Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking-up" or "an untying;" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses.
As a formal concept, the method has variously been ascribed to Alhazen, René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name).
Hello everybody,
I'm currently helping a friend on an assignment of his, but we are both stumbled on this exercise, I'm posting it here
We define a function ##f## which goes from ##\mathbb{R}## to ##\mathbb{R}## such that its argument maps as
$$
x \mapsto...
I am working on a problem, where I have arrived at the following nonlinear state space equation:
dx1/dt = x2;
dx2/dt = c11 x1 + c21x2 + c31x3 + c41x4 + c51x1x22;
dx3/dt = x4;
dx4/dt = c12 x1 + c22x2 + c32x3 + c42x4 + c52x1x22;
c11, c21, c31, c41, c51, c12, c22, c32, c42, c52 are all a function...
So I always thought that geometry is somewhat different from the rest of math. I mean, most of math is about numbers and relations. While geometry is about space.
Does analysis connect the two? For example, the hypotenuse of a triangle is just a truncated portion of the number line that has...
1. Homework Statement
The circuit is driven by a voltage source,
Vs(t)= 8.2 cos(1.8 t − 0.25 )V .
The circuit elements are given as follows.
G1= 5 S,G2= 7.6 S,G3=3.8 S
(Gi is the conductance of corresponding resistor Ri)
L1= 20 H,C1= 5×10−2 F
If we select Node 4 as the reference node...
Homework Statement
I need to use mesh analysis to find the three currents:
Homework EquationsThe Attempt at a Solution
The answers are I1= -1.25A, I2=0.125A and I3 = 1.125A
I don't know where I messed up for I3
Dear Forumers,
This question is about load-line analysis for loudspeaker driver magnetic circuits in FEMM 4.2 (Finite Element Method for Magnetics), I can't seem to get an answer from the mailing lists.
I would like to get the permeance coefficient for random points inside the magnet.
I have...
Hi all, I am quite confused by the forces relating to a horizontlly placed spring when someone directly exerts a force to the compress it. If I exert a force F to the right to compress the spring, which, say, is placed against a wall, the spring exerts an elastic force on me but I don't see how...
Is there a formulation of any of the relativity theories in terms of complex analysis? As in - I imagine - every event would be a complex number in a complex field.. or something as such..
Homework Statement
For beta = 100 and assuming ro is very large, what is the DC voltage at the collector?
Homework Equations
IB = IE(β+1)
IC = β*IB
The Attempt at a Solution
Since IE = 0.5mA, IB = 0.0505 A
Then, IC = 5.05 A (which doesn't feel right)
VC is the same potential across the 30kΩ...
What is the contribution of Eint
to the output voltage Vout?
Homework EquationsThe Attempt at a Solution
To calculate the contribution of Eint, I removed the other two voltage sources.
Then, I divided them into three potential dividers, giving me:
Vbody= (ZC2/ZC2+ZC1) x Eint...
Homework Statement
This particular question has been raised in past posts and I have studied those posts but unable to take anything from them. Basically the question comprises 2 parts. Part A requires us to find the current through "I" using mesh analysis. By studying some of the posts on...
I have this problem with a complex integral and I'm having a lot of difficulty solving it:
Show that for R and U both greater than 2a, \exists C > 0, independent of R,U,k and a, such that $$\int_{L_{-R,U}\cup L_{R,U}} \lvert f(z)\rvert\,\lvert dz\rvert \leqslant \frac{C}{kR}.$$
Where a > 0, k...
I have been trying to show that
$$\lim_{U\rightarrow\infty}\int_C \frac{ze^{ikz}}{z^2+a^2}dz = 0 $$
Where $$R>2a$$ and $$k>0$$ And C is the curve, defined by $$C = {x+iU | -R\le x\le R}$$
I have tried by using the fact that
$$|\int_C \frac{ze^{ikz}}{z^2+a^2}dz| \le\int_C...
Hi all,
I have been simulating the following rhombus compliant mechanism using Ansys Modal analysis to have a quick understanding about its mode shapes,,,, the problem is that the deformation is extremely large you can see this as the scale is (*10^-5 ) . This result is for sure unrealistic but...
Hi all,
I am currently in my first semester of my sophomore year, taking Real Analysis I. This class covers formal proofs, properties of the real line, sequences, series, limits, continuity and differentiation, and Riemann Integration. I apparently got stuck with the worst professor at my...
Hello everyone,
I am interested in analyzing sounds (both spectral plots and time plot). What type of hardware would I need? There are a lot of free softwares online...
Are there educational hardware tools that are not too expensive?
thanks!
Homework Statement
Find the differential equation for Vo
Homework Equations
KCL
The Attempt at a Solution
At node v1:
##\frac{V_1-V_{in}}{R_1}+\frac{V_1-V_p}{R_2}+C_2(\dot{V_1}-\dot{V_2})=0##
At node vp:
##C_1\dot{V_P}+\frac{V_P-V_1}{R_2}=0##
At node vn...
I am using Lang's book on complex analysis, i am trying to reprove theorem 4.1 which is a simple theorem:
Let Compact(S \in \mathbb{C}) \iff Closed(S) \land Bounded(S)
I will show my attempt on one direction of the proof only, before even trying the other direction.
Assume S is compact
Idea...
I am trying to perform a simple simulation in ANSYS WB Mechanical. Description is given below in image, thickness of the plate is 5 mm. Problem is I am unable to decide which type of support should I provide for this.
Homework Statement
consider ##f## a meromorphic function with a finite pole at ##z=a## of order ##m##.
Thus ##f(z)## has a laurent expansion: ##f(z)=\sum\limits_{n=-m}^{\infty} a_{n} (z-a)^{n} ##
I want to show that ##f'(z)'/f(z)= \frac{m}{z-a} + holomorphic function ##
And so where a...
Assuming that a TLP platform is examined and the wave forces acting on the tendons of the mooring lines are presented in RAOs (as a function of wave frequency). Using Jonswap spectra for North sea (i.e peakness factor equal to 3.3) we can obtain Hs (significant wave height); Tp (peak period) and...
Homework Statement
Homework Equations
Torque and Newton's 2nd Law Equations
The Attempt at a Solution
Apart from drawing a free-body diagram, I couldn't do much else. I can't seem to find the source of torque causing the car to rotate clockwise about its pivot (i defined it as the right...
Homework Statement
Reduction from top network to bottom network in the screen shot. I can not find the steps that have been taken to do this.
Fault impedance = Zfa = Zfb = Zfc = j0.5
Homework EquationsThe Attempt at a Solution
in hand written screenshot, sorry for the mess, just to show it...
Hello!
1. Homework Statement
I need to find the instantaneous height of a liquid during the simultaneous filling and emptying (through a hole) of a cylinder. I have varying Qin at incremental time of 1 sec. with cylinder area=5 cm and orifice area=0.5 cm.
Homework Equations
Torricelli's...
Homework Statement
Vs = 100cos(2000t)
Homework Equations
KVL, KCL
The Attempt at a Solution
My mesh equations are:
-Vs + I1(30-12.5j)-I2(120j)=0
4Ix+I2(120j+20)-I1(120j)=0
Ix = (I1-I2)
Are these correct? When I solve I get a different result than when I do nodal analysis.
lets say for example, the air drag (ϑ) that wind exerts on a tile is a function of the tile's width (w), height (h), viscosity of air (μ), density of air (ρ) and velocity of the air (V)
then ϑ = f(w,h, μ, ρ, V)
ϑ : MLT-2
w: L
h: L
μ : ML-1T-1
ρ: ML-3
V: LT-1
I understand there are 3 basic...
Suppose u(x,y) and v(x,y) are harmonic on G and c is an element of R. Prove u(x,y) + cv(x,y) is also harmonic.
I tried using the Laplace Equation of Uxx+Uyy=0
I have:
du/dx=Ux
d^2u/dx^2=Uxx
du/dy=Uy
d^2u/dy^2=Uyy
dv/dx=cVx
d^2v/dx^2=cVxx
dv/dy=cVy
d^2v/dy^2=cVyy
I'm not really sure how to...
I'm testing a part for fatigue, and I got a time series of Forces and Moments on three different parts of the body (A wind turbine hub). From the static structural fatigue analysis, I noticed that you need a von mises stress input - that's not a problem.
My problem is, how do I place different...
Homework Statement
Homework Equations
V=IR
All of them actually
The Attempt at a Solution
So I Started off by transforming the voltage source into the 's' domain
vs(s) = (4/s) -(4/s)*e-.5t
I know the initial conditions are zero, in other words at t=0, the voltage and currents at the...
Homework Statement
[/B]
All voltages and impedances are in per unit values.
After all the source transformations, why is the voltage source still 1 ?
Homework EquationsThe Attempt at a Solution
[/B]
Homework Statement
Homework Equations
KVL
The Attempt at a Solution
This is the solution given:
VB = (VCC*30k)/(70k+30k) = 3V
Why is a voltage divider being used to find Vb?
Dear forumers,
In advance, thank you for reading this post and helping me solving this.
The problem is the following :
I have a population (say, a bag) from which i take 3 samples.
Each sample gets analysed once by a laboratory in order to know their concentration of a product.
The result...
Hey everyone I'd be really grateful if anyone could help me out here, been going round in circles for two weeks now and I need to get going soon. Jumping right to the point, here's my problem:
We are currently working on a student project and designing a Wind Turbine for future opensource use...
Homework Statement
Homework Equations
N/A
The Attempt at a Solution
I am confused as to where the ω3sin(θ)k term disappeared to? It is not included in the very last line? I asked my lecturer and he said it's ''constant'' but he kind of shrugged off the question. I understand everything...
I have a document-word matrix and I need to do latent semantic analysis to match a query document with a set of key-words to the best possible match among other documents in the matrix. The matrix is in the form of documents-words occurrence array of 1 and 0 input. What is the best software I...
Homework Statement
Find the:
-Complex power delivered by source
-Power factor of total load
-Is the power factor leading, lagging, or in unity?[/B]
Homework Equations
KVL/KCL
The Attempt at a Solution
I want to solve this via mesh analysis to get currents.
Mesh1: -10V + V1 + 0.75V1 = 0
V1 =...
Homework Statement
Find power absorbed by resistor, capacitor and inductor. Find the total complex power absorbed by all the loads.[/B]
Homework Equations
KVL/KCL
The Attempt at a Solution
I want to solve this using Mesh analysis. There is a supermesh where the 5A source is, so I start it...
Hi everyone,
I am a complete beginner when it comes to circuit analysis that involves anything more than a few resistors and capacitors. Currently, I am working on a project that requires the transmission and reception of IR signals to control a motor. I know the requirements for the motor I...
Homework Statement
Find expressions for VL1, VL2, IC1, IC2 for each of the two intervals of a SEPIC converter under CCM operation.
link: http://i.imgur.com/EY98QbC.png
Homework EquationsThe Attempt at a Solution
link: http://i.imgur.com/SskXRoC.jpg?1
The observation model will be ##z=H\theta+v##, where ##z## is column vector containing the results, ##H## is the observation matrix, ##\theta## is the parameter vector and ##v## is a vector containing random additive noise.
b.)
In this case ##z##=[1 1 0; 1 0 1; 0 1 1; 1 1 1]*[##m_1## ##m_2##...
Hello,
I am taking a class in RA, where we're using Bartle/Sherbert. Since I have studied few chapters from it in the summer before, I decided to take a look at a more rigorous book, like baby rudin, but since many have advised against that book, I turned to Pugh's real mathematical analysis...
Hi Guys,
The schematic
What do you think the effect of changing the value of the output tube cathode capacitor from 50uf to 250uf would be?
Also the original schematic showed 500K pots and other newer schematics show 1M pots. What do you think the effect of that change would be?
Next...
I am using Abacus 6.13 for development of FEM for test setup on shear capacity of cold formed steel section. it has some complicated interactions with those interaction only solid section model gives answers.but with web openings on section it has convergence problems. i tried with different...
Homework Statement
Determine the output voltage Vo(t) in terms of Vs
Homework EquationsThe Attempt at a Solution
If I were to use Nodal Analysis to solve this, would these be the proper nodal equations?\frac{V1}{-j1.6} + \frac{V1-Vs}{175} = 0
\frac{V_{I2}-Vo}{10k} + \frac{V_{I2}}{1k} = 0
Homework Statement
Find Va(t) using Nodal Analysis:
Homework Equations
Zc = 1/(jwC)
Zl = jw*L
The Attempt at a Solution
W = 250
Z36mH = j9 ohm
Z80mH = j20 ohm
Z0.25mF = -j16 ohm (is capacitor impedance always negative? It says so in my instructor's notes but I forgot why)
20cos(250t) ->...