Search results with tag "Opencourseware"
Overview: ray transfer matrices - MIT OpenCourseWare
ocw.mit.eduOverview: ray transfer matrices optical axis Propagation through uniform space: Refraction at spherical interface: distance d, index of refraction n left radius R, indices n left, n right By using these elemental matrices, we may ray trace through an arbitrarily long cascade
Subgroups and Cyclic Groups - MIT OpenCourseWare
ocw.mit.eduLecture 2: Subgroups and Cyclic Groups 2 Subgroups and Cyclic Groups 2.1 Review Last time, we discussed the concept of a group, as well as examples of groups. In particular, a group is a …
18.703 Modern Algebra, Subgroups - MIT OpenCourseWare
ocw.mit.eduSubgroups Consider the chain of inclusions of groups. Z ⊂ Q ⊂ R ⊂ C. where the law of multiplication is ordinary addition. Then each subset is a group, and the group laws are …
Lecture 16: NP-Completeness - MIT OpenCourseWare
ocw.mit.eduLecture NP-Completeness Spring 2015 • A problem X is NP-hard if every problem Y ∈ NP reduces to X. – If P =NP,then X/ ∈ P. • A reduction from problem A to problem B is a …
Rigid Body Dynamics - MIT OpenCourseWare
ocw.mit.eduThe acceleration of the center of mass of a rigid body is related to the sum of forces in a very intuitive way: FE = Ad mAv CE CE = mAa dt. (EQ 3) where FE is the total force on the rigid …
3D Rigid Body Dynamics - MIT OpenCourseWare
ocw.mit.edu3D Rigid Body Dynamics: Euler Angles. The difficulty of describing the positions of the body-fixed axis of a rotating body is approached through the use of Euler angles: spin ψ ̇, nutation θ and …
The Problem of Evil - MIT OpenCourseWare
ocw.mit.eduThe Problem of Evil as an Argument Against the Existence of God. (1) There is evil. (2) If an omnipotent (=all powerful) benevolent (=all good) being existed there would be no evil. (3) An omnipotent benevolent being does not exist.
Agarose Gel Electrophoresis - MIT OpenCourseWare
ocw.mit.eduAgarose gel electrophoresis is a simple and highly effective method for separating, identifying, and purifying 0.5 to 25 kb DNA fragments. Voltage applied at the ends of an agarose gel generates an electric field with a strength defined by the length of the gel and the potential difference at the ends (V/cm). ...
2.72 Elements of Mechanical Design - MIT OpenCourseWare
ocw.mit.eduMechanical system design is cost and time intensive. Mastery of: Concepts, principles & design processes necessary, but not sufficient Math, physics and engineering models are necessary, …
Lecture 2: Divide and Conquer - MIT OpenCourseWare
ocw.mit.eduLecture 2 Divide and Conquer Spring 2015. Lecture 2: Divide and Conquer • Paradigm • Convex Hull • Median finding. Paradigm. Given a problem of size. n. divide it into subproblems of size. …
Vector bundles and principal bundles - MIT OpenCourseWare
ocw.mit.edu4. If ˘: E #Band ˘0: E0#Bare two vector bundles over B, we can form another vector bundle ˘ ˘0over Bby taking the fiberwise tensor product. Likewise, taking the fiberwise HomproducesavectorbundleHom(˘;˘0) overB. Example 16.8. Recall from Example 16.5 the tautological bundle over RPn1. The tangent bundle˝ RPn1 alsolivesoverRPn1 ...
6.092 Lecture 4: Classes and Objects - MIT OpenCourseWare
ocw.mit.eduDefining Classes Using Classes References vs Values Static types and methods. Today’s Topics Object oriented programming Defining Classes Using Classes ... Classes and Instances // class Definition public class Baby {…} // class Instances Baby shiloh = …