@Madhukesh J K Okay, in that case the Nu vs M plot (for several phi) that you want is the middle plot of the three in Tom's most-recent Reply. This plot could be improved (made smoother) by using a greater number of values of M (Tom only used 3). Other than that, it seems to match the plot that you got with other software.

@nm Yes, I understand all that. The issue is primarily linguistic: You (even still!) continue to incorrectly refer to generalized eigenvectors as eigenvectors, as if the generalized eigenvectors were some special type of eigenvector. It's actually the other way around: Eigenvectors are a special type of generalized eigenvector. So, when you mean "generalized eigenvector", you must always include the word "generalized". The phrase cannot ever be shortened to simply "eigenvector", even if it's in the very next sentence. Doing so will cause confusion. The textbook passage that you quoted does not make this mistake. Read it again carefully. I am not saying that you are misinterpreting the mathematical information in the passage; on the contrary, it appears that you understand well the mathematical distinction between eigenvectors and generalized eigenvectors. I mean that you should reread it to see that they never refer to a generalized eigenvector as simply an eigenvector.

Unfortunately, there is nothing in the language itself that can help you avoid making this type of conceptual error. You just need to know the mathematical definitions involved. In the vast majority of cases, the phrase A B (where A is an adjective and B is a noun) does specify a special type of ​​​​​​B. For example, a black cat is a special type of cat, and if a specific black cat is meant, it can be referred to as simply "the cat" in subsequent sentences without any chance of confusion. I think that exceptions to this rule are more common in mathematics than in other fields. When those exceptions occur, it's often the case that the B is a special type of A B. I suppose that the reason that this arises is that B was defined first and the usage long established before someone decided that their was a need for a super-category of B. That seems to me like a likely explanation for the case of eigenvector and generalized eigenvector. 

@Madhukesh J K The formula that you've given so far requires the Reynolds number (Re) to compute the Nusselt number (Nu). But you have not provided the Reynolds number!! It appears nowhere in your formulation of the problem!! We've been trying to tell you this repeatedly.

@itsme I agree totally with you, and I was about to write something that said essentially the same thing.

@Anthrazit What other software are you familiar with that correctly does what you're asking for? It's not a standard feature of end-user software.

@acer My guess is that the CSV file contains instances of two consecutive commas with no intervening characters other than possibly white space.

@VaughanR Back ticks that enclose no characters denote a symbol, the empty symbol. It's not quite the same thing as NULL, but it works well in matrices because no characters are shown in its display. You could also do subs(0= NULL, A) or subs(0= (), A). These give true NULL values, but are ugly in matrices because they prettyprint as NULL.

The problem with any of these approaches: What if you have a datum that's legitimately 0?

@itsme Your points about Code Edit Regions (CERs) are well made. I never use them for codes less than 50 lines, so my experience has been different than yours. Yes, if I made every execution group in a typical worksheet into a CER, I would find them very difficult to work with.

You are slightly misusing the terms surface, level surface, and solid. An equation (not an algebraic expression) in 3 variables such as x^2 + y^2 + z^2 =1 defines a surface: an essentially 2-dimensional object that lives in 3-dimensional space, such as a sphere. A solid is an essentially 3-dimensional object, such as a ball: a sphere and the volume it encloses. An example of a relation defining a solid is the inequality x^2 + y^2 + z^2 <= 1. An expression (or function) of three variables such as f(x,y,z) = x^2 + y^2 + z^2 has level surfaces, which are the surfaces defined by f(x,y,z) = L for specific levels L.

@a_simsim It is possible to generate the numeric data without plotting, but why do you ask? I find Tom's method quite convenient, and the marginal effort required to produce the plots is insignificant. 

@Madhukesh J K There are two basic types of 3D plots, and they can be distinguished by the number of dimensions of independent variables (real values that you directly vary) and dependent variables (real values that are computed using the independent variables). So far, you have not given us a complete set with which to construct either type of plot. The two types are a space curve (1 independent variable, 3 dependent variables) and a surface (2 independent variables, 1 dependent variable).

Your Reply immediately above implies that you want 1 independent variable (phi2) and 2 dependent variables (skin friction and Nusselt). That's not one of the types of 3D plot that I discussed, although it's enough to make a 2D plot, a plane curve.

These are mathematical limitations, not limitations of Maple.

@Mac Dude I have the same problem. It has been there for years. I do not use a .bat file.

Currently, my := is lowercase d and my -> is numeral 1. One the problem infects one worksheet, it infects all open ones. The only solution I've found is to shut down and restart Maple entirely.

@Bohdan Like this:

MyA(1, 1, 2, 2, 2, 2, 2, gamma, beta, pi, alpha, epsilon):
diff(%, pi[1,2,1,2]);
 

@tomleslie The Question shows chi(eta) and its derivatives in eq4.

@9009134 You wrote:

• I think I need to plot the 2D gradient of V in-plane xz and xy, according to the relation between x,y,z, and tau and sigma.

I think that you need to plot in an alternate coordinate system. Maple knows many, or you can define your own.

@9009134 The problem was that you didn't remove the line V:= Gradient(V) like I said.