Introductory textbooks in mathematics Some time ago I started self studying physics and I did quite well, despite my limited knowledge of maths (some basic algebra and geometry). Now I would like to understand calculus, but I don't know what books I should use. Clearly, first I need to revisit the basic and intermediate notions of algebra.  For this task I tried using this book:     but I found it to be somehow simplistic (problems are too easy, the theorems are not demonstrated, etc.)  What textbooks do you think are appropriate for someone with very basic knowledge of elementary algebra who wishes to self study calculus for use in physics?
Introductory Calculus textbook for physics? I have the summer to prepare myself for a high school calculus-based physics course; however, I will have to study calculus by myself. I've completed a course in precalculus and I'm beginning to read .   I am looking for a textbook that has mathematical rigor (i.e. not memorizing formulas), yet also provides adequate foundations for a physics course. From similar stack exchange questions, my top candidates are  and . Which one of these textbooks, if any, would be the best choice for my situation?
How close would you have to be to the merger of two black holes, for the effects of gravitational waves to be detected without instruments? Assume two black holes in the most common size range, spiraling into each other until they merge. The event releases significant amounts of energy via gravitational waves, which warp the space-time.  If the distortion is powerful enough, it would get noticed in daily life, or perhaps even detected by the proprioceptors in the human body.  How close, as an order of magnitude estimate, would you have to be to the merger to perceive it like that, without any instrument? Split comma-separated strings in a column into separate rows Prove the map has a fixed point bash variables in for loop range I want to print list of numbers from 1 to 100 and I use a for loop like the following:  number=100 for num in {1..$number} do   echo $num done   When I execute the command it only prints {1..100} and not the list of number from 1 to 100. An easy question on complex Let $\{u_{k}\}_{k=1}^{\infty}$ be a complex number sequence. If $\sum_{k=1}^{\infty}\lambda^{k}u_{k}=0$, for each $\lambda\in \mathbb{D}(0, 1/3)$(where the $\mathbb{D}(0, 1/3)~$denotes an open disc centered at $0$ and radius $1/3$). Then can we conclude $u_{n}=0$, for $n=1, 2, 3...$ ? We know (from the accidents that happened between 1999-2005) that      The Sith rely on their passion for their strength. They think inward, only about themselves.   and we also know that     Always two there are, no more, no less. A master and an apprentice.   And from the EU, we know that each Sith apprentice will (try to) kill and replace their master at some point, in order to become the one who bundles the entirety of the Sith power (so to say).    Q1: Given these points, why do Sith bother to take up apprentices at all? It doesn't make sense to pass on their knowledge of the dark side, because they only care about themselves, and it would also contradict this philosophy to teach competition that will endanger their power and ultimately their life.    Q2: As a special case of this question in The Empire Strikes Back, Vader tries to turn Luke by saying     Luke, you can destroy the Emperor. He has foreseen this. It is your destiny. Join me, and together we can rule the galaxy as father and son.   (emphasis by me)  Now, the same question rises: If the Emperor has foreseen that Luke can destroy him, why would he want Luke to become a Sith? I live in Hong Kong, and the Play Store displays everything in the local Cantonese language. I have set everything I can (Android language, Account language, even the app locale via Xposed Module "App Settings") to English, but I still see all the categories in the store in Chinese. Can someone help me change those to English?  (Click image to enlarge) What is the meaning of $\exp(\,\cdot\,)$? What is the meaning of the notation $\exp(\text{expression})$ ?  I think that it's something of the form $a^\text{expression}$ but does it mean that the base $a=e$ or can it be any base? Non-numerical citation mark like [Str91] [Samar] [Tro77] I need to display math in my report, but is it possible to remove the vertical space around align*?  A little example is the following (where I just want the align* to have the same vertical space as a \\  \documentclass[10pt,danish,a4paper,oneside,fleqn]{report}  \usepackage[english]{babel} \usepackage{amsmath}  \begin{document}  ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss \begin{align*}   A{\cap}B\ &amp; =\ {\left\{{b,d,e}\right\}}{\;}{\cap}{\;}{\left\{{a,b,f,g}\right\}}   \\   \nonumber\ &amp; =\ {\left\{{b}\right\}} \end{align*} ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss \\ ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss  \end{document} I can get the element like this $("#txtEmail") but I'm not sure how to get the actual value. We all know that Superman changes in the phone booth. But where does he put his regular clothes while he's on a mission? He doesn't throw it out, because he changes back. But we don't see him carrying a bag of dirty laundry while he's on a mission.  ("In his right hand, Superman has Lois Lane, and in his left hand he seems to be holding... boxers??)  And I can't imagine he leaves it in the phone booth.  So where does Superman leave his regular clothes after he changes? How can I check if an application is running from a batch (well cmd) file?  I need to not launch another instance if a program is already running. (I can't change the app to make it single instance only.)  Also the application could be running as any user. Is there an easy way to put a box around a theorem in LaTeX? For example to state an important theorem. I tried using page 20 of the ntheorem , but I do not know how to use the package. I was supposed to find all possible Jordan canonical forms of a $5\times 5$ complex matrix with minimal polynomial $(x-2)^2(x-1)$ on a qualifying exam last semester.  I took the polynomial to mean that there were at least two 2's and one 1 on the main diagonal, and that the largest Jordan block with eigenvalue 2 is $2\times 2$ while the largest Jordan block with eigenvalue 1 is $1\times 1$.  Did I miss any matrices or interrupt the minimal polynomial incorrectly?  \begin{pmatrix}   2 &amp;1  &amp;0  &amp;0  &amp;0\\   0 &amp;2  &amp;0  &amp;0  &amp;0\\   0 &amp;0  &amp;2  &amp;1  &amp;0\\   0 &amp;0  &amp;0  &amp;2  &amp;0\\   0 &amp;0  &amp;0  &amp;0  &amp;1 \end{pmatrix}  \begin{pmatrix}   2 &amp;1  &amp;0  &amp;0  &amp;0\\   0 &amp;2  &amp;0  &amp;0  &amp;0\\   0 &amp;0  &amp;2  &amp;0  &amp;0\\   0 &amp;0  &amp;0  &amp;2  &amp;0\\   0 &amp;0  &amp;0  &amp;0  &amp;1 \end{pmatrix}  \begin{pmatrix}   2 &amp;1  &amp;0  &amp;0  &amp;0\\   0 &amp;2  &amp;0  &amp;0  &amp;0\\   0 &amp;0  &amp;2  &amp;0  &amp;0\\   0 &amp;0  &amp;0  &amp;1  &amp;0\\   0 &amp;0  &amp;0  &amp;0  &amp;1 \end{pmatrix}  \begin{pmatrix}   2 &amp;1  &amp;0  &amp;0  &amp;0\\   0 &amp;2  &amp;0  &amp;0  &amp;0\\   0 &amp;0  &amp;1  &amp;0  &amp;0\\   0 &amp;0  &amp;0  &amp;1  &amp;0\\   0 &amp;0  &amp;0  &amp;0  &amp;1 \end{pmatrix}  \begin{pmatrix}   2 &amp;0  &amp;0  &amp;0  &amp;0\\   0 &amp;2  &amp;0  &amp;0  &amp;0\\   0 &amp;0  &amp;1  &amp;0  &amp;0\\   0 &amp;0  &amp;0  &amp;1  &amp;0\\   0 &amp;0  &amp;0  &amp;0  &amp;1 \end{pmatrix} How to prevent "Delhi Belly"? A field that is conservative must have a curl of zero everywhere. However, I was wondering whether the opposite holds for functions continuous everywhere: if the curl is zero, is the field conservative? Can someone please give me an intuitive explanation and insight into this, and if it is true, why? Also, please try to not be too rigorous (only in grade 9). Why is MixColumns omitted from the last round of AES? How to configure splash screen after plymouth I have configured my splash screen for plymouth - and it works perfectly. I've also configured the display manager (I'm using gdm). In between these two I get a very brief splash screen - a kind of swirl of multi-coloured ubuntu like colours. Where does this splash screen get set, and how do I change it?  Edit: Here is a video of my boot sequence, showing the screen in question: When you lift a box from the floor, the potential energy changes but kinetic energy does not change. Does it violate conservation of energy? Please try and answer this question.