16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course will include: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms will include: Variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout.

An interactive applet and associated web page that provide step-by-step animated instructions on how to construct a line parallel to a given line through a given point off the line. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Describes how serial to parallel conversion was implemented in our DMT project.

This course is designed to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, query optimization, query processing, and transactions. This is not a course on database design or SQL programming (though we will discuss these issues briefly). It is designed for students who have taken 6.033 (or equivalent); no prior database experience is assumed though students who have taken an undergraduate course in databases are encouraged to attend.

Students investigate circuits and their components by building a basic thermostat. They learn why key parts are necessary for the circuit to function, and alter the circuit to optimize the thermostat temperature range. They also gain an awareness of how electrical engineers design circuits for the countless electronic products in our world.

In this Cyberchase video, Inez and Digit identify the location of the transformation using their knowledge of parallel and intersecting lines.

Introduction to the concept of a system, which is a mechanism for manipulating signals. Feedback concepts and superpositions are also briefly mentioned.

A discussion of combination rules for circuit elements connected in series and of the voltage divider rule.

This module serves as the introductory module for the Open Education Cup contest (http://OpenEducationCup.org) collaborative book. This introduction outlines the primary focus of the contest and provides examples to help authors get started with their contest entries.

Activities for introducing children to parallel harmony.

An interactive applet and associated web page that demonstrate the concept of parallel lines. The applet shows two lines, one of which has draggable endpoints. As the line is changed by dragging them, the other line changes to remain parallel to it. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the properties of parallel lines in coordinate geometry. The applet presents two lines, each defined by a pair of draggable points. If they are parallel the slopes are the same and the applet adds the parallel arrow marks to them. The slope of each line is continuously recalculated and the case of vertical lines (with undefined slope) is handled correctly. The is a software 'detent' that snaps the lines to parallel if they are close to it. The grid, axis pointers and coordinates can be turned on and off. The slope calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining if lines are parallel, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Properties of different types of systems.

Propiedades de diferentes tipos de sistemas

A brief look at series and parallel circuits. Also defines voltage and current divider.

This is an activity for circuit testing. This object is also designed for presentation via Windows-based hand-held devices.

In this video segment from Cyberchase, Bianca gets injured while skateboarding, so her friend brings her a device to use to reach objects while she's recovering in bed.

Series and parallel combination rules.

An interactive applet and associated web page that demonstrate the transversal, a line that crosses two other (usually parallel) lines. The applet shows two lines that are initially parallel, and a transversal line. All eight angles thus formed are shown. As you drag the transversal end points, you can see that the angles form congruent, supplementary and complementary sets. If you move one of the parallel lines to make it non-parallel, you can see that these angles lose some of their relationship with each other. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.