"The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill."

– Attributed to A. Einstein in [Dan Meyer: Math class needs a makeover]

"People who wish to analyze nature without using mathematics must settle for a reduced understanding."

– Richard Feynman [Google search].

Plagiarism: Don't copy verbatim, rewrite in your own words, give references

As I prepared my lecture on first-order PDEs, I found the following passage in Lapidus & Pinder 1982, p.6, rather obscure to explain to students, and reread it several times:

Obviously, both equations must hold on the solution surface and yet one can interpret each equation as a plane element; these plane elements intersect on a line along which different values of $\displaystyle u_x$ and $\displaystyle u_y$ may exists. In other words, $\displaystyle u_x$ and $\displaystyle u_y$ are indeterminate along this line, but at the same time they are related or determinate to each other since the equations must hold.
To exploit this feature, we use a well-known principle of linear algebra. If a square coefficient matrix for a set of $\displaystyle n$ linear simultaneous equations has a vanishing determinant, a necessary condition for finite solutions to exist is that when the right-hand side is substituted for any column of the coefficient matrix, the resulting determinants must also vanish.

Then one day, I looked at Selvadurai 2000, p.90, I saw a passage, equally obscure, that I recalled seeing somewhere before:

Both equations must hold on the solution surface and one can interpret each equation as a plane element, where they intersect along a line along which different values of $\displaystyle \partial u / \partial x$ and $\displaystyle \partial u / \partial y$ may exists; i.e., $\displaystyle \partial u / \partial x$ and $\displaystyle \partial u / \partial y$ are indeterminate along the intersection line, but they are related to or determinate to each other since (3.8) must hold.
Using a principle of linear algebra, if a square coefficient matrix for a set of $\displaystyle n$ simultaneous equations has a vanishing determinant, a necessary condition for finite solutions to exist is that when the right hand side is substituted for any column, the determinants of the resulting coefficients matrices must also vanish.

Since the above passage in Selvadurai 2000, p.90, was so similar to that in Lapidus & Pinder 1982, p.6, the way I quickly reproduced it was to simply copy the passage in Lapidus & Pinder 1982, p.6, that I already retyped further above, and then just changed a few words, thus showing how close the two passages were.

Note that Selvadurai 2000 obscurely and remotely referred to Lapidus & Pinder 1982 on p.571, in a list of references related to first-order PDEs. It is unlikely for any reader to see the above close similarity between the two passages in Selvadurai 2000 and Lapidus & Pinder 1982 without reading carefully both books.

A more appropriate way is to put the reference where the material is used, and avoid repeating verbatim the words of the original authors. It is best to rewrite the material in your own words. A model for writing and referencing is the wiki article Configuration integral (statistical mechanics).

In my lecture, I present the above matter from a completely different angle, which, it is hoped, is clearer to students.

Egm6322.s09 12:56, 26 January 2009 (UTC)

Collaboration, not plagiarism: When you copy certain any existing wiki article so to extend (e.g., adding more material) and to improve upon it (e.g., rewriting it), you play the role of a co-author, not the author, of the existing work; always cite the original work with appropriate links.

Egm6321.f09 18:27, 8 September 2009 (UTC)