BME332quiz_+1_Solutions.pdf

BME332quiz_+1_Solutions.pdf - BME 332 Quiz 1 Index Notation...

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BME 332 Quiz 1, Index Notation Jan. 24, 2013 1. Consider the following second order derivative 2 ij kl W E E What is the tensorial order of this entity and many components does it have in 3D? Note that indicates a partial derivative. a. 4 th order tensor, 4 components b. 4 th order tensor, 16 components c. 4 th order tensor, 81 components d. 2 nd order tensor, 9 components Answer is C. There are four unique indices, so it is a 4 th order tensor 3 4 is 81. 2. The result of the following multiplication, im mj kj F S F is an entity B with the following indices: Answer is A. The unique indices are i and k, so these are transferred to the left hand side 3. If you wanted to write the equivalent matrix form for, im mj kj F S F which of the following would be correct (where the superscript T denotes transpose of the matrix): a.   F S F b.  T F S F c.
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