Courses tagged with "Before 1300: Ancient and Medieval History" (183)
The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions.
We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.
6.336J is an introduction to computational techniques for the simulation of a large variety of engineering and physical systems. Applications are drawn from aerospace, mechanical, electrical, chemical and biological engineering, and materials science. Topics include: mathematical formulations; network problems; sparse direct and iterative matrix solution techniques; Newton methods for nonlinear problems; discretization methods for ordinary, time-periodic and partial differential equations, fast methods for partial differential and integral equations, techniques for dynamical system model reduction and approaches for molecular dynamics.
This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5211 (Introduction to Numerical Simulation).
In this subject, we consider two basic topics in cellular biophysics, posed here as questions:
- Which molecules are transported across cellular membranes, and what are the mechanisms of transport? How do cells maintain their compositions, volume, and membrane potential?
- How are potentials generated across the membranes of cells? What do these potentials do?
Although the questions posed are fundamentally biological questions, the methods for answering these questions are inherently multidisciplinary. As we will see throughout the course, the role of mathematical models is to express concepts precisely enough that precise conclusions can be drawn. In connection with all the topics covered, we will consider both theory and experiment. For the student, the educational value of examining the interplay between theory and experiment transcends the value of the specific knowledge gained in the subject matter.
This course is jointly offered through four departments, available to both undergraduates and graduates.
This subject is aimed at students with little or no programming experience. It aims to provide students with an understanding of the role computation can play in solving problems. It also aims to help students, regardless of their major, to feel justifiably confident of their ability to write small programs that allow them to accomplish useful goals. The class will use the Python programming language.
Course Format
This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:
- A complete set of Lecture Videos by Prof. Guttag.
- Resources for each lecture video, such as Handouts, Slides, and Code Files.
- Recitation Videos by course TA's to review content and problem solving techniques.
- Homework problems with sample student solutions.
- Further Study collections of links to supplemental online content.
- Self-Assessment tools, including lecture questions with answers and unit quizzes with solutions, to assess your subject mastery.
Other Versions
Other OCW Versions
OCW has published multiple versions of this subject.