Spring 2012 MATH 275 002 LEC

Topics in Applied Mathematics
Schedule: 
SectionDays/TimeLocationInstructorCCN
002 LECTuTh 930-11A 736 EVANSBARENBLATT, G I54556
Units/CreditFinal Exam GroupEnrollment
4NONELimit:5 Enrolled:5 Waitlist:0 Avail Seats:0 [on 05/03/12]

Restrictions: CURRENTLY FULL

Additional Information: 

Office: 735 Evans
Prerequisites: NB Only students enrolled in Part A of this course in Fall 2011, and who pass the exam, may enroll in Part B.
Recommended Reading:
Landau, L. D. and Lif*bleep*s, E. M., Fluid Mechanics (Pergamon Press, London, Yew York, 1987);
Landau, L. D. and Lif*bleep*s, E. M., Theory of Elasticity (Pergamon Press, London, Yew York, 1986);
Chorin, A. J. and Marsden, J. E., A Mathematical Introduction to Fluid Mechanics (Springer, 1990);
Barenblatt, G. I. Scaling (Cambridge University Press, 2003);
Batchelor, G. K., An Introduction to Fluid Dynamics (Cambridge University Press, 1998).
Syllabus: Fluid Mechanics, including Turbulence and Mechanics of Deformable Solids, including Fracture Mechanics are fundamental disciplines, playing an important and ever-growing role in applied mathematics, including computing, and also physics, and engineering science. The models of fluid flow, deformation and fracture of solids under various conditions appear in all branches of applied mathematics, engineering science and many branches of physical science. Among the problems of these sciences which are under current active study there are great scientific challenges of our time such as turbulence, fracture and fatigue of metals, damage accumulation and nanotechnology.

The proposed course will present the basic ideas and methods of fluid mechanics, including turbulence, mechanics of deformable solids, including fracture as a unified mathematical, physical and engineering discipline. The possibility of such a unified presentation is based on the specific 'intermediate-asymptotic approach' which allows the explanation of the main ideas simultaneously for the problems of fluid mechanics and deformable solids. The basic distinction of this year-long course will have special emphasis on turbulence. The instructor expects to present the basic ideas and to evaluate the current state of the turbulence studies. In particular, scaling laws for the shear flows and local structure of the developed turbulent flows will be presented and discussed.
Homework: There will be no systematic homework. Some problems will be presented shortly at the lectures, their solutions will be outlined, and interested students will be offered the opportunity to finish the solutions. This will not be related to the final exams.
Comments: In the end of the course the instructor will give a list of 10 topics. Students are expected to come to the exam having an essay (5-6 pages) concerning one of these topics which they have chosen. They should be able to answer questions concerning the details of these topics. After that general questions (without details) will be asked concerning the other parts of the course.