Chapter1exercises - AE 221 Aerospace Structures II Spring...

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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 0 , where ( ) < = 0 0 0 x x 1 x x 0 x x for for stp is the so-called 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 0 , for 2 1 0 a , , = . You may also make up a title and axis-labels. 3. Compute [ ] ( ) ( ) dx a x f x a x f 2 1 L a g L 0 2 2 + = , , , , where ( ) a x f , has been defined in problem 2. Plot [ ] 1 L 3 a 0 g = , . 4. Solve the following linear system = 2 3 2 1 4 2 2 2 L 4 L 2 0 C C C L 3 0 L 2 0 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 0 Boundary conditions: ( ) ( ) ( ) ( ) 0 1 w 0 1 w 1 0 w 0 0 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 π z 0 3 y 1 , 7. Let ij δ be the identity tensor. Show that
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