Recommend a Maths Textbook for Calculus
What are the recommended textbooks for introductory calculus?
i have read most of the related postings and answers allready ... (e.g.  and  ... among others)  but (!) unfortunately none of them solved my problem. as someone postet on 2012-01-04 12:27 definition of properly defined *.csvt doesn't effect field-import - they are expected to be numbers and still are string.  her is a sample of my csv  InputID,Mean,Stdev,min,max 1,334.7617168,36.87450474,294.4334857,383.5583136 2,446.3946568,207.949905,153.2494524,613.3182137 and the csvt "Integer","Real","Real","Real","Real"  .. i have already:    checked field names (no blanks), checked separators, ... which are qgis' default because the csv is distance matrix calculation result defined the csvt with simle "Integer","Real" and the precision-type-style "Integer(6)","Real(8.3)" changed country settings in win7, win8, osx 10.9 due to known decimal separator issues   used csv as specified as well as "excel-style" csv (";"-separated)    checked all that in qgis 2.0, 2.2, 2.3(master)   and: at the beginning this problem was related to distance matrix output  ... where qgis calculates the results (and writes the csv-outputs), which of course are numbers (mean, stdev, min, max)  so, initially i was just looking for a straight forward way to use qgis' own calculation results for mapping of distance-distribution ...  is there a way to solve or completely bypass the csv-t issue in a way, i can easily communicate to gis-beginners ? Calling Table with custom iterator Is $(B_t^2)$ Markov where $(B_t)$ is Brownian motion? I am pretty sure $(B_{t}^{2})$ not Markov because the squared random walk is not.    I guess I can repeat the method since to be Markov it must satisfy the discrete.  Thanks Can a probability distribution value exceeding 1 be OK? What spell slot count formula can I use to base my homebrew mechanic on? I'm trying to match SHA1's in generic text with a regular expression.  Ideally I want to avoid matching words.   It's safe to say that full SHA1's have a distinctive pattern (they're long and a consistent length) - so I can match these reliably - but what about abbreviated SHA1's?  Can I rely on the presence of numbers?  Looking at the SHA1's in my commit log - numbers always appear in the first 3 characters. But is this too short? How many characters of SHA1 do I need to consider before I can assume a number would have appeared?    This does not have to be 100% accurate - I just need to match an abbreviated SHA1 99% of the time. This may be a simple question, but how do I use files starting with "-" with command line programs?   For example,  I am trying to use pdfgrep on a file named -2013-01-01.pdf but it complains that there are no options defined for 2, 0, 1, 3 and so on.  Changing the filename to something that does not start with "-" solves it, but this is not an option since the files aren't created by me. I simply want to check for a specific change I know is coming. So I have a program written in C++.  It can tell me how long it took to do all the calculations and it does a lot of quite heavy, multi-threaded calculation.   I've just noticed that if I run the program on the exact same machine, it takes around 20-21 seconds to do all the calculations if started from the TTY, and only about 0.2 seconds if I start it from GNOME terminal.  What is causing that? It's literally the exact same file on the same machine. Conditional Expectation of Composite Function Preliminaries  Let $(\Omega, \mathcal{G}, \mathbb{P})$ be a complete probability space.  Let $D$ be a complete, separable, metrizable topological space with Borel $\sigma$-algebra $\mathcal{B}(D)$ (such as $D = \mathbb{R}^q$ with $\sigma$-algebra $\mathcal{B}(D) = \mathcal{B}(\mathbb{R}^d)$).  Let $\mathbb{R}$ be equipped with its canonical Borel $\sigma$-algebra $\mathcal{B}(\mathbb{R})$.  Let $g: \Omega \times D \rightarrow \mathbb{R}$ be a bounded $(\mathcal{G} \otimes \mathcal{B}(D) ) / \mathcal{B}(\mathbb{R})$-measurable function.  Let $\Pi: \Omega \rightarrow D$ be a $\mathcal{G}/\mathcal{B}(D)$-measurable random variable.  Let $H : \Omega \rightarrow \mathbb{R}$ be a $\mathcal{G}/\mathcal{B}(\mathbb{R})$-measurable random variable, defined by $$ H(\omega) := g(\omega, \Pi(\omega)).$$ Note, that, since $g$ is bounded, we have $H \in \mathcal{L}^2(\Omega, \mathcal{G}, \mathbb{P})$.  Let $j: D \rightarrow \mathcal{L}^2(\Omega, \mathcal{G}, \mathbb{P}) $ be defined by $$ j(\pi)(\omega) := g(\omega, \pi)  $$  For all $\pi \in D$, let $j(\pi)$ be independent of $\Pi$.  Question  I am interested in the conditional expectation $$\mathbb{E}[H \mid \Pi] :\Omega \rightarrow \mathbb{R}$$ of $H$ with respect to $\Pi$. More specifically, I suspect that (a $\mathbb{P}$-unique version of) this condititional expectation is given by  $$ \mathbb{E}[H \mid \Pi] (\omega) = \mathbb{E}[j(\Pi(\omega))], \quad (\dagger)  $$ whereby $\mathbb{E}[j(\Pi(\omega))]$ can of course also be written as $$\mathbb{E}[j(\Pi(\omega))] = \int_{\Omega} j(\Pi(\omega))(\tilde{\omega}) d\mathbb{P}(\tilde{\omega}) . $$  How can I prove, that $(\dagger)$ is the case? I have tried, tracking the definition of conditional expectation and using Fubini, but with little success so far.  Thanks for any advice! Some icons are correct, and some are whack. Turns out it's not just the hot questions list, but the whole icon set. Determining if an arbitrary point lies inside a triangle defined by three points? Is there an algorithm available to determine if a point P lies inside a triangle ABC defined as three points A, B, and C? (The three line segments of the triangle can be determined as well as the centroid if they are needed.)  Grid space is defined as Screen Space, that is, 2D Cartesian with the Y-Axis flipped so "up" is negative y and the origin is the upper left corner. I am running Windows 8.1 N Pro x64 and there are 2 Internet Explorer processes that must be for 32 bit. It stays there even if Internet Explorer is closed. I tried ending the processes but they just come back. I run a x64 Internet Explorer. How can I stop those processes? Determine Which of the following Sets is a Vector Space Determine which of the following sets is a vector space.  $V$ is the line $y=x$, in the $xy$-plane: $V =\{[x,y]: \; y=x\}$  $W$ is the union of the first and second quadrants in the $xy$-plane: $W=\{[x,y]: \; y\geq0\}$  $U$ is the line $y = x+1$ in the $xy$-plane: $U=\{[x,y]: \; y=x+1\}$    I know that the answer is that "$V$" is the only vector space. However how do I come up with a quick proof to show that $V $is a vector space and that the other $2$ aren't? Why are certain example URLs like https://site.com/ and https://mysite.com/ blocked from post content? Why is  and  blocked from the post content on the main site? I tried to make a sample URL and I had to use  instead. Why is the Sun approximated as a black body at ~ 5800 K? Random spawn location despite sleeping in a bed I am trying to make Minecraft harder, and one of the ways I wish to do this is to have a "pseudo-hardcore" mode where dying spawns you in a random location rather than completely locking you out of the world.  I intend to do this by setting the spawn radius to be very high.  However, I also want to make this "bed-proof" - that is, if someone places a bed and sleeps in it, I want the player to still be spawned in a random location, regardless of their personal spawn point.  How do I do this? Command blocks are fine, but data packs are not preferred. What's the difference between STDIN and arguments passed to command? I am looking for easy(!) counterexamples that the product of two quotient maps is not necessarily a quotient map and that the quotient space of a Hausdorff space is not necessarily Hausdorff. How to prove this inequality $ x + \frac{1}{x} \geq 2 $ Ignore .DS_Store and Icon files in a folder with Cocoa NSFIleManager