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The semantic object model made it easy to study the classes that will make up the database and allowed some normalization. The entity-relationship model emphasized the entities relationships and made it easy to remove many-to-many associations. Now it s time to use what you ve learned by building the semantic object and entity-relationship models to create a relational model. Start by making a table for each of the models classes and entity sets. Look at the nal ER diagrams shown in Figures 12-8, 12-9, and 12-12, and make tables for the entities drawn in rectangles. The following list shows the tables that you need to create: CustomerCourses Customers Pets

For the table you built for Exercise 2:

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The material of all trains in D3 needs to be positioned at the sidings during the night. Since D3 is the largest set, the last planning period is the tightest one. Main Routine. Now that the pre-processing steps are done, the heuristic searches for a good positioning and matching of all arriving and departing trains. Starting with the subproblem of planning period 3, it solves in a backward fashion until the overall shunting problem is solved. Below we summarize the steps performed by the heuristic: Step 1. Generating a blueprint for planning period 3 of all trains in D3. Step 2. Matching the arriving trains in A3 onto the blueprint of planning period 3. Step 3. Copying the unmatched part of the blueprint of planning period 3 to an initial blueprint of planning period 2. Step 4. Completing the blueprint of planning period 2 by adding the trains in D2 to it. Step 5. Matching the arriving trains in A2 onto the blueprint of planning period 2. Step 6. Copying the unmatched part of the blueprint of planning period 2 to an initial blueprint of planning period 1. Step 7. Completing the blueprint of planning period 1 by adding the trains in D1 to it. Step 8. Matching the arriving trains in A1 onto the blueprint of planning period 1. Stop: Since all arriving and departing trains are matched and positioned on the tracks. Figure 16.12 illustrates the working of the heuristic by visualizing the results of every step. Blocks without a border are positions reserved for departing train

Object databases don t work well if: Your program needs to interact with external tools where storing the data in a more common format such as a relational database is an advantage. You need to perform complicated queries that will execute faster in a relational database. You aren t using an object-oriented language (for example, if a Microsoft Access database can do everything you need without any programming). You need to perform data validations that the object database cannot provide.

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We can say more about the accuracy of the Euler method: Theorem 10.2: For dx(t)/dt = f (x(t), t) let f (x(t), t) be Lipschitz continuous with constant (De nition 10.1), and assume that x(t) C 2 [t0 , tf ] (tf > t0 ). If xn x(tn ) = xn , where (tn = t0 + nh, and tn tf ) xn+1 = xn + hf (xn , tn ), (x0 x(t0 )) then e (tn t0 ) 1 1 , |x(tn ) xn | e (tn t0 ) |x(t0 ) x0 | + hM 2 where M = maxt [t0 ,tf ] |x (2) (t)|. Proof Euler s method is xn+1 = xn + hf (xn , tn ) and from Taylor s theorem x(tn+1 ) = x(tn ) + hx (1) (tn ) + 1 h2 x (2) ( n ) 2 for some n [tn , tn+1 ]. Thus x(tn+1 ) xn+1 = x(tn ) xn + h[x (1) (tn ) f (xn , tn )] + 1 h2 x (2) ( n ) 2 = x(tn ) xn + h[f (x(tn ), tn ) f (xn , tn )] + 1 h2 x (2) ( n ) 2 so that |x(tn+1 ) xn+1 | |x(tn ) xn | + h|x(tn ) xn | + 1 h2 |x (2) ( n )|. 2 For convenience we will let en = |x(tn ) xn |, = 1 + h, and rn = 1 h2 x (2) ( n ), 2 so that en+1 en + rn . It is easy to see that3 e1 e2 e3 . . . e0 + r0 e1 + r1 = 2 e0 + r0 + r1 e2 + r2 = 3 e0 + 2 r0 + r1 + r2 .

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