MATLAB Functions and Elementary Math Operations

Important Note: You must define a variable (assign it a value) before you can use it as an argument in a function. If you try to use an undefined variable, MATLAB will return an error: Undefined function or variable.

Built-in Functions

MATLAB comes equipped with a vast library of built-in functions that handle common mathematical tasks without requiring you to write the underlying logic yourself. These functions are categorized based on their mathematical purpose.

Elementary Math Functions

For standard arithmetic and algebraic operations, MATLAB provides several essential functions:

Elementary Trigonometric Functions

Trigonometric functions are vital for engineering and physics. MATLAB provides two ways to calculate these: using radians or using degrees.

• Radian-based functions: sin(x), cos(x), tan(x), and cot(x).
• Degree-based functions: sind(x), cosd(x), tand(x), and cotd(x).

Using the "d" suffix (e.g., sind) is a convenient way to avoid manually converting degrees to radians using the formula: $\text{radians} = \text{degrees} \cdot \frac{\pi}{180}$

Number Rounding Functions

When working with floating-point numbers, you often need to control the precision of your results. MATLAB offers several functions to manipulate how numbers are rounded:

1. round(x): Rounds $x$ to the nearest integer.
2. fix(x): Rounds $x$ towards zero (effectively "chopping off" the decimals).
3. ceil(x): Rounds $x$ towards positive infinity (the "ceiling").
4. floor(x): Rounds $x$ towards negative infinity (the "floor").
5. rem(x, y): Returns the remainder after $x$ is divided by $y$ (also known as the modulus).
6. sign(x): Returns $1$ if $x$ is positive, $-1$ if $x$ is negative, and $0$ if $x$ is zero.

Pro Tip: Because of how computers represent numbers in binary (floating-point precision), comparing two numbers with == can be unreliable due to tiny rounding errors. Instead of checking if x == y, it is much safer to check if the difference between them is very small: abs(x - y) < 0.0001

Summary of Mathematical Precedence

When combining functions with standard arithmetic operators, MATLAB follows a specific order of operations (precedence):

1. Parentheses: The innermost parentheses are evaluated first.
2. Exponentiation: Operations like ^ are performed next.
3. Multiplication and Division: These have equal precedence and are evaluated from left to right.
4. Addition and Subtraction: These are performed last.

By using parentheses effectively, you can override this default order to ensure your mathematical models are calculated correctly.