As we've seen, in Matlab we can do calculations by simply typing them:

$2+2$

If we run this code we get the answer, which by default is called ans:

ans $=$

$4$

If we want to specify a name for it$,$ we can do so:

myresult $=2+2$

if we run this we get:

myresult $=$

$4$

If we put a semicolon at the end of the line the calculation is still performed but no output is given:

myresult $=2+2$;

If we run this then there will be no output but myresult will still equal $4.$

For example we can take myresult and add $3$:

myresult $=2+2$;

myresult $+3$

This will yield:

ans $=$

$7$

When we perform numerical calculations, by default Matlab shows us an approximate answer:

$1/7$

If we type this in and run it$,$ this gives us:

ans $=$

$0\mathrm{.}1429$

Variable Names

We need to be careful about how we name variables. Matlab will happily let us overwrite its own commands and then if we try to use these commands later we might be in for a surprise. Consider the code:

sin $=5$;

sin$(40)$

The result of executing this code will be:

Index exceeds the number of array elements $(1).$

'sin' appears to be both a function and a variable. If this is unintentional, use 'clear sin$\text{'}$ to remove the variable 'sin' from

the workspace.

Matlab is telling us that it's confused $-$ we assigned sin to be $5,$ thereby trashing the internal sin $($sine$)$ command, but then we tried to use sin as a function. Matlab can tell something is up$.$

An even more common mishap is that Matlab knows that the letter i represents the complex number $.$ If you just type i into the Code box:

i

And run it you'll get:

ans $=$

$0\mathrm{.}0000+1\mathrm{.}0000$i

However Matlab will happily let you overwrite this and forget it ever exists. The following line of code:

i $=10$

Will completely trash Matlab's knowledge of the complex number and any references to i from then on will use the number instead.

Getting Lots of Digits

We can get more digits by wrapping the answer in vpa, which stands for variable precision arithmetic. This gives us a lot more digits:

vpa$(1/7)$

ans $=$

$0\mathrm{.}14285714285714285714285714285714$

If we want, say, $10$ digits of precision, we can ask for it:

vpa$(1/7,10)$

Now we'll see, if we run this:

ans $=$

$0\mathrm{.}1428571429$

Matlab has other ways to handle approximations but vpa is good for now. It'll show up here and there throughout the assignments so remember if something is wrapped in vpa it's because we want to see lots of digits of output.

Some Common Mathematical Expressions

Here are some common mathematical functions in Matlab. One or two might be unfamiliar, and that's okay, but think about what they all are. Each is listed followed immediately by its result:

Code:

cos$($pi$/4)$

Result:

ans $=$

$0\mathrm{.}7071$

Code:

cosd$(30)$

Result:

ans $=$

$0\mathrm{.}8660$

Code:

sqrt$(5)$

Result:

ans $=$

$2\mathrm{.}2361$

Code:

log$(6)$

Result:

ans $=$

$1\mathrm{.}7918$

Code:

exp$(0\mathrm{.}2)$

Result:

ans $=$

$1\mathrm{.}2214$

Code:

asin$($sqrt$(2)/2)$

Result:

ans $=$

$0\mathrm{.}7854$

Code:

nthroot$(5,3)$

Result:

ans $=$

$1\mathrm{.}7100$

Code:

tanh$(3)$

Result:

ans $=$

$0\mathrm{.}9951$

Code:

abs$(-7\mathrm{.}3)$

Result:

ans $=$

$7\mathrm{.}3000$

Code:

factorial$(5)$

Result:

ans $=$

$120$

Code:

log$10(3)$

Result:

ans $=$

$0\mathrm{.}4771$

Code:

log$2(3)$

Result:

ans $=$

$1\mathrm{.}5850$

Errors

When you run or submit code pay close attention to any errors that might appear in red. While it's true that sometimes the errors that Matlab shows are confusing, more often than not they tell you exactly what the problem is$.$

For example before doing the assignment try typing and running and submitting the following snippets of code, one by one. Take a few minutes to see what Matlab is telling you in its error message. Type them exactly as they are as each has an error.

First:

$((3+2)/2+1$

Second:

x$=2$

$2$x$+3$

Third:

arcsin$(1/2)$

Comments

A percentage symbol $\%$ in Matlab indicates the beginning of a comment. Anything following a $\%$ will be ignored so you can start lines with $\%$ or put them at the end of lines. For example:

$\%$ Let's make x$=2$

x $=2$

$\%$ Now let's add $1.$

x $=$ x $+1\%$ Here x has been changed and will be $3.$

$\%$ Now Let's find the sine of pi$/7...$

sin$($pi$/7)$

Keey an eye out $-$ there will be comments here and there in the assignment descriptions so be aware that they're just comments helping to explain what's going on$.$

Note: If you're copying my code for testing you don't need to copy the comments $-$ they're completely ignored by Matlab! As soon as it sees a $\%$ it stops reading.