1. Evaluate the Taylor series and find the error at a given point

I have the following function $$f^{(0)}\left(x\right)=f\left(x\right)=e^{x}$$ And want to approximate it using Taylor at the point ##\frac{1}{\sqrt e} ## I also want to decide (without calculator)whether the error in the approximation is smaller than ##\frac{1}{25} ## The Taylor polynomial is...
2. I Derive local truncation error for the Improved Euler Method

I'm trying to find the local truncation error of the autonomous ODE: fx/ft = f(x). I know that the error is |x(t1) − x1|, but I can't successfully figure out the Taylor expansion to get to the answer, which I believe is O(h^3). Any help would be greatly appreciated!
3. Engineering Derivation of the error due to a finite load attached to a potentiometer

x = fraction of potentiometer connected to load Vp in parrallel with VL = x/(Rp/RL.x.(1-x) + 1) If RL = infinite, then Ro = x and Vo = x.Vs If RL = finite, then Ro = x/(Rp/RL.x.(1-x) + 1) and Vo = x.Vs/(Rp/RL.x.(1-x) + 1) Therefore error is x.Vs - x.Vs/(Rp/RL.x.(1-x) + 1) Trying to break the...
4. Change in the time period of a pendulum

I tried taking log and then diffrentiate the standard equation for time period of a pendulum but i am not getting the correct answer
5. Relative error and measurement precision

NOTE: this is a programming exercise (Python). I started adding to ##x_{true}## an error related to a (for example) 10% relative error, obtaining ##x_{measurement}##. Then i computed ##y_{measurement}##. To find the precision, i calculated ##(y_{true}-y_{measurement})/y_{measurement}##. If it is...
6. I Missing exponent in "Theoretical Minimum"?

In "The Theoretical Minimum" (the one on classical mechanics), on page 218, the authors write a Lagrangian $$L=\frac m 2 (\dot r^2 +r^2\dot \theta ^2)+\frac {GMm} r$$ They then apply the Euler-Lagrange equation ##\frac d {dt}\frac {dL} {d\dot r}=\frac {dL} {dr}## (I know there should be...

I know I am posting this in the wrong sub-forum, but I am unable to enter certain sub-forums (and when I login I just get a "security" error), where as in other sub-forums I am automatically logged in. Is there a problem with the site or just me experiencing these problems?
8. Standard deviation and probability for decay

Homework Statement (b) A nuclear research reactor produces radiation for neutron scattering measurements. A safety procedure shuts the reactor down if a radiation level monitoring detector measures more than 3 counts per minute. In a test, 156 counts are recorded during a random 24 hour...
9. Propagation of Error and Relative Error

Homework Statement 2) A student is performing an angry bird experiment in real life. He calculates the range of the projectile by shooting the bird with a 30 degree angle and an initial velocity of v0 = 20 m/s. a) If the relative accuracy of setting the projectile angle is delta theta/theta =...
10. B Greatest Possible Uncertainty and Sig Figs

There is something I seriously don't understand about uncertainty. Suppose there is an electric balance that reads 5.67g The limit of reading is 0.01g The greatest possible error is half of the limit of reading and is thus 0.005g By this logic, and assuming the very best possible situation, I...
11. Fractional uncertainty of g on the surface of the Sun

Homework Statement Homework Equations The Attempt at a Solution it looks like I got too big numbers for the uncertainty
12. Fortran Modifying a library not to stop at runtime errors

Hello everyone, I'm trying to solve a BVP that seems to be very sensitive, for which I have to provide a starting guess and hope the program can fix it to find a solution. The program has been tested many times and it is very solid, the only problem should be that I can't find the right guess...
13. Harmonic Frequency of a String

Homework Statement A string (m = 1 kg) fixed at both ends is vibrating in its second harmonic mode. If the length of the string is 2 m and it feels 50 N of tension, which of the following is NOT a possible harmonic frequency for this string? a) 1.25 Hz b) 2.5 Hz c) 5 Hz d) 10 Hz e) 20 Hz...
14. Ambiguity in finding errors using natural logarithm method

Homework Statement [/B] I was reviewing this stuff and although I excelled at it once, I seem to forget some of it. For example, please consider this: Homework Equations R_C=\frac {R_1R_2} {R_1+R_2} + R_3 Here's the correct formula for its error: \Delta R_C=\frac {R_1R_2} {R_1+R_2} \left[...
15. MCNP Why does it say F5 tally is not in any cell?

Sorry for two questions in a row, this one we have been stumped on for the entire day We're getting "fatal error. detector no. 1 of tally 5 is not in any cell.", What could be causing this? In the manual and all examples we've seen, nobody has parameters specifying cell location for the...
16. Numerical/Analytical Solution to a Complex Integral

Homework Statement I have the following integral I wish to solve (preferably analytically): $$I(x,t) = \int_{-\infty}^{0} \exp{[-(\sigma^2 + i\frac{t}{2})p^2 + (2\sigma ^2 p_a + ix)p]} \ dp$$ where ##x## ranges from ##-\infty## to ##\infty## and ##t## from ##0## to ##\infty##. ##\sigma##...
17. Uncertainty/error of a volume is greater than the normal volume

Homework Statement I have an empty cylinder with an external diameter of (23.0 ± 0.5) mm, an internal diameter of (22.5 ± 0.5) mm and a height of (60.0 ± 0.5) mm. I need to calculate its volume with its uncertainty/error. Homework Equations The Attempt at a Solution I do it like this...
18. Ansys Maxwell: Boundary definition

Hello, I am trying to find a Magnetostatic(3D) solution for my design. My design consist of a coil embedded in Ceramic material developed by LTCC technology. I am below queries: 1. Is it important to define a material"Insulating"? How it will affect the Inductance of the system and the...
19. I Why do particle physicists use Gaussian error estimates?

There is solid empirical evidence that error in particle physics measurements is not actually distributed in a Guassian manner. Why don't particle physicists routinely use student t error distributions with fat tails that fit the reality of errors in experimental measurement more accurately...
20. Writing integrals in terms of the error function

Homework Statement I have the following integral, $$\frac{1}{\sigma \sqrt{2\pi} t} \int_{-\infty}^{0} \exp[\frac{-1}{2\sigma ^2} (\frac{x-x_0}{t} - p_0)^2]dx$$ that I wish to write in terms of the error function, $$erf(x) = \frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-g^2}dg$$ However, I can't seem...
21. I Error in the average of same-value measures

My question is simple, and I'm only asking it because most places talk about more advanced problems than this one: I've measured the radius of a sphere (a very regular one) with a micrometer of 0.01 mm resolution. I took 3 measures (rotating it between each measure), and all of them were...
22. [Math Processing Error]

Anyone recognise this problem? When looking at posts with (presumably) Latex formulae, I get [Math Processing Error] instead of the formula. It looks like everyone else can read them ok and even stranger, I sometimes see the formula for a brief moment before it is replaced by the message...
23. I Error Propagation (Percentage) - sin(x)^2 / x^2

Hey, I'm trying to propagate my percentage errors through some hefty equations and come up on a bit of snag: I've got a percentage error for x and know how to deal with it for trig functions and powers, however since both errors are from the same source: y = sin(x)^2 / x^2 Should I just...
24. K

Error analysis E/M experiment -- help please

So I am doing the charge to mass experiment and determining the relationship between: 1. accelerating voltage and radius formed by the electron beam 2. magnetic field strength and radius formed by electron beam Theoretically I should obtain an equation of the form: r = (1/B) *sqrt(2mV/e) where...
25. Using Maxima to plot error in Fourier series

I'm trying to use Maxima to examine the error in a Fourier series as the number of terms increases. I've figured out how to produce a Fourier series and plot partial sums, but this has me stumped. If anyone experienced with the Maxima CAS has some insight into this, I would greatly appreciate...
26. An Error Formula for Linearization (involving second Derivative)

Homework Statement In textbook i was given formula to calculate error. I know that: E(t) = f(t)- L(x) = f(t) - f(a)- f'(a)(t- a) [L(x) is linear approximation]; [Lets call this Formula 1] I understand that, but that I have formula: E(x) = f''(s)/2 * (x-a)^2 [lets call this Formula 2] Here...
27. I Error in declination of linear regression

During a lab exercise we measured different masses of a magnetic material on a scale while changing the strength of the magnetic field it was in. Afterwards we plotted the masses and the fieldstrength hoping to find a linear slope. Then we drew a linear slope by using linear regression and found...
28. I How to write measured value with error

During a labexercise we measured a value to be 26.3 mT. The teslameter was said to have an accuracy at +- 0.05%. This means we measured 26.3 +- 0.0132mT. However we are supposed to write a measured value with it's error in the last digit. But the error is smaller than the smallest digit we got...
29. Material definition problem in ANSYS Maxwell

HI Guys, I am getting an error in Ansys Maxwell that says Maxwell2d solver, process solver2d: Internal Solver Error: 'In the Material: M270-35A_12 , the SLOPE of the End Two Points in this BH curve is 56519.1, which is more than 2 times of Mu0; This may lead to a non-physical solution...
30. Error message in PSpice

Homework Statement Run a transient simulation and plot the three outputs, Vo(t), on the same plot. Use the following settings: 1. Set the Run Time (or Stop Time) so that you plot 3 cycles of Vo(t). 2. Set the Maximum Step Size so that you get at least 100 points per period for Vo(t). 3. Set...