This document discusses using calculus in programming. It provides examples of defining functions in functional programming languages like Scheme. It discusses evaluating expressions by replacing formal parameters with actual parameters. An example program in C++ is provided that calculates the derivative of an expression using the power rule.

1. Introduction of calculus
in programming
Is it possible to write calculus function for c.
It would be very useful, I am sure it is possible because
there are math programs out there today

2. Use of calculus in programming
 A program in a functional language is a set of function definitions and an
expression usually
 formed using the defined functions. The Interpreter of the language evaluates this
expression by
 means of a discrete number of computation steps, in such a way its meaning turns
out to be
 represented in an explicit way. In general in programming we have not to produce
anything; in
 functional programming, in particular, what we modify is only the representation
of the
 information.
 A function can be defined in several ways.

3. Example:
 f: R -> R , g: R -> R
 f '' - 6g' = 6 sin x
 6g'' + a2 f ' = 6 cos x
 f(0) = 0, f '(0) = 0, g(0) = 1, g'(0) = 1
 This set of equations precisely identify two precise f and g.

4. To evaluate an expression in Scheme
 the application of a function to some arguments and then to evaluate the body of the
function
 in which the formal parameter is replaced by the actual parameter. In this way, in a
sense, we
 make the meaning of such sub-expression more explicit.

5. Example: let us evaluate Inctwo 3
 Inctwo 3 Inctwo is a user defined function, and it is applied to an argument, so we take
the
 body of the function, replace the formal parameter n by the actual parameter 3,
obtaining
 3+2, and then we evaluate 3+2 obtaining 5

6. evaluation strategy
 a policy enabling to decide on which sub-expression we shall perform the next
evaluation step.
 Some evaluation strategies could led me in a never ending path (this fact is
unavoidable)

7. Uses of calculus in
‘c++’ Language
#include<iostream.h>
Using name space std;
Int a,x,n,derivative;
Int main()
{
Cout<<”hellow.i am a computer program.I can calculate
the derivative of an expression using power rule.”;
Cout<<”n please type the values of a and n for use exp”;
Cout<<”n y=ax^n”;
Cin get();
Cout<<”a=?n”;
Cin>>a;
Cout<<”x=?,n=?n”
Cin>>x,n;
Derivative=a*n*(x^(n-1));
Cout<<”dy/dx=”<<derivative;
Return 0;
}

8. Thanks…………….
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