Mathematica
Tutorial Q's(next class)

There's an excellent article on mathematica on the web. Go to

http://www.maths.tcd.ie/ richardt/1S3/

and click on notes.
Mathematica is available on the maths systems(Seems to run on salmon but not walton) and on PC's and Mac's around college.
It has a very good help.
We'll look at some of its features which include:
- Factorising: polynomials, for example x²+2x+1 = (x+1)² or integers as in 6 = {{2,1},{3,1}}. Here would type
```
FactorInteger[457890]
```
  and then press enter, on the bottom right of the keyboard where the numbers are AND NOT return. This produces
```
{{2, 1}, {3, 1}, {5, 1}, {15263, 1}}
```
  as output.
- Solving equations both symbolically and numerically. Sybolically means that by manipulating the variables like a person would. Numerically means by trying (systematically) loads of numbers till you get one that works (get close enough to the solution).
  Here I typed in
```
Solve[x^3 + 2x + 1 == 0, x]
```
  Note the x after the comma at the end since that is what i want to find. Also have == and not =. This produces the horrible with many square roots. So if I just use NSolve, same as above except add an N. This gives me something like:
```
{{x -> -0.453398},
{x -> 0.226699 - 1.46771 i},
{x -> 0.226699 + 1.46771 i}}
```
- Differentiation, for example typing in
  
  D[x²+2x+Sin[x],x]
  
  give
  
  2+2x+Cos[x]
  
  Note that you have to type Sin and not sin. Also square brackets are used after Sin. Finally you need ,x to tell it to differentiate with respect to x.
- Integration, for example we get
  
  Integrate[x²,x] = x³
  3
  .
- Performing various other tasks such as:
  - Solving differential equations.
  - Plotting functions.
  - Defining our own functions.
  - Working with vectors and matrices.
There are tutorials on I think, which rotate between classes. So will give out some questions for you to look at for them in the next class on Friday.

File translated from T_EX by T_TH, version 2.70.
On 1 Nov 2002, 09:58.