## 105 Reputation

18 years, 35 days

## A different workaround...

Thank you. Your suggestion gave me an idea. It is a little simpler than yours. Try it. You might like it. Change the code by replacing a semicolon by a colon and add one line. > assume(a, real): > interface(showassumed=0): > equa:=a^2+a-1: > subs(a=’a’,’equa’=%); In fact, with this change, I see no reason for the second line in the syntax.

## Too Simple...

There must be some reason why the simple even part even(x):=(f(x)+f(-x))/2; and the simple odd part odd(x):=(f(x)-f(-x))/2; was not used.

## Too Simple...

There must be some reason why the simple even part even(x):=(f(x)+f(-x))/2; and the simple odd part odd(x):=(f(x)-f(-x))/2; was not used.

## Great! Works well....

Thanks a lot. That really works well. It raised a question, however. How can I remove the boundary surrounding the table? The document would look better without that boundary.

## Great! Works well....

Thanks a lot. That really works well. It raised a question, however. How can I remove the boundary surrounding the table? The document would look better without that boundary.

## That led to a better idea...

Thanks, Joe Riel. I understand better what is happening. This led me to think of with(RealDomain), but this did not do the trick. Somehow, I don't remember now how I came to it, I found that the following is just what I want. > restart: > with(LinearAlgebra): > A:=Matrix([[a,b],[b,c]]); > BilinearForm(Vector([x,y]),Vector([u,v]),A,conjugate=false): > expand(%); Your suggest let to this better idea. It is better in ways to complicated to explain here. However, see five lines from the bottom of page 302 in the Maple Conference 2005 Proceedings.

## Another choice...

The following is an alternate: plot([5,y,y=0..10]);

## a different perspective...

About calculus texts, let me present another perspective. This perspective is one from at least two faculty members at Georgia Tech. It was a common observation at Georgia Tech that most students began their undergraduate education having had a year of calculus in high school. A moment’s consideration would lead most educators to say this is no surprise. After all, Georgia Tech historically has the reputation as being a good engineering school, and it is. Because entering students think they already know the calculus, they often fail to note that the college course expects a deeper understanding of the concepts. Or, the students are bored because their high school calculus was such a good course. Whatever the reason, freshmen calculus students who took the first term calculus class did not realize that they needed to go a little deeper than what they learned in their high school course. Cain and I wanted to make the materials fresh and exciting. Our decision was to present the notions of calculus in a multidimensional setting at the outset, making the one dimensional setting an important and often examined example. You might be interested in seeing the electronic text that both Cain and I used before we retired. If so, see Item 1 at http://www.math.gatech.edu/~herod/ Jim Herod

## equality or an approximation...

Hello, Robert. Thanks for stepping into this discussion. I think that, especially for young engineering students, it is important to distinguish equality ("the same as") and approximation. In the second example, one must be aware that the zeros for the Bessel functions which I listed in that worksheet are approximations of those zeros and that, as a consequence, the "solution" is going to be an approximation for the solution. By doing the 3.14 thing, I intended to emphasize that. All kind of good discussions arise from this second example. For example, it leads to discussions about where the maximum value of the solution for such a PDE can occur, and about how to measure how far an approximation misses the real solution ... especially in case the real solution is not computable for some reason. These are important ideas for engineering students. It's a whole hour lecture. Right? During my afternoon walk, I made examples in my head of bad approximations for which different norms hide how bad they were. Essentially, I ended the walk saying, again, "A graph is worth a thousand equations." You will note that I posted this in the Math Education Section of Maple Primes. Jim

## Thanks for posting the pictures...

Will, Thanks for posting these. It is good that I can show my grandchildren what I do and what I enjoy! Jim Herod
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