Intended Audience: Students interested in formulating, understanding, analyzing, and implementing numerical methods, and in using existing numerical tools critically and effectively. Material is centered around the partial differential equations of incompressible fluid flow and heat transfer, however the methods presented apply to a broad range of engineering problems. The focus is mathematical, but not to the exclusion of physical arguments.Prerequisites: Basic knowledge of heat transfer and incompressible fluid mechanics; familiarity with ODEs, standard PDEs, and linear algebra; proficiency in C and MATLAB; modest exposure to elementary numerical procedures.
Course Content: Most of the term will be spent on the formulation, analysis, and implementation of finite element spatial discretizations of linear problems: symmetric coercive problems (heat conduction and, briefly, linear elasticity); nonsymmetric coercive problems (convectiondiffusion phenomena); and saddle problems (creeping flow: the incompressible Stokes equations). Additional topics to be discussed include: direct and iterative solution methods; nonlinear problems, in particular the NavierStokes equations; and finitedifference in time/finiteelement in space treatment of unsteady problems.
Required Text: ProtoBook Lecture Notes.
Class Format: Students are expected to review relevant Lecture Notes prior to class. Class time will be devoted to elaboration and clarification of the reading assignment, and interactive solution of associated examples and exercises.
Grading: 75% problem sets (involving both analysis and computation); 25% class participation.
Problem Sets: The assignments involve some formulation, some analysis, and some programming and computation (in C and MATLAB). In the latter case, the numerical method should be summarized (Lecture Notes or other texts may be referenced), and the results of the program displayed in tabular or graphical form. Only minimal algebraic details should be included; do NOT submit a copy of your program as part of your problem set solution.
The problem sets will indicate explicitly which programs are to be written by the student, and which may be incorporated or derived from (legally accessed and properly referenced) thirdparty sources. Students may collaborate on problem sets, but only to the extent of oral communication and untranscribed blackboard derivations.Computer and Software Resources: Students may use either their ?own? (workstationequivalent) machines, or Project Athena publiccluster computers. All thirdparty software required or recommended is available on Athena, in particular MATLAB (with the PDE Toolkit) and Numerical Recipes. Any coursespecific software to which students must directly link will be available in C or MATLAB on Athena.
Communication: Any updates to the course material or the class schedule will be announced in class or distributed via email and archived on the course Web site http://web.mit.edu/2.274/www.
Office Hours:
Instructor: open
T.A.: Tuesday, 3:004:00 & Wednesday, 10:3011:30.Makeup Classes: As needed, makeup classes will be held on Fridays, 9:00  10:30, in Room 1273.




W Sept 16 

W Sept 30 

M Oct 5 

T Oct 13 



M Oct 19 

M Oct 26 



W Nov 4 



W Nov 18 



M Nov 30 W Dec 2 

W Dec 9 
(and TimeDependent Problems) 