Books about electromagnetism/electrodynamics using the language of differential forms I’m staring to learn electromagnetism and electrodynamics and I’m not very satisfactory with the language and concepts of traditional vector analysis. I’ve heard about the modern formulation of the theory in the language of differential forms. Can anyone give me some references (books, papers, etc.) on this?
What is a good reference for rigorous Electromagnetism and Electrodynamics? Is there any good book on Electromagnetism from a more mathematical point of view? By this I mean a book which makes use of differential forms and maybe De Rham cohomology. I was also searching for something that would include E&amp;M in the big picture of Gauge theories.
How to get GUI sudo password prompt without command line? Currently, for all my commands that require root access, I have to type them out on a command line.  I would like for the GUI to prompt me to key in my password, when sudo is required, instead of having to type out the commands from command line.  Is there any way to enable this? Previously one version of Ubuntu desktop had this feature out of the box.  This version of Ubuntu (that I am now running) I upgraded from a server installation.  I will add, my user account is already added to sudo group. Thus I can run commands such as sudo gedit or sudo apt-get but I'm not able to install software in the Ubuntu Software Center. Recently, I read in the journal  that Stephen Hawking wrote a paper claiming that black holes do not exist.  How is this possible? Please explain it to me because I didn't understand what he said.  References:   Article in Nature News:  (Zeeya Merali, January 24, 2014). S. Hawking, Information Preservation and Weather Forecasting for Black Holes, . I am familiar with the set-theoretical definition of functions.   A function $f : A \rightarrow B$ from a set $A$ to a set $B$ is a subset $f \subseteq A \times B$ of the Cartesian product $A \times B$ such that the following conditions hold:   $\forall a \in A : \exists b \in B : (a,b) \in f$ $\forall a \in A : \forall b, b' \in B : (a,b), (a,b') \in f \rightarrow b=b'$   Is there a purely set-theoretical definition of the function evaluation $f(a)$ for every $a \in A$? I get as far as defining  $f(a) = \{ b \in B : (a,b) \in f \}$ but that defines rather the set of values of a multi-valued function. I have a couple of eggs that I've picked up from some Pokestops (I'm lucky enough to live above one).   I walk a lot. I get to work through a 2 mile walk / train journey every day, so I should be picking up loads of steps for the eggs I have. However, because I'm normally always running late... for everything, I have to rush everywhere, so I walk at an above average pace.   Today I've walked around 5 miles, but the game has registered 100 metres. Is this because I walk too fast, or because of something else?  It's worth pointing out that I have the app open when walking... mostly because I have to catch them all. (This made me miss a train this morning... luckily I was early :D) What is the relation between electromagnetic wave and photon? Can I get a \widebar without using the mathabx package? One can use \bar to put a bar over a letter in math mode, but often the bar isn't wide enough. An alternative is \overline, but this isn't an accent, so it doesn't take into account the skew of the letter. In the following example, the bar extends too far to the left:    Now the mathabx package offers a \widebar accent, but this has several drawbacks:   mathabx changes a lot of other things, The \widebar sits slightly higher than \bar and \overline, In previewers (checked with kpdf and acroread), the \widebar appears fuzzy, which \bar and \overline don't.   So my question is: How can I put a wide bar over a letter in math mode without the above drawbacks? I want to create a circuit that can detect audio frequencies and flash RGB LEDs different colors depending on the detected frequency. The frequency range will be from 20 Hz to 12 kHz, after looking at the chart below.   (source: )    So my question is: what circuit design should I choose to make a good frequency detector? I suppose I would need    Preamp for the microphone (is it necessary for the ADC?) Band pass filters (active or passive?) A microcontroller with an onboard ADC that has a sampling rate of at least 24 kHz.   Before I get too excited, are there any circuits out there that already do this? how is this picture made? Good day guys, i have to something like this, any idea how is this picture made ?  so it looks like negative i did invert it in photoshop but the bright side of his face was blue, so there been negative effect and smting been used to change his face to blue before nagative or smting that changed his face to normal skin color after negative ? what can it be ? what do you guys think ? THANKS ! for help. ArgumentNullException or NullReferenceException from extension method? What would you consider to be the best exception type to throw when an extension method is called on a null instance (where the extension method does not allow it)? Since extension methods are nothing but static methods you could argue that it should be ArgumentNullException, but on the other hand they're used like instance methods so it might be more natural to use the NullReferenceException. Let's take the following example:  public static string ToInvariantString(this IFormattable value, string format) {     return value.ToString(format, CultureInfo.InvariantCulture); }   This way a NullReferenceException will be thrown if the value parameter is null.   The other example would be:  public static string ToInvariantString(this IFormattable value, string format) {     if (value == null) throw new ArgumentNullException("value");     return value.ToString(format, CultureInfo.InvariantCulture); }   EDIT: In some of the answers you have pointed out that an extension methods can be called like a static method and in those cases a null reference exception would be wrong, which is a great point, and actually one of my concerns, not sure why I forgot to mention that in the question in the first place.   Someone also pointed out that it's wrong to throw a NullReferenceException, and yes, it is. That's why I don't throw it, I just let it happen (let the CLR throw it) by not guarding the method.  I think I favor the ArgumentNullException (that's what I've use so far) but I still think there is at least room to argue for an against the NullReferenceException since it seems more natural in most places where the method is going to be used. How to rename wp-includes folder? Is there a way that we could rename wp-includes folder   I have found out there are ways to do for other folders. But how do we do it for wp-includes folder? Can matter really fall through an event horizon? libpng problems for QGIS I'm using ubuntu 18.04 and if I download QGIS 2.18 and I try to run it, I get this:  libpng warning: Application jmp_buf size changed Segmentation fault (core dumped)   If I try with QGIS 3.2, the error is:   libpng warning: Application was compiled with png.h from libpng-1.6.34 libpng warning: Application  is  running with png.c from libpng-1.2.56 libpng error: Incompatible libpng version in application and library   So it's clear that the problem is with libpng.   I purged libpng-dev and reinstall again but nothing changed.   I tried to purge libpng16-16 but I get:  sudo apt purge libpng16-16 Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  libgdk-pixbuf2.0-0 : Depends: libpng16-16 (&gt;= 1.6.2-1) but it is not going to be installed                       Recommends: libgdk-pixbuf2.0-bin  libgtk-3-0 : Depends: libcairo-gobject2 (&gt;= 1.10.0) but it is not going to be installed               Depends: libcairo2 (&gt;= 1.14.0) but it is not going to be installed               Depends: libfontconfig1 (&gt;= 2.12) but it is not going to be installed               Depends: libpango-1.0-0 (&gt;= 1.40.5) but it is not going to be installed               Depends: libpangocairo-1.0-0 (&gt;= 1.40.5) but it is not going to be installed               Depends: libpangoft2-1.0-0 (&gt;= 1.40.5) but it is not going to be installed               Depends: adwaita-icon-theme               Recommends: libgtk-3-bin E: Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.   and then:  ~$ sudo apt install libgdk-pixbuf2.0-bin libgtk-3-bin Reading package lists... Done Building dependency tree        Reading state information... Done libgdk-pixbuf2.0-bin is already the newest version (2.36.11-2). libgtk-3-bin is already the newest version (3.22.30-1ubuntu1). 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. ~$ sudo apt install libgtk-3-0 libgdk-pixbuf2.0-0 Reading package lists... Done Building dependency tree        Reading state information... Done libgdk-pixbuf2.0-0 is already the newest version (2.36.11-2). libgtk-3-0 is already the newest version (3.22.30-1ubuntu1). 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   At this point I'm afraid of breaking something if I continue trying things, so I come here for advice before.  I deleted and reinstalled ubuntu. I installed first thing qgis and it was working. Afterwards I compiled gdal, from source to have it from python as stand alone. It might be this, but I had done this previously without any problems. 'undefined reference to symbol 'pthread_create@@GLIBC_2.2.5' while compiling bochs I'm trying to compile bochs with this command:  ./configure --with-x11 --with-wx --enable-ne2000 --enable-iodebug --enable-disasm --enable-debugger --enable-e1000 --enable-usb --enable-pci   it works, but then when I run make I got:  usr/bin/ld: gui/libgui.a(gtk_enh_dbg_osdep.o): undefined reference to symbol 'pthread_create@@GLIBC_2.2.5' /lib/x86_64-linux-gnu/libpthread.so.0: error adding symbols: DSO missing from command line   Any Help ? :/ How to find an unknown Steam User I was playing with someone on Ark: Survival recently, I CTD'd and couldn't get his information. Are there any means that I could find this user's Steam account even though he hasn't logged in since?  I know of the function View: Players in Steam, but it only shows me the last 24 hours and I haven't played with this player in 3-4 days. Is there a way I could extend the view recent players function on Steam? Is there a record of this somewhere? Or do I have any further options? How can I hibernate or sleep my Ubuntu 10.10 desktop and have it "wake up" the next day?  I have seen software that can do this on windows, so it can't be hard on Ubuntu! Why does the sizeof operator return a size larger for a structure than the total sizes of the structure's members? Stopping a Thread in Java? I'm in the process of writing a piece of code that connects to a server spawns a bunch of threads using that connection and does a bunch of "stuff".  There are certain instances where the connection fails and I need to stop everything and start from scratch with a new object.  I wanted to clean up after the object but calling thread.stop on the threads, but this method is seemingly deprecated.  What is the recommended alternative to doing this? Should I write my own cleanup and exit method for each of the threads? Set the thread to null? or something else? What are the criteria for questions to be selected for Hot Network Questions? FTPS versus SFTP versus SCP What do Family Tree Maker users do, now that FTM has been discontinued? I was considering purchasing Family Tree Maker only to find it has been discontinued.    What do they plan for a replacement ?