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# Basic Mathematical Operations

Based on: Using MATLAB by Anders Gjendemsjø

Summary: This module covers basic mathematical operations in an m-file environment.

## Operations and Expressions

An m-file environment has all of the standard arithmetic operations (addition, subtraction, etc.) and functions (sine, cosine, logarithm, etc.). The table 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.)

Table 1: Some Common Scalar Mathematical Operations
Operation m-file
xyxy x-y
x+yxy x+y
xyxy x*y
xyxy x/y
xyxy x^y
exex exp(x)
log10xlog10x log10(x)
lnxlnx log(x)
log2xlog2x log2(x)
cosxx cos(x)
sinxx sin(x)
xx sqrt(x)

Expressions are formed from numbers, variables, and these operations. 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

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

Table 2: Example Expressions
formula MATLAB Expression Computed Value
52+42 52 42 5^2+4^2 41
5+42 54 2 (5+4)^2 81
2+345 23 45 (2 + 3)/(4 - 5) -5
log10100 log10 100 log10(100) 2
ln4×(2+3) ln 4 23 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

Splitting the expression 2+345 23 45 over multiple lines.


(2+3)...
/(4-5)


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