LEC1 - 12.005 Lecture notes#1 1 12.005 Lecture Notes 1...

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12. 005 Lecture notes #1 1 12.005 Lecture Notes 1 Handouts - Course description & reserve list • Motivation for core course • Instructor background • Student background Courses in physics and mathematics? EAPS area of focus? • Textbooks Mechanics : the study of the motion of matter and the forces that cause such motion. Based on concepts of time, space, force, energy, matter. Applications to point masses, solid bodies familiar from introductory physics. Continuum mechanics - mechanics of parts of "bodies." Continuum - define values of fields (e.g., density) as functions of position, i.e., at points. Example : density ρ ( P ) = V n 0 lim M n V n V i —> Sequence of volumes converging on P M i —> Mass enclosed by V i
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12. 005 Lecture notes #1 2 Breakdown at small V (e.g., gas) Figure 1.1 Figure 1.2 Figure by MIT OCW. Figure by MIT OCW.
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12. 005 Lecture notes #1 3 Ignore fine structure. Assume: Continuity : completely fills space (no pores or voids) and has properties describable by continuous functions. [Scale dependent. E.g., sand will be treated as a continuum] Homogeneity - identical properties at all points [Scale dependent.] Isotropy - properties same in all directions. [Often not true. e.g., schist] Behavior describable in terms of partial differential equations subject to boundary conditions. All functions will be "well behaved," except at a finite # of surfaces. Logical contradiction between mathematical process of taking limits & physical breakdown of continuum description at small scales ignored. (Assume - fields varying slowly enough that math defined before description falls apart.) At core:
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This note was uploaded on 10/25/2010 for the course MIT Geodynamic taught by Professor Ywn during the Fall '10 term at MIT.

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LEC1 - 12.005 Lecture notes#1 1 12.005 Lecture Notes 1...

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