UCES Modules

An introduction to the mathematics and computation of public key encryption, a technique for passing coded information from point to point securely. This subject has achieved tremendous attention of late due to its possible use as a means of securely transacting business on the internet. An interactive encryption/decryption engine is included in the module.

Variable Mass Rocket

An examination of the kinematics and dynamics of a rocket in flight and burning sufficient fuel that the change in mass needs to be treated carefully. Computational examples are provided in Maple.

Monte Carlo Methods in Physics

Pseudo-random numbers can used to simulate naturally random processes, such as the thermal motion of particles or radioactive decay, or to approximate the performance of some mathematical operation. Indeed, much of the recognition of computational physics as a specialty has come about from the ability of computers to solve previously intractable thermodynamic and field theory problems using Monte-Carlo techniques.

This module demonstrates how to produce random numbers in order to perform a random walk, simulate radioactive decay and calculate Pi in a rather unusual way using Monte Carlo techniques.

Oscillations and Differential Equations

An analysis of various aspect of simple harmonic motion, including damped and driven oscillations, through the solution of second order differential equations.

This work was recognized by the Department of Energy with an Undergraduate Computational Science Education Award.

Draining a Tank, Does the Shape Matter?

This module examines a simple question, "When draining fluid from two tanks of equal volume, does the shape of the tanks effect which one empties first?" Computational exercises are provided in Maple.

World Population

This lesson uses Maple to study the problem of determining the number of square feet that every human on earth would have if all of the dry land were divided up evenly. It illustrates the five-step approach to solving computational problems, with an emphasis on the importance of assessment. It discusses the notions of significant digits and interval arithmetic.

Kitty Hawk

This lesson uses Maple to determine the distance out to sea one can see from the top of a hill. It illustrates the importance of using diagrams to come up with a model, introduces the idea of floating-point error, and shows how algebraic simplification can convert an unstable computation into a stable one.

Cantilevered Blocks

This lesson uses Maple to determine how far out beyond the edge of a table a simple stack of blocks can be cantilevered. It illustrates the role that Maple can play in developing an initial model, and introduces the idea of using built-in functions.

Exponential Growth

This lesson uses Maple to study the phenomenon of exponential growth. It illustrates the power of user-defined functions and shows how Maple can be used to solve equations.

Ballistic Trajectories

This lesson uses Maple to study the problem of visualizing ballistic trajectories. It illustrates the power of visualization in science and engineering through the use of two-dimensional plots, parametric plots, and animations.

Destroyers

This lesson uses Maple to study the problem of modeling the power consumption of a modern destroyer. It illustrates the calculus capability of Maple, the idea of abstracting a function from an expression, and the power of building complicated functions from simple building blocks.

Rates of Chemical Reactions

The rate at which a chemical reaction proceeds can be modeled via a first order differential equation. This module uses Mathematica to solve several representative rate equations both analytically and numerically. The module is available in UCES interactive format.

Quantum Mechanical Wavefunctions

This module calculates quantum mechanical wavefunctions by numerically solving the time independent Schrödinger equation. It illustrates how a simple finite difference scheme (and, optionally, the more accurate Noumerov method), can be used to calculate wavefunctions for an atom colliding with a surface of a solid, which is first represented simply as a hard wall, but then more realistically with a Morse interaction potential function. The module is available in UCES interactive format.

Normal Modes of Molecular Compounds

In this exercise the vibration of molecules is analyzed using classical mechanics. To motivate and illustrate the concept of normal modes, the vibration of a linear triatomic molecule confined to one dimension is first simulated and then analyzed. Then, the vibrational dynamics in three-dimensions of CO₂ and H₂O are simulated. The module is available in UCES interactive format.

Electrostatic Potential in a Wire

An in-depth treatment of various computational approaches (both symbolic and numeric) to determine the electrostatic potential generated by a charged wire.