Fundamental equation of thermodynamics
The rst and second laws of thermodynamics imply that dU = T dS + Y dX + dN with U S U X U N
[tln16]
(1)
= T,
X,N
= Y,
S,N
=
S,X
is the exact dierential of a function U (S, X, N ). Here X stands for V, M, . . . and Y

MMAE 510 Fall 2009 Rm 241 E1 2:00 to 3:10 Test 1: In Class, Open One Undergraduate Text Book, and Calculator Wednesday, August 26 Solve any 4 of following 6 problems Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6

Institute for Mechanical Systems Center of Mechanics ETH Zurich Department of Mechanical and Process Engineering
Prof. Dr. Edoardo Mazza
1
Useful rules for index notation
(i,j,k)=(123),(231),(312) (i,j,k)=(132),(213),(321) (all other combinations)
The per

Index Notation for Vector Calculus
by
Ilan Ben-Yaacov and Francesc Roig Copyright c 2006
Index notation, also commonly known as subscript notation or tensor notation, is an extremely useful tool for performing vector algebra. Consider the coordinate syste

CBE 6333, R. Levicky
1
Tensor Notation.
Engineers and scientists find it useful to have a general terminology to indicate how many directions are associated with a physical quantity such as temperature or velocity. A scalar, such as temperature, has no di

Strain Rate Tensor in Cylindrical Coordinates
u = velocity component in r direction v = velocity component in direction w = velocity component in z direction
( u u w u 1 v / r ) 1 1 + + r r r r 2 r z 2 1 v / r ) 1 ( u v v w 1 u 1 1 & + + = r + r r r r z 2

MMAE 510 Fall 2007 Rm ? E1 1:25 to 3:30 Test 1: In Class Open One Text Book Wednesday, August 29 Solve any 5 of following 9 problems; solve the rest as Homework due Wednesday Sept 5. Problem 1
Sketch your results. Problem 2
Problem 3
Problem 4
Problem 5
P

MMAE 510 Plan and Assignments for Fall 2010 (updated 9/19/2010)
Days we will not have a class: Monday - Sept. 6 (Labor Day) Monday - Oct. 11 (Fall Break) Wednesday - Nov. 24 (Day before Thanksgiving) Days we will have tests: Wednesday - Aug. 30 (Test 1) W