Just looked at the table of contents / some sections... and wow. Literally a perfect match (more or less, about as close as I could hope) step by step to my course outline. Same style and cheap too. Perfect suggestion and supplement. Thank you for pointing me towards it, dover always has gems.
So the course I'm taking doesn't have a textbook requirement just lecture notes as the study material. While these are sufficient I would like to supplement with an outside reference that is a bit more in depth / explanatory.
It's your typical undergrad real analysis course covering:
The least...
I'm taking an abstract algebra course that uses Hungerford's "An Introduction to Abstract Algebra" 3rd Ed. And while I feel like I'm following the material sufficiently and can do most of the proofs it's hard to learn and practice the material without a solutions guide. How am I supposed to know...
In my calculus textbook (section on vector calc) it is showing that the gravitational field is conservative. I followed fine except for the first part, defining the scalar function f.
Showing the field is conservative went something like this:
f(x,y,z) = MM'G/\sqrt{x^2+y^2+z^2}...
I've put the problem statement below and worked it out. I typically don't post questions like this as they're a lot to go through, but I am wondering if I have worked the problem correctly as my book does not have the solution and I feel like I am not understand the material correctly.
1...
I think A student's guide to maxwell's equations is what I was looking for. Purcell has a great exposition as does griffiths, but I'm lacking at the problem solving and understanding applying the techniques. More or less going from thinking like a mathematician to a physicist, and that looks to...
I'm using purcell and I find the notation (CGS units) to be a bit confusing at times in formulas, but trying to struggle through it as I should go ahead and get exposed to different systems of units and I've had an undergraduate course on Newtonian mechanics.
In purcell I don't find most of the...
Can anyone recommend a good book that deals with the mathematics of E&M? I've read through my calculus books and feel like I understand the material there and can solve the problems. However, when it comes to it's applications in electricity and magnetism I find that I have enormous difficulty...
I was missing the sign! That was it. I always get confused about whether to include signs or take the absolute value/magnitude. In columb's law we don't use the signs do we? Every time I've tried to use negatives in coulumbs law it came out wrong, or maybe I'm just doing it wrong. That's why I...
Homework Statement
A proton is composed of three quarks: two "up" quarks, each having charge +2e/3, and one "down" quark, having charge -e/3. Suppose that the three quarks are equidistant from one another. Take the distance to be 3×10-15 m and calculate the potential energy of the subsystem of...
I'm not sure what you mean? I'm very bad at using symmetry doing these types of problems typically takes me ages as I can't identify the symmetry / relations correctly in square arrays of charge etc. Could you explain what you mean?
I didnt understand where the Q went until I reworked it and yes you're right. Is the below correct? It gives me the correct answer but as far as best way to solve technique etc goes not sure its close to good.
My notation could probably use some work... I realize I could have forgotten about...
Homework Statement
Consider the figure below, we need to find the charge on Q_0, both charges Q are negative. It is given that the net charge on Q_A is zero.
The figure of the problem is attached.
The Attempt at a Solution
I understand how to get the solution except for one part. I'm just...
Couldn't solve the derivative for b. I think I messed the derivative up I was getting high powers of b that couldn't be solved.
Sample of what I tried to solve...
d/db [b/(9+b^2)^{3/2}] \Rightarrow [3b(9 + b^2)^{1/2} - (9 + b^2)^{3/2}]/(9 + b^2)^3
After that it turned into a mess trying...
I don't understand? Q is restricted on the y-axis at a height of a = 3m the charge q is arbitrary at a location b. The first part of the problem is to find the value b at which the x-component of the force between the two charges is at it's miniumum which would be at b = 0. To find it's maximum...
Here's the picture of the figure, where a = 3m in this specific case. I guess I should have also stated that the b in the numerator and the 3/2 power came from the cosine to be more correct in terminology?
A charge Q is placed at a distance a = 3m and a charge q is placed at a distance b
For what value(s) of b is the x-component of the force maximized?
I know to maximize the force we need to maximize F_Qq = k Qq b/(3^2 + b^2)^{3/2}.
To do this we need to set the first derivative to zero and...
I think I messed up a little bit. The diagonal will be the side length, a, times square root of three.
I only need one face so I just need to multiply the result by 1/\sqrt 3. So, the result would be
F_Q = 4[1/4\pi \epsilon_o * q^2/r^2 ] * 1\sqrt 3
In the way I worked it I placed the...
Homework Statement
Four charges of 2*10^-7 are placed on the corners of one face of a cube of 15 cm. A charge of -2 * 10^-7 C is placed at the center of the cube. What is the force on the charge at the center of the cube?
Homework Equations
F = k q_1*q_2/r^2
The Attempt at a Solution...
Ah fair point forgot about those being strictly on the x-axis, so need to fix that then resolve into E_x and E_y for the respective terms and then take the square root of those squared for the magnitude.
The missing term is the -5q charge, yes? So it should be
E=k[−2q/(\sqrt2 * d)+q/(\sqrt 2 * d) + 2(5q/(\sqrt 2 * d))= k[9q / (\sqrt 2 * d)]
Also, changed q^2 to q since this is the electric field not force... silly mistake, and the bottom term should be \sqrt 2 * d instead of d^2?
This is...
Homework Statement
Find the magnitude and direction of net electric field at the center of the square array of charges. Find E_x and E_y
The square array of charges http://postimg.org/image/4gf94ymmf/
The Attempt at a Solution
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My attempt at drawing in the force vectors...
Can someone walk me through calculating the final step in this problem.
Problem statement:
If the charge q is produced by adding electrons to the mass, by how much will the mass be changed?
It was calculated that the charge q is 2.374 * 10^-7 C which is correct and I know that we need to...
Homework Statement
The Earth is constantly being bombarded by cosmic rays, which consist mostly of protons. Assume that these protons are incident on the Earth’s atmosphere from all directions at a rate of 1366. protons per square meter per second. Assuming that the depth of Earth’s atmosphere...
Have a quick question about taylor series. We covered taylor series somewhat in class, but there was a complete lack of explanation and our calculus book literally covers the topic in a single page.
I understand the idea of a taylor series and how its related to a power series, but what I don't...
Thanks for the detailed reply. Talked to a few different people today and that was pretty much the same conclusion we all came to that there would really be no graph theory applications. The only thing that I may be apply to apply is machine learning to possibly predict locations of where new...
Im not entirely sure what section of PF this post should be in so I apologize in advance if this is not in the correct section.
I don't know that much graph theory or the various fields that it can be applied to, but I do know that graph theory can be used in social media etc by using dynamic...
1. Compute the area of the region S between the graphs of f and g over the interal [a,b] specified in each case Make a sketch of the two graphs and indicate S by shading.
Question 9 -F(x)=x^2 g(x)=x+1,a =-1, b = (1+√5)/2
Homework Equations
The Attempt at a Solution
I think...
Sorry this is a bit late and off topic after reading everythign you guys posted and browsing around I decided to hold off for now on buying a laptop in the hopes of finding a good deal on a higher end model. With that being said i found the laptop I've been looking at for awhile as a discounted...
That's exactly what i was looking for thank you. If my budget allows it i'd love to get the first laptop you linked and the fact that it actually has decent reviews is always a plus.
That's mostly what I use my computers for as well. If I didn't think the flexibility of a laptop would be...
My budget is around $300 possibly closer to $400 and yes I'm positive I'll be using mathematica in my math classes and labs. I found a thinkpad t410 2.53 GHz for 299 but would prefer to not buy a refurbished laptop for any potential problems they may have.
I found some reviews after a lot of digging around seems to be decent from the reviews. The only other question I have is would a quad-core at a higher GHz processor be better than a dual core at a lower speed processor? After browsing around it seems that mathematica cannot utilize all four...
I tried looking around for reviews on Google and couldn't find any for the exact model. That's why I posted here I didn't want to pass up what might be a good deal based off of one bad review on the newegg website.
Can anyone out there recommend an affordable laptop for a college student. Going in as a physics/math major so needs to be able run mathematica and similar programs decently.
This is the one I was thinking about going with. Thoughts...
I thought an inductive set could have an upper bound but not a greatest upper bound / supremum because for every x in the set x+1 is also in the set?
and to fix my assumption issue could i do something along the lines of- Suppose S is a nonempty set of real numbers and suppose there is a...
1. Question I 3.12 from Apostle's calculus volume 1
If x is an arbitrary real number, prove that there are integers m and n such that m<x<n
2. Theorem I.27:Every nonempty set S that is bounded below has a greatest lower bound; that is, there is a real number such that L= infS...
Yeah they're physics outline looks pretty typical as does USC's. If these are the best of my options would you consider it even worthwhile to go in as a physics major? The way I'm seeing my options as of right now is that since they're not outstanding schools (Ivy League MIT etc) my chances of a...
I was going to do that today actually lol. I know Roanoke has a strong focus on computer science from my college tour when I went so that would work out if I decided to switch majors and their small student body would make it easier to do undergrad research compared to USC which has a very large...
Okay the time has come where deposits are soon to be due. However, I'm still stuck between two schools USC and Roanoke. Links for each are below. I have other college options but they are party schools and don't make sense academically / career wise.
http://sc.edu/
https://roanoke.edu/
I...
Ok thank you that cleared up a few questions I had concerning proofs.
Yes, I had thought about doing that but I didn't know if that would be considered "rigorous" enough for a proof. Spivak's text is my first encounter with any rigorous math and I assumed my proof could only be based on the...
Here's my attempt at this proof. Is this correct?
Homework Statement
Prove \frac{a}{b}/\frac{c}{d} = \frac{ad}{bc}
Homework Equations
P 1-12
The Attempt at a Solution
\frac{a}{b}/\frac{c}{d} = \frac{ad}{bc}
\frac{a}{b}/\frac{c}{d} = (ad)(bc)^{-1}...
A book that I personally like is "University Physics with Modern Physics" by Young and Freedman. Might be worth checking out. It uses calculus, don't know if you've taken it yet or have any familiarity with it.
Sounds like an interesting branch from the replies. Could your recommend any good introductory books on the subject? I haven't had too much crazy math yet just up to calculus and about to start linear algebra. I don't know if anyone has read this book, but I found a copy of Thermodynamics and...