Fortran    Programming  Lect.5                                               2nd-2019-2020 
                 Example:: Write a program from the following series and print (S) where
                 the difference between any two term is (5*10−5)as absolute value:
                  3     2    πxx 4     2πxx  6    3πxx 8    4πxx
                 s =1− cos      + cos      − cos      + cos      −……
                        3     2  5      2    7     2   9      2
                 sol:
                       Real  I,J
                       Read *,x
                      y=1.0; k=-1;J=2;I=1
                      Z=(3.14*X)/2.0
                 10  T=J/(J+1) *COS(I*Z)
                      IF(ABS(T).LE.5E-5)     GO TO 30
                      Y=Y+K*T
                      K=-K
                      I=I+1
                      J=J+2
                      GO TO 10 
                 30  S=Y**(1.0/3.0)
                       WRITE(*,20)  X,S
                 20  FORMAT (2X,F10.4,F10.4)
                       STOP
                       END
                 EXAMPLE: Write a program from the following series and print (S) where
                 the maximum of term is (2*10-3      −5)as absolute value:
                                                   10
                  Fortran    Programming  Lect.5                                               2nd-2019-2020 
                          7           5           3
                         x sin10πxx  x sin7πxx  x sin 4πxx
                  s=6−             +          −           +………………
                             2         2∗4        2∗4∗6
                  sol:
                      L=10 ;J=7;S=6.0;K=-1;N=2
                      READ *,X
                      Z=3.14*X
                  20 F=1;I=2
                  10 IF(I.LE.N) THEN
                        F=F*I
                        I=I+2
                         GO TO 10
                  END IF
                       T=X**J*SIN(L*Z)/F
                       IF (ABS(T).LE.2E-3)  GO TO 30
                      S=S+K*T
                      K=-K
                      L=L-3
                      N=N+2
                  GO TO 20
                  30 WRITE(*,40)  X,S
                  40  FORMAT(5X,'X=',F8.3,/,5X,'S=',E16.8)
                        STOP
                         END
       Fortran    Programming  Lect.5                                               2nd-2019-2020 
              8. Loops
       For repeated execution of similar things, loops are used. If you are familiar
       with other programming languages you have probably heard about for-loops,
       while-loops, and until-loops. 
         8.1 Do-loops
       The do-loop is used for simple counting. Here is a simple example that
       prints the cumulative sums of the integers from 1 through n (assume n has
       been assigned a value elsewhere): 
             integer i, n, sum
             sum = 0
             do 10 i = 1, n
                sum = sum + i
                write(*,*) 'i =', i
                write(*,*) 'sum =', sum
         10  continue
       The numerical value of statement labels have no significance, so any integer
       numbers can be used. Typically, most programmers increment labels by 10
       at a time. 
       The variable defined in the do-statement is incremented by 1 by default.
       However, you can define any other integer to be the step. This program
       segment prints the even numbers between 1 and 10 in decreasing order: 
             integer i
             do 20 i = 10, 1, -2
                write(*,*) 'i =', i
       Fortran    Programming  Lect.5                                               2nd-2019-2020 
         20  continue
       The general form of the do loop is as follows: 
             do label  var =  expr1, expr2, expr3
                statements
       label continue
       var is the loop variable (often called the loop index) which must be integer.
       expr1 specifies the initial value of var, expr2 is the terminating bound, and
       expr3 is the increment (step). 
       Note: The do-loop variable must never be changed by other statements
       within the loop! This will cause great confusion.