TEST BANK FOR Numerical Methods for Engineers By Steven C. Chapra

2.1
IF x < 10 THEN
IF x < 5 THEN
x = 5
ELSE
PRINT x
END IF
ELSE
DO
IF x < 50 EXIT
x = x - 5
END DO
END IF
2.2
Step 1: Start
Step 2: Initialize sum and count to zero
Step 3: Examine top card.
Step 4: If it says “end of data” proceed to step 9; otherwise, proceed to next step.
Step 5: Add value from top card to sum.
Step 6: Increase count by 1.
Step 7: Discard top card
Step 8: Return to Step 3.
Step 9: Is the count greater than zero?
If yes, proceed to step 10.
If no, proceed to step 11.
Step 10: Calculate average = sum/count
Step 11: End
2.3
start
sum = 0
count = 0
INPUT
value
value =
“end of data”
sum = sum + value
count = count + 1
T
F
count > 0
average = sum/count
end
T
F
2.4
Students could implement the subprogram in any number of languages. The following
Fortran 90 program is one example. It should be noted that the availability of complex
variables in Fortran 90, would allow this subroutine to be made even more concise.
However, we did not exploit this feature, in order to make the code more compatible with
Visual BASIC, MATLAB, etc.
PROGRAM Rootfind
IMPLICIT NONE
INTEGER::ier
REAL::a, b, c, r1, i1, r2, i2
DATA a,b,c/1.,5.,2./
CALL Roots(a, b, c, ier, r1, i1, r2, i2)
IF (ier .EQ. 0) THEN
PRINT *, r1,i1," i"
PRINT *, r2,i2," i"
ELSE
PRINT *, "No roots"
END IF
END
SUBROUTINE Roots(a, b, c, ier, r1, i1, r2, i2)
IMPLICIT NONE
INTEGER::ier
REAL::a, b, c, d, r1, i1, r2, i2
r1=0.
r2=0.
i1=0.
i2=0.
IF (a .EQ. 0.) THEN
IF (b <> 0) THEN
r1 = -c/b
ELSE
ier = 1
END IF
ELSE
d = b**2 - 4.*a*c
IF (d >= 0) THEN
r1 = (-b + SQRT(d))/(2*a)
r2 = (-b - SQRT(d))/(2*a)
ELSE
r1 = -b/(2*a)
r2 = r1
i1 = SQRT(ABS(d))/(2*a)
i2 = -i1
END IF
END IF
END
The answers for the 3 test cases are: (a) -0.438, -4.56; (b) 0.5; (c) -1.25 + 2.33i; -1.25 -
2.33i.
Several features of this subroutine bear mention:
· The subroutine does not involve input or output. Rather, information is passed in and out
via the arguments. This is often the preferred style, because the I/O is left to the
discretion of the programmer within the calling program.
· Note that an error code is passed (IER = 1) for the case where no roots are possible.
2.5 The development of the algorithm hinges on recognizing that the series approximation of the
sine can be represented concisely by the