice differentiable, we could say that $\int_0^1 f(t) \phi''(t) dt= \int_0^1 f''(t) \phi(t)...

We know that in the space of functions, its possible to find a complete set so that you can write for an arbitrary function f, ## f(x)=\sum_n a_n \phi_n(x) ## and use the orthonormality relations between ## \phi##s to find the coefficients. But is it possible to find a set of functions ##...

Is it correct to say that if a relation between a few numbers is represented on a graph and it comes out to be a curve than it can be written in the form of an equation?

What are different ways of ensuring efficiency in a recursive function in C++? i.e. Prevent calling your recursive function when not necessary.

Homework Statement differentiate ∫ e^(-x*t^4)dt from -x to x with respect to x.[/B]Homework Equations erf(x) = (2/sqrt(π)) ∫e^(-t^2)dt from 0 to x. Leibniz rule. I know that ∫t^2e^(-t^2)dt from 0 to x = (√π/4)*erf(x) - (1/2)*x*e^(-x^2)[/B]The Attempt at a Solution By using Leibniz rule...

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...

[FONT=Verdana]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...

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 $$ \Delta=b^2-4ac. $$...

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...