Some useful Maple commands

The following commands are briefly summarized for your use. For further information about any of these commands, as well as examples of their usage, use the on-line Help Browser or type ?commandname. Note: The plotting commands we will be using are described in the next section.

diff

This command is used to compute the (partial) derivative of a function. To differentiate an expression f with respect to the variables x1, x2, , xn use

     diff(f, x1, x2, ..., xn);

For example, the derivative of is computed by

     diff( x^3-3*x^2 - sin(Pi*x), x);

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QUESTION 2: What is the derivative of ?

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evalf

This command is used to evaluate a symbolic expression numerically to n digits accuracy.

     evalf(expr, n);

For example, evalf( 1 + (Pi/12)^21, 20);

int

This command can be used to calculate the indefinite or definite integral of an expression f with respect to a variable x. To compute the indefinite integral use

     int(f, x);

To compute the definite integral use

     int(f, x=a..b);

To numerically evaluate the definite integral , use

     evalf(Int(f, x=a..b));

For example, the indefinite integral of is int(x*sin(x^2), x); while a definite integral is int(x*sin(x^2), x=0..sqrt(Pi));

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QUESTION 3: What is the exact value of ? What is approximate numerical value?

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limit

This command computes the limit of f as x approaches a.

  
     limit(f,x=a);

simplify

This command simplifies the expression entered. It has several options associated to it.

     simplify(expr);

For example, simplify( (x+3)^3 - (x-3)^3 );

solve, fsolve

These commands can be used to solve an equation or set of equations for a variable or set of variables. The fsolve command solves the equations numerically for real solutions, whereas solve may give complex numbers as solutions. The syntax is

     solve({equations},{variables});
     fsolve({equations},{variables});

For example, solve( {x-y=3, 3*x-2*y=-1}, {x,y} ); will solve for values of x and y that satisfy the two equations. The fsolve command sometimes doesn't find all of the roots of an equation. If you know how many roots you expect to find, you can use the option fsolve( -4*x^3 + 4*x + 1, x, maxsols=3 );

subs

This is a powerful command that enables you to substitute in a value (or a new expression) for some portion of an expression. The syntax is

     subs(subexpression=newexpression, expression );

For example, if you want to evaluate the expression when x=3: subs(x=3, x^3-4*x-1 ); Or if you want to substitute a more complicated expression (perhaps x is parametrized by : subs(x=sin(t), x^3-4*x-1 );

Linear Algebra The following commands are found in the package linalg. In order to use these commands, you should load the package linalg using the command with(linalg);.

vector

To enter a vector of length m with entries in a list use

     vector(m,[list]);

If you omit the parameter m, a vector is created of length equal to the number of elements on the list. If you eliminate the list parameter, Maple creates a vector of length m with no predefined elements. For example, vector([1,2,3]) sets up the vector with components . Often we can shorten this notation (see the next example) since many operations on vectors accept lists.

crossprod

This command computes the cross product of two vectors of length 3. To compute the cross product of the vectors u and v use

 
     crossprod(u, v);

For example, crossprod([1,2,3], [4,5,6]);

dotprod

This command computes the dot product of two vectors of length n. To compute the dot product of the vectors u and v use

 
     dotprod(u, v);

For example, dotprod([1,2,3], [4,5,6]);

grad

This command computes the gradient of a scalar function of several variables. For example, to compute the gradient of the function use

 
     grad(x^2+x*y*z, [x,y,z]);

diverge

This command computes the divergence of a vector field. For example, to compute the divergence of the vector field , use

 
     diverge([x,x*y,x*z], [x,y,z]);

curl

This command computes the curl of a vector field. for example, to compute the curl of the vector field , use

 
     curl([x,x*y,x*z], [x,y,z]);