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where xb(n) is the amount borrowed in the nth month and xp(n) is the amount paid in the nth month. Combining terms, we have y(n) - vy(r - 1) = xh(n) - x,,(n) = x(n) and x(n) is the net amount of money in the nth month that leaves the bank. Because where v = I B = 1 a principal of p dollars is borrowed during month zero, and payments of d dollars begin with month I, the driving function, x(n), is x(n) = .wh(n)- .u,,(n) = p8(n) - du(n - 1) and the difference equation for y(n) becomes

will advance the locator variable p to the next node, as shown in Figure 3.15. This same assignment can thus be executed as many times as is needed to advance through the linked list.

+ 9,

advances through the nodes of a linked list just as i advances through the elements of an array. Consequently, it is natural to use p in a for loop, just as we would use the array index i. For example, compare Example 3.7 with Example 3.8.

CHAP. I]

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Example 3.5 shows how we could have used this technique to build the linked list in the first place. EXAMPLE 3.5 Constructing a Linked List

1 2 3

Because we are assuming zero initial conditions, y(- 1) = 0, and because the input consists of a linear combination of a scaled unit sample and a scaled delayed step, the solution to the difference equation is simply

where h(n) and s(n) are the unit sample and unit step response, respectively. To find the unit sample response, we write the difference equation in the form

1 2 3 4

for (Node p = start; p != null; p = p.next) { System.out.println(p.data); }

and the homogeneous solution is y(n)=Avn n>O Because the input x(n) = S(n) is equal to zero for n > 0, the particular solution is zero (all that the unit sample does is set the initial condition at n = 0). Evaluating the difference equation at n = 0, we have

The step response may now be found by convolving h(n) with u(n):

start = new Node(22); Node p=start; p.next = new Node(33); p = p.next;

for (int i=0; i < n; i++) { System.out.println(a[i]); 3 } In both listings, the for loop prints one element on each iteration. The for statement has a three-part control mechanism. The first part declares the control variable (p for the list, i for the array) and initializes

We now want to find the value of d so thal after 360 equal monthly payments the mortgage is paid off. In other words. we want to find d such that

With v = % and p = 100,000, we have d = 877.57 The total payment to the bank after 30 years is C = (877.57)(360) = 315,925.20

CHAP. 3]

it to the first element:

Every second, each a particle within a reactor splits into eight P particles and each , 3 particle splits into L Y an L particle and two P particles. Schematically,

5 6 7 8 9

a+8P P-a+2/3

The second part gives the continuation condition, asserting that there are more elements:

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