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refcard - Math 215(Calculus III General Description Command...

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Math 215 (Calculus III) Maple Quick Reference Card The University of Michigan, Ann Arbor General Maple Example Description command Input Output Basic mathematical operations and constants Command termination ; >2+2; 4 Suppressing output : >2+2: Math operations ( never omit the multiplication symbol) +, -, *, / >2*3+9^2; >33/6; 87 11 2 Conversion to decimals evalf() >evalf(33/6); 5 . 500000000 π Pi >evalf(Pi); 3 . 141592654 e exp(1) >evalf(exp(1)); 2 . 718281828 Elementary functions x, sin( x ) , cos( x ) , e x , ln( x ), etc. sqrt(x), sin(x), cos(x), exp(x), ln(x),... >sqrt(18); >evalf(sqrt(18)); >sin(3*Pi/4); >arcsin(sqrt(2)/2); 3 2 4 . 242640686 1 2 2 1 4 π Defining your own functions and expressions Expressions := >y:=x^2; >y; >eval(y, { x=2 } ); >subs( { x=-3 } ,y); x 2 x 2 4 9 Functions -> >f:=x->x^2; >f(x); >f(4); x 2 x 2 16 Differentiation and integration Differentiation diff >diff(x^2,x); >diff(x^2 + y^3,x); >diff(x^2 + y^3,y); 2 x 2 x 3 y 2 Integration int >int(sin(x),x); - cos( x ) Definite: π 0 x sin x dx >int(x*sin(x),x=0..Pi); π Iterated: 1 0 x 2 0 y dy dx >int(int(y,y=0..x^2),x=0..1); 1 10 Solving equations and systems of equations Equations solve >solve(x^2=4,x); 2 , - 2 Systems: x + y = 3 x - y = 7 >solve( { x+y=3,x-y=7 } , { x,y } ); { x = 5 , y = - 2 } Defining the intervals of change of variables (for plotting, integration, etc) a x b .. >x:=a..b; a..b Working with packages (e.g., many plotting functions are in the plots package) Including the plots package with

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