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Next: Plotting with Maple Up: Maple for Vector Previous: Basic Maple Syntax

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.

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);

QUESTION 2: What is the derivative of ?

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);

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));

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

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

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

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);.

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

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]);

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]);

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]);

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]);

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]);

next up previous
Next: Plotting with Maple Up: Maple for Vector Previous: Basic Maple Syntax

Bob Hesse
Wed Oct 23 21:17:40 CDT 1996