MATLABit
MATLAB stands for MATrix LABoratory. It’s a powerful programming language and software tool created by MathWorks. Its extensive application across engineering, scientific research, academic instruction, and algorithmic design stems from its strengths in numerical computation, data analysis, graphical visualization, and simulation. With a foundation in matrix algebra, MATLAB efficiently manages large datasets and complex mathematical models. Thus, we are well-positioned to commence our exploration of its capabilities. So, let's get started using MATLAB as a calculator.
Table of Contents
Mathematical Operations
In this chapter, we focus exclusively on arithmetic operations with scalars, which are simply numbers.
Scalars can be used in calculations in two ways:
- Directly, just like you would on a calculator
- Through variables, where numbers are first assigned to variables and then used in expressions
Below is a list of common arithmetic operations along with their symbols and examples. These operations are similar to what you'd find on most calculators, except for left division, which is used primarily in array operations.
| Operation | Symbol | Example | Description |
|---|---|---|---|
| Addition | + | 8 + 2 | Adds two numbers |
| Subtraction | - | 10 - 4 | Subtracts second number from the first |
| Multiplication | * | 6 * 7 | Multiplies two numbers |
| Right Division | / | 12 / 4 | Divides 12 by 4 (normal division) |
| Left Division | \ | 12 \ 4 | Equivalent to 4 / 12 (inverse of right division for scalars) |
| Exponentiation | ^ | 3 ^ 4 | Raises 3 to the power of 4 (i.e., 3⁴ = 81) |
Order of Precedence
MATLAB follows a specific order when executing arithmetic operations. This order of precedence is similar to what is used in most standard calculators. The table below outlines the order in which MATLAB evaluates expressions:
| Precedence Level | Mathematical Operation | Description |
|---|---|---|
| First | Parentheses | Expressions within parentheses are evaluated first. For nested parentheses, the innermost set is evaluated first. |
| Second | Exponentiation | Operations using exponents (e.g., ^) are evaluated after parentheses. |
| Third | Multiplication and Division | Both have equal precedence and are evaluated from left to right. |
| Fourth | Addition and Subtraction | These operations have the lowest precedence and are also evaluated from left to right. |
When an expression has more than one operation, the ones with higher precedence are done first. If two or more operations have the same level of precedence, MATLAB evaluates them from **left to right**.
Applications
The output appears on the next line, typically starting with
ans =, which stands for "answer." This is the default variable MATLAB uses to store the result if no specific variable name is provided.
For example, if you type
3 + 5 and press Enter, MATLAB will respond with:
ans = 8
| Expression | Explanation | Result |
|---|---|---|
| 10 + 6 / 2 | 6 / 2 is evaluated first, then added to 10 |
13 |
| (10 + 6) / 2 | 10 + 6 is grouped and added first, then divided |
8 |
| 3 + 6 / 2 + 4 | 6 / 2 is done first, then the additions left to right |
10 |
| 4 ^ 3 / 2 | 4^3 = 64 is done first, then divided by 2 |
32 |
| 64 ^ (1/3) + 25 ^ 0.5 | Cube root of 64 and square root of 25 are calculated, then added | 4 + 5 = 9 |
| 64 ^ 1/3 + 25 ^ 0.5 | 64 ^ 1 then divided by 3 (wrong precedence) |
21.3333 |
| 0.5 - (0.5)^3 / (1*2*3) + 0.5^5 / (1*2*3*4*5) | Each term is evaluated using powers and factorials | ≈ 0.4792 |
✨Conclusion
- 😊 MATLAB as a calculator: The Command Window allows you to do direct calculations, just like with a standard calculator.
- 😊 The order of operations in MATLAB is as follows: Brackets or grouping "()", Powers ".^" , Multiplication "✖️" & Division "➗", then Addition "➕" & Subtraction "➖".
- 😊 Use of variables: Expressions can involve direct numbers or stored variables for better flexibility and reuse.
- 😊 Left vs Right Division: Remember, `5 / 3` is normal division, while `5 \ 3` gives the inverse.
- 🙁 Common Mistake: Forgetting parentheses can lead to wrong results due to precedence rules—always double-check!
- 😊 Practice makes perfect: Try more expressions and use the Command Window to observe how MATLAB evaluates them step-by-step.
With these fundamentals in mind, you're now equipped to start exploring MATLAB more confidently and effectively. 🎯
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