1 DIFFERENTIAL EQUATIONS.
MAPLE can solve many of the differential equations that one finds in Calculus books. The basic command is dsolve. This requires two arguments, the first should be the differential equation you want to solve, and the second the variable you want to solve for. There are a variety of extra options that we won't go into here. However, if the differential equation has initial conditions, then these extra equations go together with the first argument (the differential equation) and one puts everything together as a set of equations inside curly brackets .
Example. To solve the differential equation (this is # 5 from §6.5 of E & P).
If, now, you want to get explicitly as a function of then you can try:
> y(x) = solve(%,y(x));
For initial conditions the commands are as follows.
§6.5 # 15 (you have # 14 for the assignment) Solve the differential equation:
Just to remind you from last week, the command for indefinite integration is
> int(f(x), x);
but this does NOT give you an arbitrary constant at the end (you must supply that). For definite integration, the command is
> int(f(x), x=a..b);
Note that in both of these, is an expression.
MAPLE will try and do the definite integral symbolically and give an exact answer. If it cannot do so, it will return the expression for the integral. To evaluate integrals exactly, use > value(.); to get a decimal approximation use > evalf(.);
NAME STUDENT #
Before you start these exercises type
You are now in a position to use MAPLE to do your assignments if you wish. If
you do so, please indicate that that is what you have done, and give your MAPLE
command, by writing
``MAPLE command: > ''
followed by ``To which MAPLE gives ''
I don't have a lot of time to cover all the methods of integration in Chapter 9. However, MAPLE knows how to do most of them. To illustrate this the tutorial this week is to do a sample of integrals from various sections of Chapter 9 that we have not covered.
Use MAPLE to evaluate the following integrals. After getting an answer, CHECK it by differentiation ( > diff(%,x); and, if necessary, > simplify(%); or > simplify(%,trig);).
1. # 9 p.517
2. # 17 p.524
3. # 35 p.524
4. The book states the following: ``An advertisement for a symbolic algebra program claims that an engineer worked for three weeks on the following integral and never got the same answer twice''. May be the ad was for MAPLE.
# 63 p.525 . DON'T write out the solution!!! Instead evaluate (to 4 decimal places) the definite integral from 1 to 2 when and .
5. # 11 p.532
6. # 13 p.532
7. # 5 p.540
8. # 9 p.540
9. #5 p.547
10. #11 p.547