## Maple worksheets

### Two Body Gravitational Problem:

This worksheet solves and animates the 2-Body Gravitational Problem. The parameters can be easily changed to view the effects these changes have on the animation. Created for AMATH 271 in Maple 2015.

Two Body Gravitational Problem.mw

### Three Body Gravitational Problem:

This worksheet solves and animates the 3-Body Gravitational Problem. The parameters can be easily changed to view the effects these changes have on the animation. Created for AMATH 271 in Maple 2015.

Three Body Gavitational Problem.mw

### Newton's Method:

The worksheet demonstrates the use of Newton's Method to find the roots of an algebraic function through an example. Worksheet created for MATH 137 in Maple 2015.

### Riemann Sums:

The worksheet uses Maple's built in Riemann Sum function to calculate the Riemann Sum using the left, right, and midpoint methods for two different functions. Worksheet created for MATH 137 in Maple 2015.

### Solving ODEs Using Maple: An Introduction:

This worksheet explores the use of Maple to solve Ordinary Differential Equations. It includes finding general solutions, as well as solving initial value, and boundary value problems. It touches on the difference between symbolic and numerical solutions. It examines Airy's and Bessel's Equations and their solutions. Finally, it looks at power series solutions to differential equations. Worksheet created for AMATH 351 in Maple 2015.

Solving Odes Using Maple: An Introduction.mw

### Finding Absolute and Local Minimums:

This worksheet solves the basic calculus problem: finding the absolute and local minimum of a function over an interval. Created for MATH 137 in Maple 2015.

Finding Absolute and Local Minimums.mw

### Differential Equations and Eigenvalues:

This worksheet explores the relationship between the eigenvalues of a matrix and the system of differential equations defined by that matrix. It looks at examples from 3 different cases: distinct real eigenvalues, repeated real eigenvalues, and complex eigenvalues. Created for Topics in Differential Equations in Maple 2015.

Differential Equations and Eigenvalues.mw

### Slow Manifold Analysis:

This worksheet goes through the slow manifold analysis following Hek’s discussion of the predator prey system. Created for Topics in Differential Equations in Maple 2015.

### DE Phase Portraits – Animated Trajectories:

An interactive worksheet that solves a system of differential equations, and animates their trajectories on a phase portrait. Created for AMATH 251 using Maple 2015.

DE Phase Portraits - Animated Trajectories.mw

### Second Order DE Solution Examples:

This worksheet looks at solutions and plots to both homogeneous and non homogenous 2nd order differential equations. Created for AMATH 251 using Maple 2015.

Second Order DE Solution Examples.mw

### An Introduction to Maple – AMATH 251:

This worksheet provides an introduction to Maple that is required for AMATH 251. It includes Maple formatting, basic math, matrices, functions, basic calculus, and differential equations. Created for AMATH 251 in Maple 2015.

### ODEs and Normal Matrices:

This worksheet explores whether it is possible to find a normal, 2x2 matrix with real entries that has complex eigenvalues. It does so by examining symmetric matrices, the damped harmonic oscillator, and other normal matrices. It also includes examples that look at the system of differential equations defined by each matrix by solving, plotting the phase portrait, and the distance from the origin. Created for Topics in Linear Algebra and Differential Equations in Maple 2015.

### Fourier Series:

This worksheet provides three examples of using Maple to find the Fourier Series with various numbers of terms. It also demonstrates how to calculate, and plot the L-2, and L-infinity errors. Created for AMATH 231 in Maple 2015. Please note that the worksheet requires the Orthogonal Expansions Package which you can get from Maple Application Center

http://www.maplesoft.com/applications/view.aspx?SID=33406

### Burgers’ Vortex:

The Burger's vortex is a well known solution of the Navier Stokes equations that combines vorticity and shear. It allows for the study of a realistic flow in analytical form, thereby offering intuition for more complex flows. However, the cylindrical coordinate system makes certain calculations cumbersome to carry out by hand. This worksheet allows the user to explore aspects of the flow without having to carry out the calculations. Created for AMATH 463 in Maple.

### Magneto-Elastic Mechanical System:

This worksheet solves and animates the magneto-elastic mechanical system described in Nonlinear Dynamics and Chaos by S.Strogatz. The parameters can be easily changed to view the effects these changes have on the animation. Created for Topics in Nonlinear Dynamics in Maple 2015.

Magneto-Elastic Mechanical System.mw

### Overdamped Bead on a Rotating Hoop:

This worksheet solves and animates the overdamped bead on a rotating hoop problem described in Nonlinear Dynamics and Chaos by S. Strogatz. The parameters can be easily changed to view the effects these changes have on the animation. Created for Topics in Nonlinear Dynamics in Maple 2015.