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Unformatted text preview: AE 221 Aerospace Structures II Spring 2004 Chapter 1 Review Practice Problems Using the package(s) of your choice (Mathematica, Maple, Matlab, Gnuplot, ), solve the following problems, which are typical of those you will face in AE 221. 1. Plot ( ) 4 x 6 2 / 1 x x 3 x 2 3 + + + stp on 1 x , where ( ) < = x x 1 x x x x for for stp is the socalled Heavyside (step) function. 2. Plot (on the same graph and with the appropriate legends for the three curves), ( ) ( ) ( ) x a x x 3 a x f cos sin , + = on 1 x , for 2 1 a , , = . You may also make up a title and axislabels. 3. Compute [ ] ( ) ( ) dx a x f x a x f 2 1 L a g L 2 2 + = , , , , where ( ) a x f , has been defined in problem 2. Plot [ ] 1 L 3 a g = , . 4. Solve the following linear system = 2 3 2 1 4 2 2 2 L 4 L 2 C C C L 3 L 2 L 2 L 3 L 2 L 3 1 5. Solve the following boundary value problem and plot the solution Differential equation: ( ) ( ) 3 x x w 4 + = on 1 x Boundary conditions: ( ) ( ) ( ) ( ) 1 w 1 w 1 w w = = = = ' ' , , ' , 6. Plot (from an appropriate angle and with appropriate resolution) ( ) ( ) ( ) z 5 e 2 z yz 2 z y q y cos sin , + = on z 3 y 1 , 7. Let ij be the identity tensor. Show that a) 3 ii = b) 3 ij ij = c) ik jk ij = 8. Let ij...
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This note was uploaded on 01/18/2010 for the course AE 322 taught by Professor Lambros during the Spring '04 term at University of Illinois at Urbana–Champaign.
 Spring '04
 Lambros

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