## Area between Curves

by: Maple 12

The attached worksheet gives you a brief review and shows you how to use Maple to solve and better understand the area between curves. You can also view the examples through an interactive video tutorial:

(Ctrl + click on link below)

Video Tutorial: Area between Curves

Please feel free to shoot questions at me!

## Definite Integrals

by: Maple 12

Hey there,

the attached worksheet shows you how to master definite integrals using special tools that help you determine the pattern between antiderivatives and the area under a curve.

You can also view the examples done in an interactive video:

Definite Integrals - Video Tutorial

## Antiderivatives

by: Maple 12

The attached work sheet teaches you the fundamental concepts behind the antiderivative.

The examples in this worksheet are entirely done in an interactive video tutorial - follow the link below:

(Ctrl+Click on the link to view the video)

Antiderivatives - Video Tutorial

Enjoy!

## Riemann Sums: Approximating Area under Curve

by: Maple 12

The attached worksheet is a wonderful introduction to the concept of obtaining the area under a curve.

You'll see how easy it is to learn how to find the limit of the sum of a series using Maple.

An interactive video tutorial that shows you how to do Riemann sums really fast is linked below:

(Ctrl+Click on the link to view the video)

Riemann Sums...

## Two solitudes

Yesterday I watched a demonstration of Maple being applied to the modeling and simulation of the internal deformations of human bones. The researcher was a mathematician working primarily in the biomedical modeling fields. The actual technique was to utilize the symbolic mathematical power of Maple to formulate the necessary equation pieces for a finite element model (FEM) of the internals of the bone. The equations are then fed into the legendary FEM solver ABAQUS.

Due to the notoriously non-linear qualities of human flesh and bone, traditional formulation methods developed for modeling beams and metals simply do not work. So as in the case of so many impressive engineering applications, the power of Maple is being deployed in the formulation or the pre-solution phase of modeling and in doing so, previously infeasible models now become feasible.

Hi everyone,

If you want to paste a link, click on the globe beside the maple leaf.

put your cursor on it, press Ctrl and click and a new tab will open!

## Optimization...

The attached file reviews optimization problem solving and also shows you to solve hard problems though Maple's Optimization Assistant.

## Maximums, minimums, concavity - Graphing...

The file attached shows you how useful the Curve Analysis tutor is. When you enter-in a function, the Curve Analysis tutor will produce a graph of the function that shows all of the critical points of the curve, along with the maximum, minimum and inflection points.

## Differential Equations - Initial Value Problems...

The attached document shows you how to solve an initial value problem. Moreover, it shows you how to use Maple's ODE analyzer which makes it really fast and easy to solve and plot the solutions of differential equations.

## Entering expressions in Forums...

Maple's powerful notation allows you to enter math expressions that look natural.

The following steps will show you how easy it is to write expressions.

Example 1:  Write

1. If you're on the Student Center forums, click on the red maple leaf to insert maple ma

## ... Enter a function?...

In Maple, suppose we would like to enter the function and we want to know what the function is at .

Below are a few simple steps that will show you how to achieve this.

1. Make sure you're in math mode. Type , followed by a colon and an equal sign . The colon-equals notation assigns the content on the right-hand side to a variable name on the left-hand side. I

## Make Secret Codes (Elementary Cryptography)...

Maple is amazing at making secret codes.

First, let's learn two quick words. To "encrypt" a message means that you have transformed your message such that it is unreadable by others.

And to "decrypt" means to transform it back to your original message, also known as code breaking.

We will encrypt and decrypt our original message "Hello new Maple users !".

Le

## Solving Dense Linear Systems in Maple 12

by: Maple 12

Suppose you want to solve a large dense linear system AX=B over the rationals - what should you do? Well, one thing you should probably not do is directly apply Gaussian elimination. It does O(n^3) arithmetic operations, but the size of the numbers blow up, leading to an exponential bit complexity. Don't believe me? Try it:

```with(LinearAlgebra):
for N from 5 to 9 do
A := RandomMatrix(2^N, 2^N+1,generator=-10^5..10^5):
TIMER := time(GaussianElimination(A...```
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