# intro - MAPLE NOTES Exact arithmetic and basic functions...

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MAPLE NOTES Exact arithmetic and basic functions The basic arithmetic operations in MAPLE are + addition - subtraction * multiplication ^ or ** exponentiation / division MAPLE does integer arithmetic to "infinite" precision: > 2/3 + 3/5; 19 15 > 7 - 11/15; 94 15 > 12^20; 3833759992447475122176 > 12^20: > MAPLE input is entered to the right of the MAPLE prompt > and ends with a colon or semicolon. The input is executed after pressing enter (or return). If the semicolon is used the result is printed but with a colon it is executed but not printed.

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Click on the next line and press enter five times. > a:= 5^2 +12^2; > b:=13^2; > c:=a-b: > c; > sqrt(a); You should get something like: > a:= 5^2 +12^2; := a 169 > b:=13^2; := b 169 > c:=a-b: > c; 0 > sqrt(a); 13 Also notice the use of ":=" which the assignment operator. In the session above we used the command > a:=5^2+12^2; to assign the variable (or name) a the value of + 5 2 12 2 . MAPLE also has the basic mathematical functions (and much more) that are available on a scientific calculator. abs(x) absolute value x sqrt(x) square root x n! factorial
sin(x) sine cos(x) cosine tan(x) tangent sec(x) secant csc(x) cosecant cot(x) cotangent arcsin(x) inverse sine arctan(x) inverse tan arcsec(x) inverse sec log(x) ln(x) natural logarithm exp(x) exponential function e x sinh(x) hyperbolic sine cosh(x) hyperbolic cosine tanh(x) hyperbolic tan > tan(Pi/6); 3 3 > arcsin(1/2); π 6 NOTE: In MAPLE π is entered as Pi > evalf(Pi); 3.141592654 The evalf function returns floating point approximation. We can increase precision as follows:

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> evalf(Pi,50); 3.1415926535897932384626433832795028841971693993751 Algebra MAPLE can do algebra. It can manipulate polynomials and rational functions easily. > p:=x^2+5*x+6; := p + + x 2 5 x 6 > factor(p); ( ) + x 3 ( ) + x 2 > q:=1-x^7-x^8-x^9+x^15+x^16+x^17-x^24; := q - - - + + + - 1 x 7 x 8 x 9 x 15 x 16 x 17 x 24 > r:=factor(q); r ( ) + x 1 ( ) + x 2 1 ( ) + + x 2 x 1 ( ) + + x 6 x 3 1 ( ) + x 4 1 - := ( ) + + + + + + x 6 x 5 x 4 x 3 x 2 x 1 ( ) - x 1 3 > expand(r); - - - + + + - 1 x 7 x 8 x 9 x 15 x 16 x 17 x 24 MAPLE can solve and manipulate algebraic equations. > eqn:= x^2-x=1; := eqn = - x 2 x 1 Here we assigned the name eqn to the equation = - x 2 x 1. Now, we solve this equation for x. > R:=solve(eqn,x); := R , + 1 2 5 2 - 1 2 5 2 R is the list of two roots. R[1] gives first root and the root is R[2]:
+ 1 2 5 2 > R[2]; - 1 2 5 2 > expand(R[1]*R[2]); -1 We can check a root by substituting into the left side of the equation. To do this we use the subs function. > eqn; = - x 2 x 1 > lhs(eqn); - x 2 x > subs(x=R[1],lhs(eqn)); - - + 1 2 5 2 2 1 2 5 2 > expand(%); 1 Here % refers to the previous output. So we expanded the result of substituting x=R[1] into the left side of the equation which gave the result 1 as expected. Calculus

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intro - MAPLE NOTES Exact arithmetic and basic functions...

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