I really want to learn about electricity and magnetism for a long time but never have gotten to it, are there are good books that are conceptual on the topic of electromagnetism? I do not know calculus btw.
Please recommend undergraduate-level textbooks on electrodynamics which emphasize practical applications and real life examples. Please describe the book's level and contents and its intended audience in as much detail as possible.   Please provide both applications from everyday life for curious students as well as engineering applications from a physics perspective.
How can I improve my color selection skill? I'm a web developer, started to become a web designer. However, I think my understanding of colors is not practical yet. There are tools out there that can give you color harmonies, and more stuff, like , but they don't give you the start point. I mean, how should I know that for this web site, I'd better use green and for that website, choose red. How should I know that?  I think color selection is more like an art, instead of being a science, and I'm like "you should become an color artist, in order to become a web designer".  How can I improve my color selection skill? How do you change the size of figures drawn with Matplotlib? How do you change the size of figure drawn with Matplotlib? Evaluation of $\lim_{n\rightarrow \infty}\frac{n!\cdot e^n}{\sqrt{n}n^n}$ without stirling approximation Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\frac{n!\cdot e^n}{\sqrt{n}\cdot n^n}$   $\bf{My\; Try::}$we can write it as $$l=\lim_{n\rightarrow \infty}\frac{e^n}{\sqrt{n}}\cdot \left(\frac{1}{n}\cdot \frac{2}{n}\cdot \frac{3}{n}\cdots \cdots \frac{n}{n}\right)$$  $$\ln (l) = \lim_{n\rightarrow \infty}\bigg[n-\frac{1}{2}n+\sum^{n}_{r=1}\ln\left(\frac{r}{n}\right)\bigg]$$  Now how can i solve it, Help required, Thanks The isomorphism $\mathbb{Z}[i]/(a+bi) \cong \Bbb Z/(a^2+b^2)\Bbb Z$ is , when the integers $a$ and $b$ are coprime. But what happens when they are not coprime, say $(a,b)=d&gt;1$?      — For instance if $p$ is prime (which is not coprime with $0$) then $$\mathbb{Z}[i]/(p) \cong \mathbb{F}_p[X]/(X^2+1) \cong \begin{cases} \mathbb{F}_{p^2} &amp;\text{if } p \equiv 3 \pmod 4\\ \mathbb{F}_{p} \times \mathbb{F}_{p} &amp;\text{if } p \equiv 1 \pmod 4 \end{cases}$$ (because $-1$ is a square mod $p$ iff $(-1)^{(p-1)/2}=1$).  — More generally, if $n=p_1^{r_1} \cdots p_m^{r_m} \in \Bbb N$, then  each pair of integers $p_j^{r_j}$ are coprime, so that by CRT we get $$\mathbb{Z}[i]/(n) \cong \mathbb{Z}[i]/(p_1^{r_1}) \times \cdots \times \mathbb{Z}[i]/(p_m^{r_m})$$  I was not sure how to find the structure of $\mathbb{Z}[i]/(p^{r}) \cong (\Bbb Z/p^r \Bbb Z)[X] \,/\, (X^2+1)$ when $p$ is prime and $r&gt;1$.  — Even more generally, in order to determine the structure of $\mathbb{Z}[i]/(a+bi)$ with $a+bi=d(x+iy)$ and $(x,y)=1$, we could try to use the CRT, provided that $d$ is coprime with $x+iy$ in $\Bbb Z[i]$. But this is not always true: for $d=13$ and $x+iy=2+3i$, we can't find Gauss integers $u$ and $v$ such that $du + (x+iy)v=1$, because this would mean that $(2+3i)[(2-3i)u+v]=1$, i.e. $2+3i$ is a unit in $\Bbb Z[i]$ which is not because its norm is $13 \neq ±1$.  — I was not able to go further. I recall that my general question is to known what $\mathbb{Z}[i]/(a+bi)$ is isomorphic to, when $a$ and $b$ are integers which are not coprime (for instance $a=p^r,b=0$ or $d=(a,b) = a^2+b^2&gt;1$).  Thank you for your help! Okay, so I think I have a decent enough sample, taking into account the 20:1 rule of thumb: a fairly large sample (N=374) for a total of 7 candidate predictor variables.   My problem is the following: whatever set of predictor variables I use, the classifications never get better than a specificity of 100% and a sensitivity of 0%. However unsatisfactory, this could actually be the best possible result, given the set of candidate predictor variables (from which I can't deviate).   But, I couldn't help but think I could do better, so I noticed that the categories of the dependent variable were quite unevenly balanced, almost 4:1. Could a more balanced subsample improve classifications? How to derive variance-covariance matrix of coefficients in linear regression Initializing C# auto-properties Smooth structure of embedded submanifolds Can I SSH into a specific directory? I SSH into a multitude of different servers every day and some of them have different filesystem structures for their websites. Each time I change server, I have to work out where I'm going to get to the files I really want (because it's very rarely that I want to be in ~). I use Fabric files to automate all my actions (pushing to git, automated SSH to the server to pull from git, restarting the web application, changing dependencies, etc), so I was wondering if I couldn't also tell it that I want to SSH into the right directory so I can run fab ssh and be in a normal SSH session, just in the right place and start working immediately. This is not about Fabric though; please ignore it. Fabric is just running a batch of commands. My argument is with the ssh command. That's what I'll be telling Fabric to run. So how I can get ssh to cd into a specific directory on login? Note: this cannot be a server or user-wide thing. I have multiple websites under one user on some servers so sticking something in ~/.bashrc would not work for me. The definitive guide to ConTeXt MkIV documentation What is the standard error of the sample standard deviation? I read from  that the standard error of the sample variance is  $$SE_{s^2} = \sqrt{\frac{2 \sigma^4}{N-1}}$$  What is the standard error of the sample standard deviation?  I'd be tempted to guess and say that $SE_{s} = \sqrt{SE_{s^2}}$ but I am not sure. One post with multiple questions or multiple posts? I want to ask several questions about the same problem domain but each question is independent from the others. Should I put all the questions in a single post or should I split them and send multiple posts? It's so annoying to drag it over and over again. How to change default position of a console? Provided we have this truth table where "$p\implies q$" means "if $p$ then $q$":  $$\begin{array}{|c|c|c|} \hline p&amp;q&amp;p\implies q\\ \hline T&amp;T&amp;T\\ T&amp;F&amp;F\\ F&amp;T&amp;T\\ F&amp;F&amp;T\\\hline \end{array}$$  My understanding is that "$p\implies q$" means "when there is $p$, there is q". The second row in the truth table where $p$ is true and $q$ is false would then contradict "$p\implies q$" because there is no $q$ when $p$ is present.  Why then, does the third row of the truth table not contradict "$p\implies q$"? If $q$ is true when $p$ is false, then $p$ is not a condition of $q$.  I have not taken any logic class so please explain it in layman's terms.       Administrative note. You may experience being directed here even though your question was actually about line 4 of the truth table instead. In that case, see the companion question  And even if your original worry was about line 3, it might be useful to skim the other question anyway; many of the answers to either question attempt to explain both lines. Integrable - martingale Suppose $X_{n}^{(1)}$ and $X_{n}^{(2)}$ are martingales w.r.t. a filtration $F_{n}$. I have do determine whether $Z_{n}=e^{X_{n}^{1}+X_{n}^{2}}$ is a martingale, submartingale or supermartingale. I thought that because $X_{n}^{1}+X_{n}^{2}$ is a martingale I can use Jensen to say that $E[Z_{n}|F_{n-1}]\geq e^{E(X_{n}^{(1)}+X_{n}^{(2)}|F_{n-1})}=Z_{n-1}$. But I have to check whether $Z_{n}$ is integrable and I don't know how. What is the distribution of primes modulo $n$? Identify the plane defined by $|z-2i| = 2|z+3|$ I tried:  $$|z-2i| = 2|z+3| \Leftrightarrow \\ |x+yi-2i|=2|x+yi+2|\Leftrightarrow \\ \sqrt{x^2+(y-2)^2}=\sqrt{4((x+2)^2+y^2)} \Leftrightarrow \\ \sqrt{x^2+y^2-4y+4} = \sqrt{4x^2+24x+36+4y^2} \Leftrightarrow \\ x^2+y^2-4y+4 = 4x^2+24x+36+4y^2 \Leftrightarrow \\ y^2-4y-4y^2=4x^2+24x+36+x^2 \Leftrightarrow \\ -3y^2-4y=5x^2+24x+26 \Leftrightarrow \\ ???$$  What do I do next? On googling I got     Random numbers are numbers that occur in a sequence such that two conditions are met: (1) the values are uniformly distributed over a defined interval or set, and (2) it is impossible to predict future values based on past or present ones. Random numbers are important in statistical analysis and probability theory.   What if I want to pick a random integer from the number line ? The number line consists of infinitely many integers. My favorable event is to get a number (random) and the number of events possible is the complete number line i.e. infinity. I won't be considering any limits here as our number line doesn't tend to infinity but does contain infinitely many elements.  Now the probability of getting a random number  P(E) = 1 / ∞ = 0   So I won't be able to get a random number, ever. This implies, never would I ever be able to get a random number.  That's absurd as many of our science topics do depends on things being random. Real valued analytic function defined on a connected set is constant Calculating $\lim_{x\to0} \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$ Find $$\lim_{x\to0}  \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$$ where $\lfloor\cdot\rfloor$ is greatest integer function   I am a high school teacher. One of my students came up to ask this limit.  For $\lfloor\frac{\sin x}{x}\rfloor$, I have used $\sin x &gt; x$ using increasing decreasing functions.  I tried to prove $x^2 &gt; \sin x \tan x$ using increasing /decreasing  function but I am not getting it.