# Tagged Questions

63 views

I cant figure out how some transformations are made in one article on physics. Here is expression in s-domain and they want to find its asymptotic value. $$\xi(s) = \nu_1(s+1)=\frac{1}{(s+1)} ... 1answer 85 views ### Asymptotic expansion on 3 nonlinear ordinary differential equations The 3 nonlinear differential equations are as follows $$\epsilon \frac{dc}{dt}=\alpha I + \ c (-K_F - K_D-K_N s-K_P(1-q)), \nonumber$$ \frac{ds}{dt}= ... 1answer 17 views ### First Order Approximation Taylor Series I have the taylor series f(z)=f(x_0)+(x-x_0)f'(z)+1/2(x-x_0)^2f''(z) ... and I am told that "As a first order approximation," x-x_0 ~ \frac{f(x)-f(x_0)}{f'(x_0)} assuming f'(x_0) \neq 0 I ... 3answers 114 views ### A system of n equations , how does it behave for growing n? I read about the system of n equations in the link below. I wonder how it behaves for growing n. Does it converge ? http://math.eretrandre.org/tetrationforum/showthread.php?tid=889 Here it is ... 2answers 82 views ### Integration by expansion Consider the integral $$I(x)= \frac{1}{\pi} \int^{\pi}_{0} \sin(x\sin t) \,dt$$ show that $$I(x)= \frac{2x}{\pi} +O(x^{3})$$ as ... 0answers 65 views ### Saddle point method: a rigorous proof? I am trying to prove in a fully rigorous way the Saddle Point method for holomorphic functions of 1 complex variable. In books I find only complicated general statements or non-rigorous proofs. Hence ... 1answer 51 views ### Expansion of Integration Consider the integral $$I(x)=\int^{2}_{0} (1+t) \exp\left(x\cos\left(\frac{\pi(t-1)}{2}\right)\right) dt$$ show that I(x)= 4+ \frac{8}{\pi}x +O(x^{2}) ... 0answers 76 views ### Big-O Notation for remainder terms in Taylor expansion The Big-O notation is commonly used in Taylor expansions of the form$$f(x+\epsilon)=f(x)+\epsilon f'(x)+O(\epsilon^2)$$to say that the remainder term grows at least quadratic around \epsilon=0. ... 0answers 123 views ### Question about Big O notation for asymptotic behavior in convergent power series Examples of such use of Big O notation can be found for instance on Wolfram Alpha here. More details on the Wikipedia page. The idea, as I understand it, is that the term between parenthesis in Big O ... 2answers 54 views ### Expanding \ln(1+f(x)) around f(x)=0 when we do not know whether there is an x such that f(x)=0. I want to expand \ln(1+f_T(x,\theta)) about 1+f_T(x,\theta)=1. What I have in mind is something like$$ \ln(1+f_T(x,\theta))=\ln(1)+f_T(x,\theta)-\frac{1}{2} \frac{1}{1+\tilde{f}} ...
I am new around here and was hoping you will be able to help me with the following. I have the equation: $x^3 - 3x^2 +(3-\epsilon ) x + \epsilon = sin(\frac{\pi}{2} x +\frac{\pi \epsilon}{2} )$ and ...