I figured it out. This is a complex number with only a real part. e.g.:
cn = \frac{sin(\frac{nπ}{2})}{nπ}
For even n, note that cn is equal to 0. The angle of a zero complex number is 0.
For n = 1, 5, 9, ..., c = a + bj, a is 1, b is 0. arctan(0/1) is 0 degrees.
For n = 3, 7...
Hi all.
Suppose I am looking for the following quantity: \sphericalangle cn, where cn = \frac{sin(\frac{nπ}{2})}{nπ}. cn is a complex number.
According to the book, "Signals and Systems" by Edward Kamen 2nd. Ed., \sphericalangle cn = π for n = 3, 7, 11 ... , and cn = 0, for all other n.
The...
Thanks for the response. After mulling it over, I've figured it out:
One must treat f(t) in cos(t) * f(t) as simply any function (it doesn't matter what it is). After converting the cos(t) to exponentials (through) identities, one realizes that cos(t) affects f(t) through time-shifting...
I am given a function f(t) with it's corresponding Laplace Transform in the Frequency Domain (F(s)).
I'm having a hard time wrapping my head around the product of say, L{cos(t)*f(t)}. The * is multiplication and not convolution. Must I do the integration for the Laplace transform by hand...
Thanks DeadBeef. I think this is the response I needed to hear. I've been breaking the process down step-by-step and "sentence by sentence" as you say. The study of complex analysis (or the review...) gave me some insight on how some of these optimizations work.
Thanks! Will continue on...
Fourier Transform -- Completely Flustered About Recursive FFT
Hi all.
I have been banging my head about this problem for the last week and a half-- Fourier Transform. Some background about me: I am a rising Junior at an accredited university majoring in Computer Engineering & Computer...
Hi all.
I have a 4 input circuit (ABCD). I have 7 outputs that accompany this circuit. Now, I have tools (like Karnaugh maps) to solve for Standard Sum of Products (or Product of Sum) form for individual outputs. I have the minimum of each output based on the Karnaugh map.
However, I want...
I see. Based on your chart, I may have gained some insight. Let me clarify-- so we're not supposed to use all of the resistances in the circuit?
Is it correct to assume that to calculate Vab, I may simply just find the potential difference between Va and Vb?
e.g.: according your chart, Vab...
Homework Statement
Basically, find Vab
[PLAIN]http://carlodelmundo.com/hw/circuit.png [Broken]
Is this correct -- note: please tell me that my methodology is sound; DO NOT GIVE ME A NUMERICAL ANSWER.
The problem asks for VAB. What's weird to me is that there is a potential across...
Hi.
I'm trying to decipher the differences between the machine architecture and microarchitecture.
I believe Machine Architecture is:
The ISA (such as x86)
Von Neumann Model for Computing?
and I believe the Micro Architecture is:
Specific implementation of some arbitrary ISA...
The reason why I asked because I couldn't decipher why a particular textbook portrayed NAND and NOR gates with a specific implementation.
I wanted to make the distinction that this is only ONE way of implementing a particular gate. However, you just answered it: it is non-unique but the idea...
I am learning about the implementations of digital logic gates using n-type and p-type transistors.
With the advent of these two transistors, isn't it possible to have more than one implementation of the NAND gate?
Homework Statement
I am given the binary equivalent of ASCII codes and I am asked to decode a particular binary message (ASCII binary to actual ASCII character).
I am required to write it in C. Where can I get a text file of the ASCII code so I may create a look up table?
I googled...
If I recall correctly, I am going to be packaging in the IC level. The issue of thermal heat transfer (to properly release heat from the components) was also discussed. I am assuming this is part of a trial-and-error back-of-the-envelope calculation sort of thing? Or is there really a text...
Hi,
I will be volunteering my time helping my professor in the realm of "electronic packaging." There doesn't seem to be a lot of straightforward tutorials on electronic packaging, could anyone guide me with the proper resources so I can take a look?
Thanks
Carlo
It seems complex but one can break it into pieces to simplify the problem.
\sum^{\infty}_{n=0} \frac{1}{1+z^{n}}
We are looking for the convergence of the series for differing values of z where possible values of z are from (-inf, +inf). Keep also in mind that n is always a positive integer...
I've always thought of 'radius of convergence' in terms of power series. This is not a power series.
EDIT: This answer is wrong see my below post. Upon inspection, it looks like it converges for values greater than 1 as you say (by looking at its limits for different values of z).
As you said, if you let t = cos x - 1. Then naturally you'll get r3(p3(x)). Note that you forgot to cancel out the -1 (ie: 1 + -1 = 0 when substituting t for cos x - 1).
True. The expression is indeed complicated, but remember: the question asks you to write the series to the third order...
Hi estro,
Here are some questions that can get you started:
What is the difference between MacLaurin vs. Taylor Series? (Hint: Is MacLaurin centered at any point?)
What does it mean for a polynomial to have order 3? (Hint: Look at the exponent)
What is the infinite series equivalent of cos...
I understand that when we apply voltage to the Base of the PNP Transistor (Emitter, Base, Collector), we actually block current from passing from Emitter to Current.
If there is no voltage applied to base, then current flows freely.
If this is the case... how come when I wire the...
Going a mile further...
{A} is a subset of B in this example because...
Every element in {A} is in B.
The only element of the set of sets is A. A is the set of all integers. {A} therefore is the subset of B.
------------------------------------------------------------
{{A}} is a subset...
My question:
Why are we comparing set A (the set of all integers) on an element-by-element basis? I agree that "3" is an element of A such that A = { ...,-1,0,1,0,1,2,3...}.
I agree that "3" is neither the set of integers A = { ...,-1,0,1,0,1,2,3...} nor the set containing the set of...
Right. There is Calculus AB and Calculus BC.
From what I recall from a few years ago:
AB covers from Limits, Derivatives, Optimization, Newton's Method, Linearization, Related Rates, Integration + By parts, Volumes of Rotated Shapes, some Differential Equations
BC covers that plus Infinite...
Homework Statement
Let their be a set A, and let B be the set: {A, {A}} (the set containing the elements A and the
set that contains element A)
As you know, A is an element of B and {A} is also an element of B.
Also, {A} is a subset of B and {{A}} is also a subset of B.
However...
Hi StoneBridge,
Thanks for your response. How do I account for the kinetic energy of the linear 'falling of the mass' when I am only given the velocity?
For the right hand side of the equation, do I just include another kinetic energy term (... KE = (1/2)Mv^2)
Would that account for the...
Homework Statement
[PLAIN]http://carlodm.com/phys/1.png [Broken]
Homework Equations
Energy Equation
The Attempt at a Solution
As shown in the scan.
Is this the correct approach? I have a feeling that the velocity, v, needs to be used. I used the Energy Equation for this...
The original equation was pulled from an old exam of my undergrad chemistry professor. It was a little weird, so it was worth discussing.
Thank you for your analysis and general helpfulness Borek. This question was a bit weird!
Here are the spectator ions:
2K+ + 2MnO4- + 10 Fe2+ + 10SO42-
yields:
2K+ + SO42- + 2MnO4 + 10Fe1+ + 5SO42- + 8H2O
Hmm. Interesting that I found the net ionic equation. The only ions I see that are the same are the K+ and SO42- ions. The manganate ion, 2MnO4- doesn't count because...
Homework Statement
2KMnO4 (aq) + 10FeSO4 + 8H2SO4 -->
K2SO4 (aq) + 2MnO4 (aq) + 5Fe2SO4 (aq) + 8H2O (aq)
Homework Equations
Spectator ions don't participate in the reaction.
The Attempt at a Solution
What gives? Is my professor bent on making our lives miserable? The answer...
No we're not required to use the ON method... but it is a tool that we are able to utilize for ugly equations such as this. Thanks for your help! This'll come handy for reviewing my Chem exam.
I see. So I should balance the reactant iron first, to 2... then do the multiplications of irons by 3.
I've arrived at that step but the products side still looks like a mess. Is this where I stop all "techniques" and rely on intution and trial and error to figure out the balanced equation?
Homework Statement
http://carlodm.com/pictures/problem.png [Broken]
The Attempt at a Solution
I'm stuck. Usually I balance the equation by multiplying the Fe(OH)2 and Fe2O3 by 3. However, I can no longer do this because Fe2O3 has two iron's per one molecule.
Do I multiply one by...
Homework Statement
Support you wish to average 40 mph on a trip and find that when you are half the distance to your distance to your destination you have averaged 30 mph. How fast should you travel in the remaining half of the trip to attain an overall average of 40 mph?
Homework...
Homework Statement
http://carlodm.com/calc/123.png [Broken]
My question is:
Why can't we use a scalar multiple like (3/8) PQ instead of using the midpoint formula twice (to get 3/8) ?
Homework Statement
http://carlodm.com/images/chem.png [Broken]
The Attempt at a Solution
The attempt is in the image. HOW IS THIS WRONG?? I've looked at it for hours now!
Homework Statement
How many total moles of ions are released when the following sample dissolves completely in water?
2.63 g of CuSO4 * 5H2O
Homework Equations
159.611 g / mol of CuSO4
The Attempt at a Solution
I tried doing 2.63 g / [159.611 g / mol] to get .016477 mol of...
Homework Statement
A solid cylinder with a radius of 5.0 cm and a length of 10. cm is cut in half lengthwise. What is the surface area of one of the two resulting objects?
Homework Equations
SA = 2(pi)(r2) + L(pi)(r2)
The Attempt at a Solution
Is that the correct formula? If it...
Homework Statement
http://carlodm.com/images/1.png [Broken]
Homework Equations
I tried using the formula: ( C1V1 + C2V2 ) / (V1 + V2)
The Attempt at a Solution
I keep on getting .0761 M. anything wrong with this? (YES I changed mL to L)
Homework Statement
http://carlodm.com/images/math1.png [Broken]
My question is:
Isn't it possible for two planes to have one solution? Geometrically, what if their edges were touching and that was the extent of their intersection?