## 625 Reputation

17 years, 17 days

## e...

djc is correct. Do not assume the letter "e" is 2.718... I tell my students that mathematicians cannot hog the letter "e". Physicists might want to assign "e" the charge of one of those little things called "electrons". Or maybe some other person wants "e" to be the eccentricity of a conic section. If you want e to be 2.718... then you can enter > e:=exp(1); But I personally recommend you not do this. Instead, whenever you need to use e^u, enter > exp(u) Do not mis-interpret exp(u) as exp^u !!!

## e...

djc is correct. Do not assume the letter "e" is 2.718... I tell my students that mathematicians cannot hog the letter "e". Physicists might want to assign "e" the charge of one of those little things called "electrons". Or maybe some other person wants "e" to be the eccentricity of a conic section. If you want e to be 2.718... then you can enter > e:=exp(1); But I personally recommend you not do this. Instead, whenever you need to use e^u, enter > exp(u) Do not mis-interpret exp(u) as exp^u !!!

Indeed there is no agreement on ordering and roles of theta and phi. The best thing to do is know your own self and avoid built-in conventions. For example, use parametric plotting instead of coords=spherical: r:=(u,v)->1; #or whatever function you want plot3d([r(u,v)*cos(u)*sin(v),r(u,v)*sin(u)*sin(v),r(u,v)*cos(v)],v=0..Pi,u=0..2*Pi); if my mood is v=colatitude and u=longitude.

Indeed there is no agreement on ordering and roles of theta and phi. The best thing to do is know your own self and avoid built-in conventions. For example, use parametric plotting instead of coords=spherical: r:=(u,v)->1; #or whatever function you want plot3d([r(u,v)*cos(u)*sin(v),r(u,v)*sin(u)*sin(v),r(u,v)*cos(v)],v=0..Pi,u=0..2*Pi); if my mood is v=colatitude and u=longitude.

## It is not a Mac problem...

The copy/paste problem is not a Mac problem. I have had this same problem with Windows XP.

## copy paste...

I frequently have this copy/paste problem when I use the Standard Interface. Standard Interface can be very frustrating. But in practice, I rarely have the copy/paste problem because I almost always use Classic Worksheet.

## Would it make a difference?...

I cannot think of a function that one could represent in Maple that would be Lebesgue integrable and not Riemann integrable. You can't represent something like the characteristic functions of the rationals in a CAS, and so it seems that there is no meaningful difference between the two types of integration at the coarse level of a CAS.

## Would it make a difference?...

I cannot think of a function that one could represent in Maple that would be Lebesgue integrable and not Riemann integrable. You can't represent something like the characteristic functions of the rationals in a CAS, and so it seems that there is no meaningful difference between the two types of integration at the coarse level of a CAS.

## startup mode...

I am no expert on how my system administrators have set up Maple 11, but it does launch Standard in worksheet with Maple Notation input. From a university computer I can see that the installation is on each computer-Single User Profile. I think we have a network where each lab has an "image" for the computers in that lab, and each day or so they reapply the image. I guess the image has the ini file with our preferred startup choices. It can be done. Maybe knowing that a solution exists will be enough to help you figure out the solution. I could bug our system administrator for details if you would find it helpful.

## startup mode...

I am no expert on how my system administrators have set up Maple 11, but it does launch Standard in worksheet with Maple Notation input. From a university computer I can see that the installation is on each computer-Single User Profile. I think we have a network where each lab has an "image" for the computers in that lab, and each day or so they reapply the image. I guess the image has the ini file with our preferred startup choices. It can be done. Maybe knowing that a solution exists will be enough to help you figure out the solution. I could bug our system administrator for details if you would find it helpful.

## sin x, sin*x, sinx, sin(x)...

A typical exchange I have with Calculus I students learning Maple begins with their attempt to enter sin(x). Often their first attempt is > sin x; which leads to a "missing operator" error. Their next approximation is usually > sin*x; This looks really good, but eventually they realize something is rotten, so they ask for help. A golden teaching moment! After discussion, their next approximation is often > sinx; It does not look right, and one can joke about four letter words that we expect Maple to know. And then, behold, students hit on > sin(x); This is a typical example of why I think introducing Maple in a Calculus I course has instructional value: grappling with the semantics of math expressions leads students to reflect on their understanding. The unfortunate 2D-math input, with its implied multiplications and other ambiguities, does not foster this learning cycle. I had to plead with my system admin to set the campus default to 2D-math input. Their first response was, "our policy is to use the vendor defaults." With some effort, I got them to reconsider. Thankfully they did.

## sin x, sin*x, sinx, sin(x)...

A typical exchange I have with Calculus I students learning Maple begins with their attempt to enter sin(x). Often their first attempt is > sin x; which leads to a "missing operator" error. Their next approximation is usually > sin*x; This looks really good, but eventually they realize something is rotten, so they ask for help. A golden teaching moment! After discussion, their next approximation is often > sinx; It does not look right, and one can joke about four letter words that we expect Maple to know. And then, behold, students hit on > sin(x); This is a typical example of why I think introducing Maple in a Calculus I course has instructional value: grappling with the semantics of math expressions leads students to reflect on their understanding. The unfortunate 2D-math input, with its implied multiplications and other ambiguities, does not foster this learning cycle. I had to plead with my system admin to set the campus default to 2D-math input. Their first response was, "our policy is to use the vendor defaults." With some effort, I got them to reconsider. Thankfully they did.

## "really" just one variable..or do dummy ...

Look at this example: F:=proc(x) Int(f(t),t=a..x) end; Diff(F(x),x); You end up with the "partial" derivative symbol, instead of the common one-variable dy/dx notation. No big deal, except when you are writing MapleTA questions for Calculus II students, who get even more overloaded when they see the partial derivative symbol. Years ago when I wrote Maple labs for Calculus II, I would include a comment that asked the student to relax, and just read \partial as a stylized "d". Then Maple decided to recognize the difference between functions of one or "several" variables when it typeset derivatives. This was ecstasy, only to find that the example above was not recognized as a function of one variable. Anybody have a simple way to force F:=proc(x) Int(f(t),t=a..x) end; Diff(F(x),x); to use d/dx instead of partial derivative notation?

## "really" just one variable..or do dummy ...

Look at this example: F:=proc(x) Int(f(t),t=a..x) end; Diff(F(x),x); You end up with the "partial" derivative symbol, instead of the common one-variable dy/dx notation. No big deal, except when you are writing MapleTA questions for Calculus II students, who get even more overloaded when they see the partial derivative symbol. Years ago when I wrote Maple labs for Calculus II, I would include a comment that asked the student to relax, and just read \partial as a stylized "d". Then Maple decided to recognize the difference between functions of one or "several" variables when it typeset derivatives. This was ecstasy, only to find that the example above was not recognized as a function of one variable. Anybody have a simple way to force F:=proc(x) Int(f(t),t=a..x) end; Diff(F(x),x); to use d/dx instead of partial derivative notation?

## restart...

Working in Maple8, I took your worksheet and put in "restart;" just before your line "Suggested Solution #1 - Did not work." and then the one-sided limits evaluated correctly. I did not need to insert the extra "restart" in Maple11 to get the limits to evaluate correctly.
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