This course uses Maple and IDL within the context of an introductory physics course in Oscillations and Waves. The students use a self-published text “Computation and Problem Solving in Undergraduate Physics” by David M. Cook of Lawrence University. This text includes details about the use of Maple and IDL to solve many types of physics problems. The worksheets below are used in the classroom with students working individually or in pairs at computers.
Introduction to the use of IDL. link
This first worksheet gets the students to explore the graphical user interface. It also explores the different variable types (float, integer, arrays), highlights the dangers of calculating ratios of integer variables and illustrates the creation and manipulation of arrays. It finishes by getting the students to create and plot an array containing the values of a sine function.
Investigating sinusoidal functions, importing real data into IDL and matching it to a sinusoidal function. link
This worksheet continues the exploration of array creation and manipulation and plotting. Students use IDL to look at plots of the function Acos(wt+f) for various values of the parameters. They then use a motion detector to take real data on an oscillating block/spring system, put the data into a text file and then import this data into IDL. They then attempt to fit the data to the Acos(wt+f) function.
Series Expansion of functions using Maple. link
This worksheet repeats some of the exploration of the function Acos(wt+f) but this time using Maple (in Classic Worksheet mode). It then goes on to introduce the series command and students produce plots of expansions of the sine function to different orders and about different points.
The initial value problem. link
Students take derivatives and solve simultaneous equations in order to find the values of A and f in the solution, Acos(wt+f), to the SHO equation.
IDL Function Files and Root-finding. link
This worksheet returns to the small-angle approximation sin(x) ≈ x. The students are asked to find the range of x for which there is less than 1% error in this approximation. To do this they create a function file in IDL and are introduced to the newton function for finding roots.
Solving differential equations in Maple. link1 link2
These two Maple worksheets (given to the students with the output suppressed) introduce the students to several commands including dsolve, assign, expand, coeff, convert. This takes place within the context of solving the undamped SHO equation.
Mass, Center of Mass, Moment of Inertia. link
This handout defines these quantities and asks the students to evaluate them using Maple’s int command.
Simple Euler Method. link
This handout leads the students through the derivation of the simple Euler method for solving an ordinary differential equation by using a specific example that the students solve using their calculators. The IDL code to implement the method is presented and the students use it and compare the output to their previous result. They are then asked to improve the code to make it more versatile.