Partial Definition and 1000 Threads

Homework Statement [/B]Homework Equations an= bn - bn+1 which is already in the problem The Attempt at a Solution [/B] i did partial fractions but then i got stuck at 16/12 [4n-5] - 16/12 [4n+7] that part about bn confuses me please someone explain in detail

Hi, So, in order to calculate a Jacobian, I need to evaluate a partial derivative of a total derivative, i.e. Let's say I have a function f(x), how do I calculate something like: ∂(df/dx)/∂f?

I am reading D. J. H. Garling: "A Course in Mathematical Analysis: Volume I Foundations and Elementary Real Analysis ... ... and I am also referencing concepts in Derek Goldrei's book, "Classic Set Theory for Guided Independent Study" ... I am currently focused on Garling's Section 1.3...

I am reading D. J. H. Garling: "A Course in Mathematical Analysis: Volume I Foundations and Elementary Real Analysis ... ... and I am also referencing concepts in Derek Goldrei's book, "Classic Set Theory for Guided Independent Study" ... I am currently focused on Garling's Section 1.3...

struggling to remember anything about partial fractions, can anybody help me with this? 6x-5 (x-4) (x²+3)

andrewkirk submitted a new PF Insights post Partial Differentiation Without Tears Continue reading the Original PF Insights Post.

Hi everyone my name naresh. I'm doing post graduation, currently working on my project. I've completed all the calculations for it, but i have a small doubut. I've designed a mobile truck loader for which I've taken partial factors 1.35 and 1.5 for dead load and live load respectively. but BS EN...

Homework Statement a. Given u=F(x,y,z) and z=f(x,y) find { f }_{ xx } in terms of the partial derivatives of of F. b. Given { z }^{ 3 }+xyz=8 find { f }_{ x }(0,1)\quad { f }_{ y }(0,1)\quad { f }_{ xx }(0,1) Homework Equations Implicit function theorem, chain rule diagrams, Clairaut's...

Homework Statement Hi there, what is the difference between the partial derivative and the total derivative? how do we get the gradient "the actual gradient scalar value" at a point on a multivariable function? what does the total derivative tell us and what does the partial derivative tell...

Consider the Taylor series expansion of ##e^{-x}## as follows: ##\displaystyle{e^{-x}=1-x+\frac{x^{2}}{2}-\frac{x^{3}}{6}+\dots}## For ##x>0##, the partial sums ##1##, ##1-x##, ##\displaystyle{1-x+\frac{x^{2}}{2}}## bound ##e^{-x}## from above and from below alternately. How do I prove this?

Hi. I know how to calculate partial derivatives and mixed partial derivatives such as ∂2f/∂x∂y but I've now become confused about something. If I have a function of 3 variables eg. f(x,y,z) and I calculate ∂x then I am differentiating wrt x while holding y and z constant. Does that mean ∂x then...

Hey, all! I'm learning partial fraction decomposition from Serge Lang's "A First Course in Calculus." In it, he gives the following example: \int\frac{x+1}{(x-1)^2(x-2)}dx He then decomposes this into the following sum: \frac{x+1}{(x-1)^2(x-2)} =...

Homework Statement Let ##f(x,y) = \|x \| - \|y\| - |x| - |y|## and consider the surface defined by the graph of ##z=f(x,y)##. The partial derivative of ##f## at the origin is: ##f_{x}(0,0) = lim_{h \rightarrow 0} \frac{ f(0 + h, 0) - f(0,0)}{h} = lim_{h \rightarrow 0} \frac {\|h\| -|h|}{h} =...

I just realized there's a little difference between the differential and integral forms of Faraday's law I didn't notice earlier. In the differential form, it is the partial time derivative that is written, while in integral form, it is simply the time derivative. Why is that ?

$\textbf{206.5.64 integral by partial fractions} \\ \displaystyle I_{64}= \int\frac{9x^3-6x+4}{x^3-x^2} \, dx \\ \text{expand} \\ \displaystyle \frac{9x^3-6x+4}{x^3-x^2} = \frac{9(x^3-x^2)+9x^2+6x+4}{x^3-x^2} = 9 + \frac{9x^2+6x+4}{x^2(x-1)} \\ \textbf{stuck!}$

Hi! Can someone give me an example of a function ##f(x,y)## for which the mixed partial differentials are not equal, i.e. $$\frac{\partial^2 f}{\partial x \partial y} \neq \frac{\partial^2f}{\partial y \partial x}$$ It says in Boas that these mixed differentials are equal only if the first and...

I'm working through the discussion of calculus of variations in Taylor's Classical Mechanics today. There's a step where partial differentiation is involved that I don't understand. Given: $$S(\alpha)=\int_{x_1}^{x_2} f(y+\alpha\eta, y'+\alpha\eta', x)\,dx$$ The goal is to determine ##y(x)##...

I am a 7th grader who is interested in Quantum mechanics and I'm learning schroninger's equation and there is a partial derivative in it and I looked it up but the best I could find was that it was a function of variables of the variables derivatives, but that didn't make much sense. Can someone...

Homework Statement I have the function: f(x,y)=x-y+2x^3/(x^2+y^2) when (x,y) is not equal to (0,0). Otherwise, f(x,y)=0. I need to find the partial derivatives at (0,0). With the use of the definition of the partial derivative as a limit, I get df/dx(0,0)=3 and df/dy(0,0)=-1. However, my...

I believe there is a mistake in the second equation of (5.139). The equation is obtained from (5.138) using the Euler-Lagrange equation ##\frac{d}{dt}\frac{\partial L}{\partial\dot{\theta}}=\frac{\partial L}{\partial\theta}.## LHS##\,\,=\frac{d}{dt}\frac{\partial...

Homework Statement in the notes , 'by applying chain rule to LHS of the above equation ' , which equation is the author referring to ? it's given that f /x + (f/z)(z/x) = 0 , As we can see , the function contain variable x , y and z Homework EquationsThe Attempt at a Solution why not f /x +...

I'm a bit rusty on partial uniform loading on a pin. I want to find the minimum diameter a cold rolled steel pin has to be using a factor of safety of 2 with a loading of 25000 lbs. The pin in the picture is welded between two plates (the right plate bends in and is welded to the left plate...

Homework Statement I'm reading through the derivations of the linear wave equation. I'm following everything, except the passage I highlighted in yellow in the below attachment: Homework Equations I'm not understanding why partials must be used because "we evaluate this tangent at a...

Homework Statement "Under mild continuity restrictions, it is true that if ##F(x)=\int_a^b g(t,x)dt##, then ##F'(x)=\int_a^b g_x(t,x)dt##. Using this fact and the Chain Rule, we can find the derivative of ##F(x)=\int_{a}^{f(x)} g(t,x)dt## by letting ##G(u,x)=\int_a^u g(t,x)dt##, where...

Homework Statement I would just like to know if this statement is true. Homework Equations \frac {\partial^2 f}{\partial x^2} \frac{\partial g}{\partial x}=\frac{\partial g}{\partial x} \frac {\partial^2 f}{\partial x^2} The Attempt at a Solution I've thought about this a bit and I haven't...

Integration as antiderivative Question: Why isn't a distinction made between anti-total-derivatives and anti-partial-derivatives in common usage of integration? Consider the functions ##G_1(x, t)## and ##F(x, t)## such that ##F(x, t)=\frac{d}{dx}G_1(x, t)=\frac{\partial G}{\partial...

Hello guys! I'm new here, so sorry if I'm posting on wrong place or wrong way. I just need help to solve a problem: (∂E/∂V)β, N + β(∂p/∂β)N, V = - p PS: There is a bar over E and over p (this in both sides) - meaning that is an average. I don't know how to start, so any help will be amazing...

Homework Statement If the nth partial sum of a series ##\sum_{n=1} ^\infty a_{n}## is ##S_{n} = \frac {n-1} {n+1}## Find ##a_{n}## and ##\sum_{n=1}^\infty a_n## Homework Equations ##S_{n} - S_{n-1}= a_{n}## ##\lim_{n \rightarrow +\infty} {S_{n}} = \sum_{n=1}^\infty a_n = S## The Attempt at a...

I have this fraction $$x^2 / (x^2 + 9)$$ I'm not sure how to approach this problem since the denominator can't be further factored. What is the right approach for this type of problem?

I have this partial fraction: $$ 18 = (x^2 + 9) + (Bx + C)(x + 3)$$ which the textbook says is equal to: $$(B + 1)x^2 + (C + 3B)x + (9 + 3C)$$ But I don't follow this step. How do I derive this?

Homework Statement Good day, I want to ask the matrix that obtained from below formula and example. $$tr_A(L_{AB})=\sum_i [(\langle i|\otimes id)L_{AB}(|i\rangle\otimes id)]$$ this formula above can be represented as in matrix form below, $$tr_A(L_{AB})=...

Homework Statement Hello! Here is my second post on the subject partial fraction decomposition. The subject looks pretty easy to learn, but when I try exercises, I do not get to the correct answer. Please, take a look at the exercise below and help me to see my mistakes. Homework Equations...

Homework Statement Hello! I am doing a chapter on partial fraction decomposition, and it seems I do not understand it correctly. Here is the exercise doing which I get wrong answers. Please, take a look at the way I proceed and, please, let me know what is wrong in my understanding. Homework...

For a harmonic function of a complex number ##z##, ##F(z)=\frac{1}{z}##, which can be put as ##F(z)=f(z)+g(\bar{z})##and satisfies ##\partial_xg=i\partial_yg##. But this function can also be put as ##F(z)=\frac{\bar{z}}{x^2+y^2}## which does not satisfy that derivative equation! Sorry, I...

As there is a repeated root, the partial fraction decomposition we should use is: $\displaystyle \begin{align*} \frac{A}{x - 1} + \frac{B}{\left( x - 1 \right) ^2 } + \frac{C}{x - 2} &\equiv \frac{x^2}{\left( x - 1 \right) ^2\,\left( x - 2 \right) } \\ \frac{A\,\left( x - 1 \right) \left( x - 2...

I am trying to prove that the above is true when performing the change of variable shown. Here is my attempt: What I am not quite understanding is why they choose to isolate the partial derivative of ##z## on the right side (as opposed to the left) that I have in my last line. This ultimately...

Production function Q(K,L) without equation However partial derivatives are given Partial derivatives: Q(K,L) = (K^2 - KL + L^2)/(K+L) + 4K . ln(K+L) Derivative to K Q(K,L) =( K^2 + L^2) / (K+ L) Dervative to L A. Calculate the derivative in point (10,L) If I am correct...

Homework Statement The question: Scientists need to take precautions when they carry out restriction mapping. They need to make sure that the enzyme they have used has completely digested the DNA. One check they may carry out is to add the sizes of the fragments together. How could scientists...

Partial pressure must be less than or equal to the vapor pressure if there is no liquid present. However, when both vapor and liquid are present and the system is in the phase equilibrium, the partial pressure of the vapor must be equal to the vapor pressure and system is said to be saturated...

Homework Statement Find a solution of $$\frac{1}{x^2}\frac{\partial u(x,y)}{\partial x}+\frac{1}{y^3}\frac{\partial u(x,y)}{\partial y}=0$$ Which satisfies the condition ##\frac{\partial u(x,y)}{\partial x}\big |_{y=0}=x^3## for all ##x##. The Attempt at a Solution I get the following...

I've been looking at the equation for r tilde prime in the image I attached below, but I cannot understand why it is that they say "Hence, the partial derivatives ru and rv at P are tangential to S at P". How does that equation imply that ru and rv are tangential to P?

I came across a simple equation in classical mechanics, $$\frac{\partial L}{\partial \dot{q}}=p$$ how to derive that? On one hand, $$L=\frac{1}{2}m\dot{q}^2-V$$ so, $$\frac{\partial L}{\partial \dot{q}}=m\dot{q}=p$$ On the other hand...

A sample of argon gas is collected over water at 30.0oC. The level of the water is adjusted until the total pressure in the flask is 771 torr and the volume is 250.0 mL. The vapor pressure of water is 31.8 torr at 30.0oC. A. How many moles of argon are in the flask? B. What is the partial...

Hi, in the above why is the left-hand side simple differentiation, i.e V is only function of t but in the right it is function of t, x, y, and z. It is very strange that one side is different than the other. Would you like to explain it? Thank you.

Homework Statement Use the Chain Rule to find the 1. order partial derivatives of g(s,t)=f(s,u(s,t),v(s,t)) where u(s,t) = st & v(s,t)=s+t The answer should be expressed in terms of s & t only. I find the partial derivatives difficult enough and now there is no numbers in the problem, which...

Hello, I am enrolled in calculus 2. Just having started a section in our textbook about integration by partial fractions, I eagerly began trying to use this integration technique wherever I could. After messing around for multiple days, I ran into this problem: ∫ 1/(x^2+1)dx I immediately...

I know its a ridiculous question, but I'm signing up for classes and I wanted to take differential equations and its currently filled up(for now, people drop all the time at my uni) but saw partial differential equations. I assume you need differential equations before partial differential...

Homework Statement I am trying to factor a denominator so I can do a partial fraction decomposition to solve using a Laplace transform. denominator= 2s^3+3s^2-3s-2 Homework EquationsThe Attempt at a Solution

Sorry for the terribly vague title; I just can't think of a better name for the thread. I'm interested in functions ##f:[0,1]^2\to\mathbb{R}## which solve the DE, ##\tfrac{\partial}{\partial y} f(y, x) = -\tfrac{\partial}{\partial x} f(x,y) ##. I know this is a huge collection of functions...

What are some good general textbooks on the properties and solution of systems of partial differential equations? I'm most interested in the general theory of vector and tensor valued PDEs like Maxwell's, Navier-Stokes, and the bulk equations governing elasticity and deformation of solids, etc...