rlopez

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12 years, 80 days

Dr. Robert J. Lopez, Emeritus Professor of Mathematics at the Rose-Hulman Institute of Technology in Terre Haute, Indiana, USA, is an award winning educator in mathematics and is the author of several books including Advanced Engineering Mathematics (Addison-Wesley 2001). For over two decades, Dr. Lopez has also been a visionary figure in the introduction of Maplesoft technology into undergraduate education. Dr. Lopez earned his Ph.D. in mathematics from Purdue University, his MS from the University of Missouri - Rolla, and his BA from Marist College. He has held academic appointments at Rose-Hulman (1985-2003), Memorial University of Newfoundland (1973-1985), and the University of Nebraska - Lincoln (1970-1973). His publication and research history includes manuscripts and papers in a variety of pure and applied mathematics topics. He has received numerous awards for outstanding scholarship and teaching.

MaplePrimes Activity


These are answers submitted by rlopez

If I understand correctly:

y:=x^3;

plot([y,diff(y,x,x),x=0..1])

 

mtaylor(P,[x,y],3) - mtaylor(P,[x,y],2)

The first call to mtaylor creates a polynomial whose terms are of degree 2 or less; the second, a polynomial of degree 1 or less. The difference should be a polynomial of exactly degree 2.

I'm sure there is a more elegant way to do this, but I think my approach works works.

plots:-shadebetween(2,x^2+y^3,x=0..1,y=-1..1,style=surface,color=khaki,changefill=[color=pink,transparency=.5]);

To see all three solutions in Maple, include the option "implicit" in the dsolve command.

with(geometry):

point(cent,2,3);

circle(C,[cent,5]);

This will define a circle named C, center at (2,3), and radius 5.

Because the Help icon is mentioned, I infer that the question is about the Maple icons shown in a launched copy of Maple.

If that inference is correct, then note that the Tools/Options dialog contains a setting for large icons under the Interface tab.

The old linalg package required the use of the evalm command. The new LinearAlgebra package does not. The old linalg package use the "matrix" command but the new LinearAlgebra package uses the "Matrix" command. The noncommutative multiplication operator in LinearAlgebra is the period, not &*. So, it would be helpful to work within the confines of the newer LinearAlgebra package.

The simplest way to equate structures elementwise is to use the Equate command.

A complete solution to the stated problem is given in the attached worksheet.Matrix_calculation.mw

First, when you use a[i] as a variable (i.e., a Maple name), the element a[i] is actually a member of a table whose name is also "a". So, when you assign each equation to the same name "a" each time the loop cycles, you end up with just one equation, namely, the last one. And you have really clobbered your table.

So, rather than name each equation and then later feed all the names to another command, generate a sequence of unnamed equations. For example, write eqns := seq(a[i]+a[i+1]=i^2, i=0..99). Thus, you can send these equations to the solve command with the syntax solve({eqns}), However, you will have 100 equations in 101 unknowns (a[0], a[1], ..., a[100]), so Maple will pick the indeterminate variable. Either supply one more equation or provide the set of names you want solved for.

Perhaps you could use solve({eqns},{seq(a[k],k=1..100)}). This will return a[1],...,a[100] in terms of a[0], provided solve can obtain the solutions. If you have to resort to a numeric solution via the fsolve command, then there can be no indeterminates, and you definitely would have to provide that one more equation to have the same number of equations as variables.

Carl Love has provided a complete solution based on first principles. There are three built-in tools that would have drawn the region of integration and provided an appropriate integral for the volume inside the sphere but outside the cylinder.

The VolumeOfRevolution tutor in Student Calculus1 will implement the method of shells for any vertical axis of rotation.

There are two relevant Task Templates in Tools/Tasks/Browse: Calculus-Multivariate/Integration/Visualizing Regions of Integration/3D, one for integration in cylindrical coordinates, and one for integration in spherical coordinates.

See the attached worksheet for details.Tools_for_Volume.mw

The CenterOfMass command in the Student MultivariateCalculus package will provide the CM for both 2D and 3D regions that can be swept by a single mulltiple integral. Give the density function and the ranges of integration as equations of the form x=a..b, y=c..d, etc, and Maple returns either the unevaluated integrals, of the values for the coordinates of the CM.

The dchange command in the PDEtools package will also do it.

PDEtools:-dchange(_Z1=n,symbolic,[n])

q:= (x^(5/3)-5*x^(2/3)) ;

Q:=convert(q, surd);

plot(Q,x=-1..1);

Roots are principal roots, and can be complex numbers. To obtain the real root in these cases, change the expression to a surd (an old-fashioned word for radical).

RJL Maplesoft

The OP mentions "...I can't get the integral to work with the dy." This leads me to suspect that the OP, apparently new to this forum and probably to Maple, does not realize that the Int command does not require a user to input the differential dy. The syntax for an unevaluated integral is Int(f(y),y=a..b). Maple really does not have a concept of a "differential".

If the integral defining BesselJ(0,x) is implemented as an inert integral by means of the Int command, then it can be evaluated by applying the value command.

RJL Maplesoft

I agree that without a global switch to see which text-field equations are "live" it can be tedious to hover over each one to check.

Prior to Maple 2016, one would exit typeset math by pressing Function Key F5. Now, you have to train yourself to press Shft-F5 to make the typeset math inert, then press F5 again to exit the typeset math field.

I have asked GUI to fix this so that Shift-F5 both makes the typeset math inert, and simultaneously exits the field. We'll have to see if the next version of Maple makes this more convenient.

RJL Maplesoft

Looks to me like there are two problems in the last line where delta is computed. The inner sum needs its range inside the parenttheses, and the second sum needs a range, not just the equation j=i. The first problem is easily corrected, but the second one appears to be structural. You might need to rethink what you are trying to calculate in delta.

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