Introduction to MATLAB

Introduction to MATLAB

• MATLAB is a powerful tool for analyzing and designing electronic systems using computers.
• It is widely used in engineering curricula and industry for system design and simulation.
• MATLAB stands for Matrix Laboratory, reflecting its core functionality.
• MATLAB treats all variables as matrices, making matrix operations fundamental.
• For example, a * b in MATLAB performs matrix multiplication.

Benefits of MATLAB

• Programs are concise due to the matrix-based operations.
• Complex mathematical operations can be written in few lines.
• This avoids the need for extensive programming loops.
• It offers high computational efficiency and brevity in code.

MATLAB as a problem-solving tool

• MATLAB helps in solving diverse mathematical problems in engineering and technical fields.
• It can be used for simple numerical problems like solving equations with multiple variables e.g. 10 = X + 2Y and 24 = 12X - Y.
• Also for complex tasks like interpolation, matrix computations, signal processing (Fourier transforms), and neural networks.

Graphical capabilities

• MATLAB excels in plotting various types of curves and graphs.
• This allows for data visualization and analysis.
• MATLAB can analyze and represent data, performing differentiation, integration, and solving algebraic equations.
• It also handles differential equations, including partial differential equations.

Application domains

• MATLAB is utilized in various engineering fields, including control systems, electronics, mechanical engineering, automotive, aerospace, and defense industries.

Founders of MATLAB

• The program was founded by Cleve Moler and Jack Little.
• Moler has been a professor of mathematics and computer science for over 20 years.
• He taught at the University of Michigan, Stanford, and the University of New Mexico.
• Little also founded MathWorks, the company behind MATLAB.
• He contributed to the initial development of MATLAB.

MATLAB's Components

• MATLAB consists of five main parts.
• These include language constructs, environment, graphics handling, math function library, and integration with other programming languages.

MATLAB Language

• High-level language for matrix operations, including single and double dimension matrices.
• Includes support for control flow, functions, data structures, and object-oriented programming.

MATLAB Environment

• Includes tools and facilities for MATLAB users and programmers.
• Provides management of variables in the workspace, data transfer, and development tools.

Graphics Handling System

• Includes commands for 2D and 3D plotting, image processing, and presentation of graphics.

MATLAB Mathematical Function Library

• Provides a wide range of mathematical functions, including elementary functions and logarithmic functions.

Integration with Other Languages

• Allows linking with programming languages like C, Java, and C#.

MATLAB Interface Components

• The main window of MATLAB includes elements for writing commands and managing files.

Command Window

• The main interface for writing commands directly and provides various functions.
• It displays help text, translation results, and access to files.

Current Directory

• Shows the current directory.
• Allows for easy access to functions and contains all relevant files for an application.

Workspace

• Saves name of defined variables and assigned values to each variable, avoiding multiple assignments of the same value.

History

• The window saves all previously executed commands over a period of time.
• Allows easy reactivation or retranslation of the code.

Stored Functions in MATLAB

• Functions are pre-prepared codes that perform specific tasks, each with a unique name.
• There are two types of functions.

User-defined Functions

• Functions written by the user within an M-file.
• These are stored with a specific name for later use.

Built-in Functions

• Functions provided by MATLAB that can be used directly without needing to know the underlying code.

Creating M-Files

• MATLAB allows creating and adding functions to the existing basic functions.
• To add the functions they must be saved as an M-File.

Saving Functions

• The function needs to be defined in the first line, being mindful of the following.
• The function name in the definition should match the file name.
• The function name should be composed of a single section, with no spaces.
• The name should not exceed 31 characters.
• The function name should start with a letter and can be followed with a symbol.
• The program can be used or launched after being written, by using the Run application.

Common Built-In Functions

• Rem: Returns the remainder of the integer division.
• Floor: Rounds the decimal number or array towards -∞.
• Ceil: Rounds the decimal number or array towards ∞.
• Fix: Rounds the decimal number towards zero, and cancels the fraction obtaining the integer.
• Round: Rounds the decimal at the nearest integer.

Trigonometric Functions

• Includes sin, cos, tan, cot, sec, csc for basic trigonometric calculations.
• Also includes inverse trigonometric functions like asin, acos, atan, acot, asec, acsc for inverse calculations.
• Includes hyperbolic functions like sinh, cosh, and their inverse functions.

Primary Arithmetic Functions

• includes Sqrt which finds the square root.
• includes Abs which finds the absolute value.

Plotting in MATLAB

• MATLAB provides extensive capabilities for plotting vectors, matrices, and functions as graphs.
• Users can create 3D plots and animate them.

Plotting Features

• Adding textual comments to plots and printing them.
• Allows changing the colors of lines.
• Provides naming methods for axes.
• Divides the plot (for more information look at the manual.)

Commonly Used Commands for Plotting

• Plot: Used for plotting linear 2D functions.
• Plot3: Used for plotting linear 3D functions.
• Surf: Analogous to mesh, although using color on the chart, thus applying colors to entire graph and for 3D graphs.
• Mesh: Draws the graph on the three coordinate axis, in grid form
• Ezplot: Plots graph on the binary axes with a space in which you can specify the relation between a transfer and two transfers.
• Meshgrid: Defines axes to use for the 3d graph.
• Hold: Adds more functions and holds certain parameters.
• Title: to provide graph names.
• Xlabel/Ylabel: to label axes.
• Grid on: adds a grid.
• Subplot: Presents multiple separate drawings on one frame.
• Text: to write a comment on the chart.
• Legend: Key for graph.
• View: To decide from which direction to draw the function.
• Axis: to decide lengths of axes.

Plot Colors

• The following is used to draw more than one function.

Simple Calculations

• In MATLAB simple calculations can be written and are described now.
• The following are used in these samples.

Clear, Clc, Who, and Whos.

• The clear command wipes all automatically registered data in the navigation window
• Clc : Clean navigation window out of previous functions.
• Who: to demonstrate the names in the code, that save space.
• Whos : shows the variable names, that save area, size, the composition, and type.

Examples of Simple Calculations

Essential operations must have the following operators

Vector and Matrix Operations

• Vectors store a set of numbers and allow the storage of information.

Vector Sort

• Vectors can be listed as one long form, or divided into smaller sections that all have the same equation

Size

• Vectors size, max elements and min elements are all measurable.
• Sort commands will allow to list the vector and give the properties

Matrix

• The columns are measurable using matrix commands.
• All components in the matrices are measurable using a form of math

Calculating

• Calculating operations can be completed as shown
• Operations will follow the rules as can be seen through the manual.