Why DSolve and NDSolve give different answer?
Boundary condition with spatial derivative is ignored by NDSolve
NSInvocation for Dummies? How exactly does NSInvocation work? Is there a good introduction?  I’m specifically having issues understanding how the following code (from Cocoa Programming for Mac OS X, 3rd Edition) works, but then also be able to apply the concepts independently of the tutorial sample. The code:  - (void)insertObject:(Person *)p inEmployeesAtIndex:(int)index {     NSLog(@"adding %@ to %@", p, employees);     // Add inverse of this operation to undo stack     NSUndoManager *undo = [self undoManager];     [[undo prepareWithInvocationTarget:self] removeObjectFromEmployeesAtIndex:index];     if (![undo isUndoing])         [undo setActionName:@"Insert Person"];      // Finally, add person to the array     [employees insertObject:p atIndex:index]; }  - (void)removeObjectFromEmployeesAtIndex:(int)index {     Person *p = [employees objectAtIndex:index];     NSLog(@"removing %@ from %@", p, employees);     // Add inverse of this operation to undo stack     NSUndoManager *undo = [self undoManager];     [[undo prepareWithInvocationTarget:self] insertObject:p                                        inEmployeesAtIndex:index];     if (![undo isUndoing])         [undo setActionName:@"Delete Person"];      // Finally, remove person from array     [employees removeObjectAtIndex:index]; }   I get what it’s trying to do. (BTW, employees is an NSArray of a custom Person class.)  Being a .NET guy, I try to associate unfamiliar Obj-C and Cocoa concepts to roughly analogous .NET concepts. Is this similar to .NET’s delegate concept, but untyped?   This isn’t 100% clear from the book, so I’m looking for something supplemental from real Cocoa/Obj-C experts, again with the goal that I understand the fundamental concept beneath the simple(-ish) example. I'm really looking to be able to independently apply the knowledge -- up until chapter 9, I was having no difficulty doing that. But now ...    Thanks in advance! $f$ is irreducible $\iff$ $G$ act transitively on the roots Let $F$ be a field and $f\in F[X]$ a separable polynomial. Let $K_f$ be the splitting field of $f$ and $G_f=\text{Gal}(K_f/F)$ its Galois group. Show that $f$ is irreducible $\iff$ $G_f$ acts transitively on the roots on $f$. My work $\implies :$ Let $f\in F[x]$ irreducible, $\alpha \in K_f$ a root and $\alpha _1,...,\alpha _n$ the other roots of $f$ (so $K_f=F(\alpha ,\alpha _1,...,\alpha _n)$). What I have to show (I think) is that for all $i$ there is a $\sigma \in G_f$ s.t. $\sigma \alpha =\alpha _i.$ Q1) Is it right ? Q2) Is $f$ the minimal polynomial of $\alpha $ ? (To me it is, but my teacher said that it can be not the case, but I don't understand why). Since $\alpha $ and $\alpha _1$ have the same minimal polynomial, there is an isomorphism $\sigma :\alpha \longmapsto \alpha _1$. We can observe that $\sigma : F(\alpha )\longrightarrow K_f$. Now $F(\alpha ,\alpha _1)/F(\alpha )$ is algebraic, then we can extend $\sigma $ to a morphism $F(\alpha ,\alpha _1)\longrightarrow K_f$. Now, we can continue like that and extend $\sigma $ as $\psi: K_f\longrightarrow K_f$ s.t. $\psi(\alpha )=\alpha _1$. Q3) The fact that $\psi(\alpha )=\alpha _1$ comes from the fact that $\psi|_{F(\alpha )}=\sigma $, right ? The bijectivity is obvious since it's a field homomorphism and that $\sigma (K_f)=K_f$. Q4) How to conclude that $G_f$ act transitively on the roots ? I don't have particular problem for the converse. Can you find shadow orbs in terraria demo? I have the PS vita demo, and was wondering if you could find any shadow orbs in that tutorial world. Thanks. Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $ The ship flying away from Rey in her flashback of being left on Jakku looks like one of the ships in the group that takes her away when she is captured.  If so, and it is a First Order ship that dropped her off, this is an interesting Easter egg. Abelian groups of order n. Is there a number $n$ such that there are exactly 1 million abelian groups of order $n$?   Can anyone please explain. I would yes because numbers are infinitive, and so any number n can be expressed as a direct product of cyclic groups of order n.  Can anyone please help  me understand.  Thank you. How to only append to clipboard (but not overwrite current data)? Is a business card necessary for a graduate student? I know some PhD students have their own business cards, but I don't know if it is a standard practice for PhD students to have their own business cards. I think a business card can be useful for networking in conference or collaborating with some industrial partners. So, is are business cards necessary for a PhD student or other graduate students attending conferences?   PS: in case it is field-specific, I would like to know the different practices in different fields I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful.  Is there any good examples of their uses outside academia? "What more" vs "what else" do you need? I am providing you with food, shelter, clothes.      What more do you need   or      what else do you need?   Which one's correct? Would I need to delete unused assets from my Unity packaged build? I'm going to make a release for my Unity game.  Does Unity include unused assets in build output? Would removing unused assets from a project reduce build size/Time?  I want to know if Unity packages all the assets to my build (which I would need to delete), or if Unity packages only the assets that are actually used in the game. Subjunctive mood: 'was' usage after 'I wish' and 'if only' had declared the sentence below as follow: 1) STAR TURN, 2) BEST LINES.      I wish Bernard Cribbins was my grandad. Perhaps he would be willing to   adopt?     Rattigan: “If only that was possible.” The Doctor: “If only that were   possible. Conditional clause.”    Is 'was' after 'I wish', 'if only' and 'if' (in conditional clauses) colloquial?  Does it be used in formal speech and writing? How do I add myself into the sudoers group? Possible Duplicate:          I've added myself back into the admin's group I think, by following   But I still can't do commands like:  sudo aptitude update   I get the message  oshirowanen is not in the sudoers file.  This incident will be reported.   How do I add myself into the sudoers group now that I am in the admin group? I did a fresh install of trusty 14.04, but a lot of icons are missing. I installed from DVD which was painfully slow and I hope to avoid repeating the process, especially since I started customizing stuff.  Here's my settings window:    I've tried:  sudo apt-get install --reinstall gnome-control-center sudo apt-get install --reinstall gnome-settings-daemon-schemas   None of which changed anything.  Any idea? I wanna edit preferences and none of them are in System Settings, neither in Unity Dash. Dimensional analysis, and the notion that quantities with different units cannot be equal, is often used to justify very specific arguments, for example, you might use it to argue that a particular formula cannot possibly be the correct expression for a particular quantity. The usual approach to teaching this is to go "well kids, you can't add apples and oranges!" and then assume that the student will just find it obvious that you can't add meters and seconds.  I'm sorry, but... I don't. I'm not convinced. $5$ meters plus $10$ seconds is $15$! Screw your rules! What are the units? I don't know, I actually don't understand what that question means.  I'm specifically not convinced when this sort of thing is used to prove that certain formulae can't possibly be right. Maybe the speed of a comet is given by its period multiplied by its mass. Why not? It's a perfectly meaningful operation - just measure the quantities, multiply them, and I claim that the number you get will always equal the current speed of the comet. I don't see how "but it doesn't make sense to say mass times time is equal to distance divided by time" can be a valid counterargument, particularly because I don't really know what "mass times time" is, but that's a different issue.  If it's relevant, I'm a math student and know extremely little about physics. Find this integral $$\operatorname I=\int\limits_{0}^{1}\dfrac{\arcsin{\sqrt{x}}}{x^4-2x^3+2x^2-x+1}\operatorname d\!x$$  My try: let $$f(x)=x^4-2x^3+2x^2-x+1$$ I found  $$f(1-x)=(1-x)^4-2(1-x)^3+2(1-x)^2-x+1=x^4-2x^3+2x^2-x+1=f(x)$$ so $$I=\int_{0}^{1}\dfrac{\arcsin{\sqrt{(1-x)}}}{x^4-2x^3+2x^2-x+1}dx$$ so $$2I=\int_{0}^{1}\dfrac{\arcsin{\sqrt{x}}+\arcsin{\sqrt{(1-x)}}}{x^4-2x^3+2x^2-x+1}dx$$ then I can't,Thank you very much Determine the SQL Server version and edition from the available set up, before actually installing it? Are logs kept for past at jobs? I have a third-party library which consists mainly of a large number of static (.a) library files.  I can compile this into a single .a library file, but I really need it to be a single .so shared library file.  Is there any way to convert a static .a file into a shared .so file?  Or more generally is there a good way to combine a huge number of static .a files with a few .o object files into a single .so file? Difference between regex [A-z] and [a-zA-Z]