I'd like a resource---preferably a book---to learn wave mechanics at the undergraduate level without a particular application in mind. I don't have a PDEs background and my ODE knowledge is rusty.
I'm taking a course on waves and oscillations using Crawford from the Berkeley series (out of print excluding international copies), and would like to know if anyone has any suggestions for a better book. We cover:    coupled oscillators, forced oscillators,  Fourier analysis,  traveling waves,    and some other topics. Any help with the topic would be appreciated.
Which expressions can be used to close an email? At the end of written communication like emails and letters, it is customary to use a closing . Which formal and informal expressions can be used to end emails? "Reality" of length contraction in SR I was in argument with someone who claims that length contraction is not &quot;real&quot; but only &quot;apparent&quot;, that the measurement of a solid rod in its rest reference frame is the &quot;real length&quot; of the rod and all other measurements are somehow just &quot;artificial&quot; and &quot;apparent&quot;. Seemed to me like a bad conversation about poorly defined words and not really relevant to physics, but then some quotes were offered:  ...so that the back appears closer to the front. But of course nothing has happened to the rod itself.  (Rindler)  The effects are apparent (that is, caused by the motion) in the same sense that proper quantities have not changed.  (Resnick &amp; Halliday) At the same time, the  insists that length contraction and time dilation are &quot;real&quot;, with observable consequences:  Time and space dilation are often referred to as ‘perspective effects’ in discussions of STR. Objects and processes are said to ‘look’ shorter or longer when viewed in one inertial frame rather than in another. It is common to regard this effect as a purely ‘conventional’ feature, which merely reflects a conventional choice of reference frame. But this is rather misleading, because time and space dilation are very real physical effects, and they lead to completely different types of physical predictions than classical physics. [...] However, this does not mean that time and space dilation are not real effects. They are displayed in other situations where there is no ambiguity. One example is the twins' paradox, where proper time slows down in an absolute way for a moving twin. And there are equally real physical effects resulting from space dilation. It is just that these effects cannot be used to determine an absolute frame of rest.  I went through a lot of Einstein, Minkowski and Lorentz original material, and didn't find anything about what is &quot;real&quot; and what is not. Finally, I know about muons, where the effects of SR seem to be very real (from , but I had seen it in a physics class before):  When a cosmic ray proton impacts atomic nuclei in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (their preferred decay product), and muon neutrinos. The muons from these high energy cosmic rays generally continue in about the same direction as the original proton, at a velocity near the speed of light. Although their lifetime without relativistic effects would allow a half-survival distance of only about 456 m (2,197 µs×ln(2) × 0,9997×c) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half life due to their velocity. From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame. Both effects are equally valid ways of explaining the fast muon's unusual survival over distances.  So which is which? Why do Rindler, Resnick &amp; Halliday use the word &quot;apparent&quot;? Why do we yawn? I've read a new study which suggests that yawning may help you keep a cool head. Also, the findings might hold some hope for sufferers of insomnia, migraines, and even epilepsy.  Is there any conclusion about what the function of yawning is and why do we yawn? I'm missing all the usual processing tools in the Vector menu in QGIS 2.16 (eg vector overlay, analysis, etc). They do appear in the processing toolbox but there's no sign of them in the Vector menu. Has anyone come across this issue? How can I move my /home directory to another partition if it's already part of the / partition? How do I make an HTML text box show a hint when empty? Deriving Sum of a Geometric Progression I am looking for information on Heinrich Märte (my grandfather) and his family. He was born on July 1, 1912 in Sipplingen and died On April 19, 1944 when the military plane crashed in Geierswalde because its engine failed.  I am not sure if his family knows that he fathered my dad. I am hoping someone knows of him or his family. I would love to know how he met my grandmother or any further information on him.   We have always had two photo's of him, but never knew his name. We have only just found out about him and it has opened so many more questions.  How can I determine Heinrich's parents and siblings, and then locate any living family members? Email from IOS with attachments larger than 7.5Mb gets stuck in outbox and constantly tries to resend. Costs us hundreds in data fees Can we modify "Ask question" to automatically suggests tags based on your question content.   So instead that user needs to type "team-foundation-server" or "TFS" or "TeamFoundationServer" he will see list of tags auto-populated with ajax which he (or she) can then select and it will be associated with the question. So basically only thing we need is code which will cross-match question content with list of known tags while user is typing and display results in some nice ajax-enabled list/cloud/whatever UI control. This should be separate control for tags suggestions so user still has option to use standard tag list input to type-in tags.  In this case, instead of three (or more) tag variations we would have only one tag for Team-Foundation-Server. If I have an adjacency matrix for a graph, can I do a series of matrix operations on the adjacency matrix to find the connected components of the graph? Adding more than 15 digits in Excel I want to add more than 20 digits in an Excel cell.  The current format of the cell is general, it converts the number to an exponential format. I tried with a number format and accounting, but when I enter more than 15 digits it gets converted to 0's.  What are the recommended steps for stopping Excel from converting data to exponential Format for 20 digits when in the general format?     Example: 12345678901234567890   Excel converts it to 1.23457E+19 in general format.  Without using ' before the value, is there any other way to keep value same? Which variables should I transform, center, and/or standardize in my data for Principal Component Analysis? I have multiple datasets that I am attempting to use principal component analysis (PCA) on in order to infer the underlying structure of the data.  I'm attempting to predict growth increment of conifers (the response which apparently needed to be cube root transformed for my original linear models).  My predictor variables include: continuous (some log-transformed like size-related variables, some compositional, and some traditionally scaled); binary; ordinal; and nominal (of which I'm pretty sure I can order with respect to site productivity).  I'm mostly attempting to make inferences because some of my previous models from linear regression have not produced significant terms corresponding to categories like health or climate and I feel that they should have.  I've read in Joliffe (2002) that I might want to leave my compositional data uncentered.  Forgive my naiveté, but I'm wondering if I should also do this for my binary data.  It also seems that I might not want to scale these since they're already on a 0 - 1 scale but I'm not sure.  After only using my continuous predictors (including compositional variables), it appears that a size principal component makes up the largest portion of the variability and Joliffe also mentions that one might want to attempt a "double-centering" of the log-transformed data if this is the case.  I don't know if this is even possible since the log-transformed data only makes up a small portion of my datasets.  Finally, I should ask if having such a combination of data types will complicate analysis so much that it will make inferences unreliable.  I am currently using R for this analysis.  Thank you. How do you get the footer to stay at the bottom of a Web page? How do I make protocol foo hostname-aware? This is a  about hostname-awareness and proxying.   I know that some protocols are hostname-aware; that is, when I connect to the HTTP server at www.example.com it knows I want www.example.com's HTTP service, not www.example.net's, even though they are on the same IP address.  How can I do this for protocol foo?  (Temporary note: this question appears pursuant to .) AWK: Nested Conditional Subset of Rows I have a pretty specific question, and have been able to find lots on conditional subsetting using awk but none that lends enough explicit code for me to generalize to my situation. I have a file 'keys' and a file 'features'. The 'keys' table contains two variables, KEY and GROUP, toy example below.      KEY        GROUP     ---        -----     1          GROUP0     2          GROUP0     3          GROUP1     4          GROUP1     5          GROUP2     6          GROUP2     The file 'features' contains a list of features of widgets like so      ID          FEATURE      VALUE     --          -------      -----     A           num_user     10     A           KEY          4     B           num_user     2     B           KEY          2     B           battery      Large     C           num_user     10     C           KEY          15     D           num_user     2     D           KEY          2     D           battery      Small     E           num_user     2     E           KEY          7     E           battery      Small   I am trying to select all rows for an ID which has a value of 'KEY' that is in the 'KEY' column of 'keys' for a hardcoded list of 'GROUP' values. The desired result is      ID          FEATURE      VALUE     --          -------      -----     A           num_user     10     A           KEY          4     B           num_user     2     B           KEY          2     B           battery      Large     D           num_user     2     D           KEY          2     D           battery      Small   Any ideas? The category Set has the property that any morphism f can be decomposed into an epimorphism $e$ and a monomorphism $m$ with $f$ = $m\circ e$. (The intermediary set object is the image of $f$.)  Is there a name for this construction?  Is there a name for this property of categories?  In Set, the intermediary object is unique up to isomorphism. Is this the case for all categories with the property? The situation is somewhat like-  var someVar = some_other_function(); someObj.addEventListener("click", function(){     some_function(someVar); }, false);   The problem is that the value of someVar is not visible inside the listener function of the addEventListener, where it is probably being treated as a new variable. (In, On or At) GitHub? What's the difference between say:     "The project will be on GitHub",      "The project will be in GitHub" and      "The project will be at GitHub"? Number of normals from a point to an ellipse From a typical point $P$ inside an ellipse, how many points $Q_i$ on the ellipse have $PQ_i$ normal to the ellipse?  Someone asked me at school many years ago but I don't think I worked it out.