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# 3.1: Basic Mathematical Operations

Difficulty Level: At Grade Created by: CK-12

## Operations and Expressions

An m-file environment has all of the standard arithmetic operations (addition, subtraction, etc.) and functions (sine, cosine, logarithm, etc.). Table 1 lists the most commonly used operations; in this table, $x$ and $y$ are scalars. (A scalar is a single value, as opposed to a vector or matrix which consists of many values.)

Some Common Scalar Mathematical Operations.
Operation m-file
$x - y$
x - y

$x + y$
x + y

$xy$
x*y

$\tfrac{x}{y}$
x/y

$x^y$
x^y

$e^x$
exp(x)

$\log_{10}(x)$
log10(x)

$\ln(x)$
log(x)

$\log_2(x)$
log2(x)

$\cos(x)$
cos(x)

$\sin(x)$
sin(x)

$\sqrt{x}$
sqrt(x)


Expressions are formed from numbers, variables, and these perations. The operations have different precedences. The

^


operation has the highest precedence;

^


operations are evaluated before any other operations. Multiplication and division have the next highest precedence, and addition and subtraction have the lowest precedence. Precedence is altered by parentheses; expressions within parentheses are evaluated before expressions outside parentheses.

Example 1

Table 2 below shows several mathematical formulas, the corresponding expressions, and the values that are computed for the expressions.

Example Expressions
formula MATLAB Expression Computed Value
$5^2 + 4^2$
5^2+4^2

41

$(5 + 4)^2$
(5+4)^2

81

$\tfrac{2+3}{4-5}$
(2 + 3)/(4 - 5)

$\log_{10}(100)$
log10(100)

2

$\ln(4(2 + 3))$
log(4*(2 + 3))

2.9957


## Useful Tricks

These tricks are occasionally useful, especially when you begin programming with m-files.

• A semicolon added at the end of a line suppresses the output.
• Often it is useful to split input over multiple lines. To split a statement across multiple lines, enter three periods ... at the end of the line to indicate it continues on the next line.

Example 2

You could split the expression $\tfrac{2+3}{4-5}$ over multiple lines as follows:
(2+3)...

/(4-5)


Feb 23, 2012

Sep 15, 2014