Items tagged with calculus calculus Tagged Items Feed

Students using Maple often have different needs than non-students. Students need more than just a final answer; they are looking to gain an understanding of the mathematical concepts behind the problems they are asked to solve and to learn how to solve problems. They need an environment that allows them to explore the concepts and break problems down into smaller steps.

The Student packages in Maple offer focused learning environments in which students can explore and reinforce fundamental concepts for courses in Precalculus, Calculus, Linear Algebra, Statistics, and more. For example, Maple includes step-by-step tutors that allow students to practice integration, differentiation, the finding of limits, and more. The Integration Tutor, shown below, lets a student evaluate an integral by selecting an applicable rule at each step. Maple will also offer hints or show the next step, if asked.  The tutor doesn't only demonstrate how to obtain the result, but is designed for practicing and learning.

For this blog post, I’d like to focus in on an area of great interest to students: showing step-by-step solutions for a variety of problems in Maple.

Several commands in the Student packages can show solution steps as either output or inline in an interactive pop-up window. The first few examples return the solution steps as output.

Precalculus problems:

The Student:-Basics sub-package provides a collection of commands to help students and teachers explore fundamental mathematical concepts that are core to many disciplines. It features two commands, both of which return step-by-step solutions as output.

The ExpandSteps command accepts a product of polynomials and displays the steps required to expand the expression:

with(Student:-Basics):
ExpandSteps( (a^2-1)/(a/3+1/3) );

The LinearSolveSteps command accepts an equation in one variable and displays the steps required to solve for that variable.

with(Student:-Basics):
LinearSolveSteps( (x+1)/y = 4*y^2 + 3*x, x );

This command also accepts some nonlinear equations that can be reduced down to linear equations.

Calculus problems:

The Student:-Calculus1 sub-package is designed to cover the basic material of a standard first course in single-variable calculus. Several commands in this package provide interactive tutors where you can step through computations and step-by-step solutions can be returned as standard worksheet output.

Tools like the integration, differentiation, and limit method tutors are interactive interfaces that allow for exploration. For example, similar to the integration-methods tutor above, the differentiation-methods tutor lets a student obtain a derivative by selecting the appropriate rule that applies at each step or by requesting a complete solution all at once. When done, pressing “Close” prints out to the Maple worksheet an annotated solution containing all of the steps.

For example, try entering the following into Maple:

with(Student:-Calculus1):
x*sin(x);

Next, right click on the Matrix and choose “Student Calculus1 -> Tutors -> Differentiation Methods…

The Student:-Calculus1 sub-package is not alone in offering this kind of step-by-step solution finding. Other commands in other Student packages are also capable of returning solutions.

Linear Algebra Problems:

The Student:-LinearAlgebra sub-package is designed to cover the basic material of a standard first course in linear algebra. This sub-package features similar tutors to those found in the Calculus1 sub-package. Commands such as the Gaussian EliminationGauss-Jordan Elimination, Matrix Inverse, Eigenvalues or Eigenvectors tutors show step-by-step solutions for linear algebra problems in interactive pop-up tutor windows. Of these tutors, a personal favourite has to be the Gauss-Jordan Elimination tutor, which were I still a student, would have saved me a lot of time and effort searching for simple arithmetic errors while row-reducing matrices.

For example, try entering the following into Maple:

with(Student:-LinearAlgebra):
M:=<<77,9,31>|<-50,-80,43>|<25,94,12>|<20,-61,-48>>;

Next, right click on the Matrix and choose “Student Linear Algebra -> Tutors -> Gauss-Jordan Elimination Tutor

This tutor makes it possible to step through row-reducing a matrix by using the controls on the right side of the pop-up window. If you are unsure where to go next, the “Next Step” button can be used to move forward one-step. Pressing “All Steps” returns all of the steps required to row reduce this matrix.

When this tutor is closed, it does not return results to the Maple worksheet, however it is still possible to use the Maple interface to step through performing elementary row operations and to capture the output in the Maple worksheet. By loading the Student:-LinearAlgebra package, you can simply use the right-click context menu to apply elementary row operations to a Matrix in order to step through the operations, capturing all of your steps along the way!

An interactive application for showing steps for some problems:

While working on this blog post, it struck me that we did not have any online interactive applications that could show solution steps, so using the commands that I’ve discussed above, I authored an application that can expand, solve linear problems, integrate, differentiate, or find limits. You can interact with this application here, but note that this application is a work in progress, so feel free to email me (maplepm (at) Maplesoft.com) any strange bugs that you may encounter with it.

More detail on each of these commands can be found in Maple’s help pages.

 

diff(F(x,F(x)), x);

 

how to differentiate this?

 

(D[1](F))(x, F(x))+(D[2](F))(x, F(x))*(diff(F(x), x))

 

how to find (D[1](F))(x, F(x)) and (D[2](F))(x, F(x)) ?

 

i guess need define new calculus for two variables

Limit((F(x+h,F(x+h)) - F(x,F(x)))/h, h = 0);

Limit((F(x+h,F(x)) - F(x,F(x)))/h, h = 0);
Limit((F(x,F(x+h)) - F(x,F(x)))/h, h = 0);

Limit((F(x+h,F(x,y)) - F(x,F(x,y)))/h, h = 0);
Limit((F(x,F(x+h,y)) - F(x,F(x,y)))/h, h = 0);

 

if inside F(x) is F(x,y)

it seems need to find the basic definition of F(x,y) first

if i define F(x,y) as

F := (x,y) -> min(x,y)/max(x,y);

 

i may be wrong, how to differentiate correctly?

A new Maple e-book, Multivariate Calculus Study Guide, is now available. Part of the Clickable Calculus collection of interactive Maple e-books, this guide takes full advantage of Maple’s Clickable Math approach. It has over 600 worked examples, the vast majority of which are solved using interactive, Clickable Math techniques. 

Deisgned to help students taking this course, instructors may also find this e-book useful as a guide to using Clickable Math to teach Multivariate Calculus.

See Multivariate Calculus Study Guide for more information.

 

eithne

and why are there decimal points after certain numbers?

I'm taking 2nd semester calculus and in this maple lab, I can't seem to get Maple to evaluate this correctly. Any help is appreciated.

My friend did this and got the first constant, 392..., and just a2, so it was 392.07a2

I am doing a Calculus assignment and I can't find the commands for certain things.

1.Given the function f(x) = ((x+1)^2) / (1+x^2)

i) The domain of continuity of f(x)

ii) The intervals of increase and decrease of f(x) by using test points.

 

2. Use the IVT to prove existence of a root to the equation x^3 +10x^2 -100x +50=0 in the interval [-20,10]. Use again the IVT to show that there is a 1st root in [-17,-15], a 2nd toot in [0,1] and a 3rd root in [ 5,6]. Find or approximate those roots with Maple. (the bolded is what I need help).

So I am using the with(Student[MultivariateCalculus]); package to find the maximum and minimum of the fumction xyz to the given constraint: LagrangeMultipliers(x*y*z, [x^2+4*y^2+4*z^2-4], [x, y, z]) and I got 14 points. But to find the global maximum/minimum I need to evaluate all these points in the main function xyz. I tried converting it to a list and doing something and checked out this thread but it's only for single variable stuff so I am not sure how to extrappolate it to my case.

http://www.mapleprimes.com/questions/202529-Evaluating-A-Function-At-More-Than-One-Point#

These were my points by the way, Yeah lots.

[0, 0, 1], [0, 0, -1], [0, 1, 0], [0, -1, 0], [2, 0, 0], [-2, 0, 0], [(2/3)*sqrt(3), (1/3)*sqrt(3), (1/3)*sqrt(3)], [-(2/3)*sqrt(3), -(1/3)*sqrt(3), -(1/3)*sqrt(3)], [(2/3)*sqrt(3), (1/3)*sqrt(3), -(1/3)*sqrt(3)], [-(2/3)*sqrt(3), -(1/3)*sqrt(3), (1/3)*sqrt(3)], [(2/3)*sqrt(3), -(1/3)*sqrt(3), (1/3)*sqrt(3)], [-(2/3)*sqrt(3), (1/3)*sqrt(3), -(1/3)*sqrt(3)], [(2/3)*sqrt(3), -(1/3)*sqrt(3), -(1/3)*sqrt(3)], [-(2/3)*sqrt(3), (1/3)*sqrt(3), (1/3)*sqrt(3)]

How would I find inflection points? I believe it would the same as if I was finding critical points for f '.

Function is:(7-x)*sin(x^2-7)

So would it be:

a:=fsolve(f2,-2.4..2.4);
b:=fsolve(f2,-2.4..-0.06);
c:=fsolve(f2,-0.06..2.4);
d:=fsolve(f2,1.49..3);
e:=fsolve(f2,-3 ..-1.52);

 

Plz and thanks!

Hi,

Ive been trying to solve critical points for maple but i keep getting this werid equation:

(1/7)*RootOf(tan(_Z)^2+4*_Z*tan(_Z)+4*_Z^2+28*tan(_Z)-140*_Z-1176)+1+(1/14)*tan(RootOf(tan(_Z)^2+4*_Z*tan(_Z)+4*_Z^2+28*tan(_Z)-140*_Z-1176)).

 

What I have typed

f:=x->(7-x)*sin(x^2-7);

f1:=D(f);

When I try putting:

solve(f1(x)=0);

I get that werid equation

 

Hi,

i have been looking to see if i could get the source code for some of the calculus functions in maple. So far, i have tried this

kernelopts(opaquemodules = false)

interface(verboseproc = 3)

print(DiffTutor)

which shows the result

module() ... end module

does anybody have any idea how i would:

1) get the full list of sub-procedures in the module

2) get the source code of any of the sub-procedures in the module?

Thanks in advance!!

Here we see the projection of a vector onto another using different concepts ranging from linear algebra to vector calculus. Implemented components thus seen in three-dimensional space.

 

Proyecciones_Vectoriales.mw

(in spanish)

L.Araujo C.

I am planning on getting Maple 18 Student Editon and I am wondering if the calculus palette is in Maple 18 student edition.

Thanks

Nick

We're starting on indefinite integrals in my 1st year calculus class.

 

A quick example would be int(sin(x), x);=-cos(x)+C

 

Maple doesn't add the +C on the end of it's solution. Can someone explain or point me to a resource? I've tried searching but I can't find an answer. 

hello everyone..

please...

I need help to write a code to calculate the riemann sum approximation of the curve cos(sqrt(x^2+y^2)+1 

calculate the actual volume using integration

use the ranges x=[-2pi to 2pi]=y, and 20 subdivisions.

also display the curve and the parallelepiped approximations on the same plot.

 

Thank you for your help!

hi everyone,

i need help to write a maple code to generate an animation sequence showing the taylor series approximation of tan(x) from 

N=1..5.

plot the animation from x=-2pi to 2pi and y=-5 to 5.

 

thank you for your help..

1 2 3 4 5 6 7 Last Page 1 of 10