View source for Maple/Lesson 1: Getting Started

==Chapter 1: Getting Started with Maple==
===Before You Begin===
All the orders given to Maple are in the areas marked with >.<br>
These are the input areas.<br>
Press enter to give the software the order.

 >sample code;

The lines of code must end with either a semicolon or a colon. Note the difference between them:

 >p - ln( p );
<center><math>p-\ln  \left( p \right) </math></center>

 >p - ln (p ):

If the line of code ends with a semicolon, the order is validated and the software displays the answer in the output area. If the line of code ends with a colon, the order is validated, but the answer is not displayed.

===Simple computations with Maple===
 >(1-1/7)*(1+2/3)^2;
<center><math>{\frac {50}{21}}</math></center>
 > (25)^(1/2);
<center><math>5\,</math></center>
 >factorial(15);
<center><math>1307674368000\,</math></center>
 >15!;
<center><math>1307674368000\,</math></center>
 >sqrt(81);
<center><math>9\,</math></center>
 >sqrt(56.81);
<center><math>7.537240874\,</math></center>
 >%^2;
<center><math>56.81\,</math></center>

===Using variables with Maple===
You can affect a value to a variable. Here, 2.14 is affected to the ''p'' variable. We can then compute <math>p-\ln  \left( p \right) </math>.
 >p:=2.14;
<center><math>p:=2.14\,</math></center>
 >p - ln(p);
<center><math>1.379194171\,</math></center>
You can also use more than one variable in a single equation:
 >x := 2*a-p;
<center><math>x:=2\,a- 2.14</math></center>
 >x-sqrt(a*p);
<center><math>2\,a- 2.14- 1.462873884\,\sqrt {a}</math></center>
 >expr := a*x^2 + b*x + c = 0;
<center><math>expr:={a{x}} ^{2}+bx+c=0\,</math></center>

===Using functions with Maple===
Maple has a wide range of functions to help you manipulate mathematical expressions:
 >f := (a+b)^6;
<center><math>f:=\left (a+b\right )^{6}</math></center>
 >expand(f);
<center><math>{a}^{6}+6\,{a}^{5}b+15\,{a}^{4}{b}^{2}+20\,{a}^{3}{b}^{3}+15\,{a}^{2}{b}^{4}+6\,a{b}^{5}+{b}^{6}</math></center>
 >factor(%);
<center><math>\left (a+b\right )^{6}</math></center>
 >%%;
<center><math>{a}^{6}+6\,{a}^{5}b+15\,{a}^{4}{b}^{2}+20\,{a}^{3}{b}^{3}+15\,{a}^{2}{b}^{4}+6\,a{b}^{5}+{b}^{6}</math></center>
 >sin(x)^2+cos(x)^2;
<center><math>\left (\sin(x)\right )^{2}+\left (\cos(x)\right )^{2}</math></center>
 >simplify(%);
<center><math>1\,</math></center>
Here, the ''%'' symbol recalls the last computation made by Maple. ''%%'' means you recalls the computation made two steps back. To obtain the the computation made ''n'' steps back, repeat the ''%'' symbol ''n'' times.

You can also substitute variables in an expression with the ''subs()'' function:
 >subs(a=c, f);
<center><math>\left (c+b\right )^{6}</math></center>
 >subs(a=2, b=4/5, f);
<center><math>\frac{7529536}{15625}</math></center>

The ''evalf()'' function evaluates the numeric value of an expression. You may also specify the desired precision.
 >evalf(sqrt(3));
<center><math>1.732050808\,</math></center>
 >evalf(sqrt(3), 50);
<center><math>1.7320508075688772935274463415058723669428052538104\,</math></center>
 >evalf[50](sqrt(3));
<center><math>1.7320508075688772935274463415058723669428052538104\,</math></center>


''print()'', ''lprint()'' and ''printf()'' are functions used to display a mathematical expression. ''print()'' displays the expression normally, ''lprint()'' displays the function in Courier font and to the left of the screen and ''printf()'' is the same function used in C or C++ language, where you can display variables using formats: %d represents an integer variable, %f a floating number and \n breaks a line of text:
 >f:=a-3/a+1/(a*a+1);
<center><math>f:=a-\frac{3}{a}+\frac{1}{{a}^{2}+1}</math></center>
 >print(f);
<center><math>a-\frac{3}{a}+\frac{1}{{a}^{2}+1}</math></center>
 >lprint(f);
a-3/a+1/(a^2+1)<br>
 >printf("%d %f \n",123,1234/567); 
123 2.176367<br>

===Defining a function with Maple===
 >f := t -> sin(t) - t;
<center><math>f:=t\rightarrow \sin(t)-t</math></center>
 >f(3*x + 2);
<center><math>\sin(3\,x+2)-3\,x-2</math></center>
 >g:=(u,v,w)->1/u+exp(u+v)+(u-v+w)^2;
<center><math>g:=(u,v,w)\rightarrow \frac{1}{u}+{e^{u+v}}+\left (u-v+w\right )^{2}</math></center>
 >g(2*a,b,3*c);
<center><math>\frac{1}{2}\frac{1}{a}+{e^{2\,a+b}}+\left (2\,a-b+3\,c\right )^{2}</math></center>

===Calculus with Maple===
Maple can be used to find the integral of a given function. For example, to get the integral of the ''f(t)'' function according to ''t'' and the ''g(u,v,w)'' function according to ''v'', the following commands can be entered:
 >Int(f(t), t) = int(f(t), t);
<center><math>\int \!\sin(t)-t\,dt=-\cos(t)-\frac{1}{2}\,{t}^{2}</math></center>
 >Int(g(u,v,w), v) = int(g(u,v,w), v);
<center><math>\int \frac{1}{u}+e^{u+v}+u-v+w^{2}\,{dv}=\frac{v}{u}+
{e^{u+v}}-\frac{1}{3}(u-v+w)^{3}</math></center>
 >Int(f(t),t=0..Pi)=int(f(t),t=0..Pi);
<center><math>\int^{\pi}_{0}\sin(t)-t\,dt=2-\frac{1}{2}\pi^2</math></center>
<br>
Note the difference between ''Int()'' and ''int()''. The first one displays the integral while the latter computes it.

===Limits, sums and products with Maple===
You can also find numeric and symbolic values of sums, limits and products using respectively the functions ''sum()'', ''limit()'' and ''product()'':
 >limit((2*t-3)/(3*t+4),t=infinity);
<center><math>\frac{2}{3}</math></center>
 >limit((2*t-3)/(3*t+4),t=-4/3,right); #right-bound of the limit
<center><math>-\infty</math></center>
 Sum(i^2,i=1..10)=sum(i^2,i=1..10);
<center><math>\sum_{i=1}^{10}i^2=385</math></center>
 Product(1/i,i=1..10)=product(1/i,i=1..10);
<center><math>\prod_{i=1}^{10}\frac{1}{i}=\frac{1}{3628800}</math></center>
The functions ''Sum()'' and ''Product()'' only display a Sigma and a Pi symbol; they do not actually compute the sum or the product.

===Solving equations with Maple===
The ''solve(eqn,x)'' function tries to find the value of ''x'' in ''eqn''. You can also use more variables or more equations using ''solve({eqn1,eqn2,...},{x,y,...}):
 solve(2*t+3=-t+6*sqrt(2));
<center><math>-1+2\sqrt{2}</math></center>
 solve(t-15/4*u=5/2*(u-t)+3,u);
<center><math>\frac{14}{25}t-{12}{25}</math></center>
 solve({a-b=2,a+3*b=7},{a,b});
<center><math>\left\{a=\frac{13}{4},b=\frac{5}{4}\right\}</math></center>
Sometimes, the exact solution of an equation might not be found. You can then use the ''fsolve()'' to get a numerical approximation:
 fsolve(cos(t)=t);
<center><math>0.7390851332</math></center>
 fsolve({t^3+u=1,u-(t-1)^3=t},{t,u});
<center><math>\{t=0.6941457205, u=0.6655340191\}</math></center>

===Plotting functions with Maple===
To plot a ''f(x)'' function, use ''plot(f(x),x)'' function:
 plot(sin(t)/t,t=-20..20,title="function t ---> sin t / t");
<center>[[Image:Maple11.png]]</center>
 plot3d(x*exp(-x^2-y^2),x=-2..2,y=-2..2,color=x,orientation=[120,75]);
<center>[[Image:Maple12.png]]</center>
[[Category:Maple]]