Competition in Telecommunications provides an introduction to the economics, business strategies, and technology of telecommunications markets, including markets for wireless communications, local and long-distance services, and customer equipment. The convergence of computers, cable TV and telecommunications and the competitive emergence of the Internet are covered in depth. A number of speakers from leading companies in the industry will give course lectures.

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.

This graphic illustrates some of the marsupial mammals in Australia and placental mammals in North America. Even though they are not closely related, these mammals look alike because they have adapted to similar ecological roles. From The Human Evolution Coloring Book by by Adrienne Zihlman.

This module discusses the covergence of the Fourier Series to show that it can be a very good approximation for all signals.

This module will present an introduction into convergence and focus on what a sequence is and how it behaves as it approaches infinity.

This module presents two common types of convergence, pointwise and norm, and discusses their properties, differences, and relationships with one another.

This module introduces Hilbert spaces.

" This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods."

Examines the relationship between popular and high culture and the problem of evaluating texts that tell stories. Treats a range of narrative and dramatic works as well as films. May be repeated for credit, with permission of instructor. Topic for Fall: Masterminds. Topic for Spring: Popular Culture in the Age of Media Convergence. Our purpose is to consider some of the most elaborate and thoughtful efforts to define and delineate "all-mastering," and to consider some of the delineations of "all-mastering the intellect" in various guises - from magicians to master spies to detectives to scientists (mad and otherwise). The major written work of the term will be an ongoing reading journal, which you will circulate to your classmates using an e-mail mailing list. The use of that list is fundamental - it is my intention to generate a sort of ongoing cyberconversation.

This course is the second installment of Single-Variable Calculus. The student will explore the mathematical applications of integration before delving into the second major topic of this course: series. The course will conclude with an introduction to differential equations. Upon successful completion of this course, students will be able to: Define and describe the indefinite integral; Compute elementary definite and indefinite integrals; Explain the relationship between the area problem and the indefinite integral; Use the midpoint, trapezoidal, and Simpson's rule to approximate the area under a curve; State the fundamental theorem of calculus; Use change of variables to compute more complicated integrals; Integrate transcendental, logarithmic, hyperbolic, and trigonometric functions; Find the area between two curves; Find the volumes of solids using ideas from geometry; Find the volumes of solids of revolution using disks, washers, and shells; Find the surface area of a solid of revolution; Compute the average value of a function; Use integrals to compute displacement, total distance traveled, moments, centers of mass, and work; Use integration by parts to compute definite integrals; Use trigonometric substitution to compute definite and indefinite integrals; Use the natural logarithm in substitutions to compute integrals; Integrate rational functions using the method of partial fractions; Compute improper integrals of both types; Graph and differentiate parametric equations; Convert between Cartesian and polar coordinates; Graph and differentiate equations in polar coordinates; Write and interpret a parameterization for a curve; Find the length of a curve described in Cartesian coordinates, described in polar coordinates, or described by a parameterization; Compute areas under curves described by polar coordinates; Define convergence and limits in the context of sequences and series; Find the limits of sequences and series; Discuss the convergence of the geometric and binomial series; Show the convergence of positive series using the comparison, integral, limit comparison, ratio, and root tests; Show the divergence of a positive series using the divergence test; Show the convergence of alternating series; Define absolute and conditional convergence; Show the absolute convergence of a series using the comparison, integral, limit comparison, ratio, and root tests; Manipulate power series algebraically; Differentiate and integrate power series; Compute Taylor and MacLaurin series; Recognize a first order differential equation; Recognize an initial value problem; Solve a first order ODE/IVP using separation of variables; Draw a slope field given an ODE; Use Euler's method to approximate solutions to basic ODE; Apply basic solution techniques for linear, first order ODE to problems involving exponential growth and decay, logistic growth, radioactive decay, compound interest, epidemiology, and Newton's Law of Cooling. (Mathematics 102; See also: Chemistry 004, Computer Science 104, Mechanical Engineering 002)

Student groups rotate through four stations to examine light energy behavior: refraction, magnification, prisms and polarization. They see how a beam of light is refracted (bent) through various transparent mediums. While learning how a magnifying glass works, students see how the orientation of an image changes with the distance of the lens from its focal point. They also discover how a prism works by refracting light and making rainbows. And, students investigate the polar nature of light using sunglasses and polarized light film.

Mathematical models of systems from observations of their behavior. Time series, state-space, and input-output models. Model structures, parametrization, and identifiability. Non-parametric methods. Prediction error methods for parameter estimation, convergence, consistency, andasymptotic distribution. Relations to maximum likelihood estimation. Recursive estimation; relation to Kalman filters; structure determination; order estimation; Akaike criterion; and bounded but unknown noise models. Robustness and practical issues.