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# 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);
```

QUESTION 2: What is the derivative of ?

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));`

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

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]);`

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

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]);
```

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

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