Computing for Calculus by Mark J. Christensen (Auth.)

By Mark J. Christensen (Auth.)

Educational Press provides Mark J. Christensen's Computing for Calculus (in paperback), released in 1981

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There is often an upper limit to the size of Thus, if you nest too many subroutines the stack will overflow producing an error. 3) using subroutines. Handle each of the special cases with subroutines. 2 Function definitions can be altered in a subroutine. For example the two line subroutine: 2000 DEF FNF(X) = SIN(X) 2010 RETURN Using this idea, write a program that computes FNF(X) and FNF(2X) for X=0,l,2,3,4 and 5, where FNF can be any of the functions: SIN, COS, TAN, SEC, CSC or COT. 3 Write a subroutine that removes common factors from the numerator of a fraction P/Q.

Also, when we need to perform a particular task at several different places in a program we can use the GOSUB statement. For a simple example, suppose that we will need to find the maximum of two numbers at several different points in a program. This can be accomplished by the following statements, 1000 M9=X 1010 IF Y>M9 THEN M9=Y A simple usage of this set of operations is in the following program. 100 PRINT "WHAT IS X" 110 INPUT X 120 PRINT "WHAT IS Y"; 130 INPUT Y 140 GOSUB 1000 150 PRINT "THE MAXIMUM OF ";X;" AND ";Υ;" IS ";M9 160 STOP 1000 M9=X 1010 IF Y>M9 THEN M9=Y 1020 RETURN 1030 END Notice that the statements that find the maximum of X and Y actually come after the STOP statement.

12 THE IF AND GOTO STATEMENTS: DECISIONS, DECISIONS does not send us to line 700 and instead it then calculates the discriminant B*B - 4*A*C. Once the discriminant (D) has been calculated the three IF state­ ments decide, based on the value of D, which of the three remaining portions of the program BASIC should jump to. goes to line 300. If D is greater than zero then the program Lines 300 through 370 print out the necessary messages telling us that there will be two real roots and then prints out the roots.

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