Integral Equations, Spring 2006

Abstract:: Selection of material from the following topics: calculus of variations (the first variation and the second variation); integral equations (Volterra equations; Fredholm equations, the Hilbert-Schmidt theorem); the Hilbert Problem and singular integral equations of Cauchy type; Wiener-Hopf Method and partial differential equations; Wiener-Hopf Method and integral equations; group theory.

"Mechanical Behavior of Materials, Fall 2007"

Abstract:: " Here we will learn about the mechanical behavior of structures and materials, from the continuum description of properties to the atomistic and molecular mechanisms that confer those properties to all materials. We will cover elastic and plastic deformation, creep, and fracture of materials including crystalline and amorphous metals, ceramics, and (bio)polymers, and will focus on the design and processing of materials from the atomic to the macroscale to achieve desired mechanical behavior. Integrated laboratories provide the opportunity to explore these concepts through hands-on experiments including instrumentation of pressure vessels, visualization of atomistic deformation in bubble rafts, nanoindentation, and uniaxial mechanical testing, as well as writing Assignments and Labs to communicate these findings to either general scientific or nontechnical audiences."

Abstract:: 1.050 is a sophomore-level engineering mechanics course, commonly labeled "Statics and Strength of Materials" or "Solid Mechanics I." This course introduces students to the fundamental principles and methods of structural mechanics. Topics covered include: static equilibrium, force resultants, support conditions, analysis of determinate planar structures (beams, trusses, frames), stresses and strains in structural elements, states of stress (shear, bending, torsion), statically indeterminate systems, displacements and deformations, introduction to matrix methods, elastic stability, and approximate methods. Design exercises are used to encourage creative student initiative and systems thinking.

Abstract:: Introduces students to basic properties of structural materials and behavior of simple structural elements and systems through a series of experiments. Students learn experimental technique, data collection, reduction and analysis, and presentation of results.

Abstract:: Introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory and optimization techniques. Emphasis on basic ideas and on applications in mechanical engineering. Selection will change every year. This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

Abstract:: Applies solid mechanics to analysis of high-technology structures. Structural design considerations. Review of three-dimensional elasticity theory; stress, strain, anisotropic materials, and heating effects. Two-dimensional plane stress and plane strain problems. Torsion theory for arbitrary sections. Bending of unsymmetrical section and mixed material beams. Bending, shear, and torsion of thin-wall shell beams. Buckling of columns and stability phenomena. Introduction to structural dynamics. Exercises in the design of general and aerospace structures.