MATLAB Basics Quiz

MATLAB Introduction

• MATLAB is a programming language developed by MathWorks.
• MATLAB stands for MATrix LABoratory.
• MATLAB is a program for numerical computations, originally designed for solving linear algebra problems using matrices.
• It operates primarily on whole matrices and arrays, unlike other programming languages that work with numbers individually.
• MATLAB can process various data types, including images and sound, by converting them into matrices/arrays for operations.
• It is a high-level, fourth-generation programming language with an interactive environment for numerical computation, visualization, and programming.
• MATLAB offers inbuilt commands and mathematical functions for calculations, generating plots, and performing numerical methods.

Applications of MATLAB

• MATLAB is a versatile computational tool in science and engineering, encompassing various fields like physics, chemistry, mathematics, and diverse engineering disciplines.
• It supports a broad range of applications, including signal processing and communications, algorithm development, control systems, computational finance, and computational biology.

MATLAB Environment Setup

• Setting up the MATLAB environment entails a few simple steps.
• MathWorks provides licensed, trial, and student versions of MATLAB.
• The installation process involves logging in, obtaining approval, downloading the installer, and completing the installation steps.

MATLAB Desktop Overview

• The MATLAB desktop has several panels:
  • Current Folder: Used to access project files and folders.
  • Command Window: Where commands are entered and executed (indicated by the >> prompt).
  • Workspace: Displays variables created or imported from files.
  • Command History: Displays previously entered commands.

MATLAB Commands

• The Command Window allows direct execution of commands.

• Valid expressions (e.g., 20 + 21) are computed immediately.

• MATLAB handles common mathematical functions (e.g., sqrt, sin, exp).

• Special expressions like pi, Inf, i (or j) for complex numbers, and NaN for 'not a number' are supported.

• Semicolons (;) can be used to suppress the display of output for a given command.

MATLAB Comments

• Comments in MATLAB code are denoted by the percent symbol (%).
• Comments can be placed on a line by themselves or at the end of a command line, for explanatory purposes.

Commonly Used Operators

• Common mathematical operators (e.g., +, -, *, /, \ ,^, for addition, subtraction, multiplication, division, left division, exponentiation) are supported.
• Operators have a defined hierarchy regarding precedence in calculation.

Special Variables and Constants

• MATLAB utilizes built-in variables and constants for efficient computations, including:
  • ans: The most recent answer returned by a command.
  • eps: Accuracy of floating-point precision.
  • pi: The mathematical constant π.
  • i (or j): The imaginary unit √-1
  • Inf: Infinity
  • NaN: Not a number.

Naming Variables

• Variable names in MATLAB must start with a letter, followed by any number of letters, digits, or underscores.
• MATLAB is case-sensitive.
• The 'who' command lists all variables used, and the 'whos' command provides detailed information.

Multiple Assignments

• Multiple assignments can be performed on a single line (e.g., a = 2; b = 7; c = a * b;).

Clearing Variables and Workspace

• The 'clear x' command removes the variable 'x' from the workspace.
• The 'clear' command deletes all variables from the workspace.
• The 'clc' command clears the Command Window, leaving a clear screen.

Long Assignments

• Long calculations can be extended across multiple lines, with the result displayed in the same line

The Format Command

• The 'format' command controls how numbers are displayed (e.g., short, long, bank, short e, long e).
• 'format short' displays numbers with four decimal places, while 'format long' shows 15 decimal digits.
• 'format bank' rounds numbers to two decimal places.

Creating Vectors

• A vector is a one-dimensional array in MATLAB.
• Row vectors enclose elements in square brackets, separated by spaces or commas.
• Column vectors use semicolons to separate elements.

Creating Matrices

• A matrix is a two-dimensional array represented by nested square brackets.
• Separate rows using semicolons.

Elementary Math Functions

• MATLAB provides various built-in mathematical functions.
  • sqrt(): Square root
  • nthroot(): nth root of a number.
  • exp(): Exponential function (e^x)
  • abs(): Absolute value.
  • log(): Natural logarithm
  • log10(): Base-10 logarithm
  • factorial(): Factorial function.

Trigonometric Functions

• Several trigonometric functions are built-in, working in degrees and radians.
  • sin(x), cos(x), tan(x), cot(x): Sine, cosine, tangent, cotangent (radians).
  • sind(x), cosd(x), tand(x), cotd(x): Sine, cosine, tangent, cotangent (degrees).
  • asin(x), acos(x), atan(x): Inverse sine, cosine, tangent.
  • asind(x), acosd(x), atand(x): Inverse sine, cosine, tangent (degrees).

Rounding Functions

• Functions for rounding operations:
  • round(x): Rounds to the nearest integer
  • fix(x): Rounds towards zero
  • ceil(x): Rounds towards positive infinity
  • floor(x): Rounds towards negative infinity
  • rem(x ,y): Returns the remainder after x/y

Plotting in MATLAB

• Plotting graphs for mathematical functions involves specifying the variable range (x) and the function values (y). Functions like plot(x,y) create two-dimensional plots.
• Further plotting options (e.g., title, labels) can customize a graph.
• Plotting tools are available for parametric curves, polar curves, etc.

MATLAB Three-Dimensional Plots

• Creating 3D plots involves using points and assigning the function to those points to generate a surface plot, using commands like meshgrid and surf.

M-Files (Script and Function Files)

• MATLAB programs are typically written, saved, and executed in M-files.
• These M-Files are simple text files containing MATLAB commands written in text format, ending in the ".m" extension.
• Script files contain sequences of commands that are executed in the order they are listed.
• Function files are designed to perform and return specific calculations, and are called by commands during execution

Solving Differential Equations

• Using MATLAB's dsolve() function, various first-order linear and nonlinear differential equations (ODEs) and higher-order equations can be solved analytically and displayed graphically.
• The dsolve function aids in solving ODEs without initial conditions or with specified initial conditions.

Non-Homogeneous Differential Equations

• MATLAB's dsolve() enables the solution of non-homogeneous differential equations.

Partial Differential Equations

• Partial differential equations (PDEs) can be derived using MATLAB to eliminate arbitrary constants using symbolic manipulation (e.g., using the syms command to create symbolic representations of variables and expressions) and solving for arbitrary constants.

Beta and Gamma Functions

• The gamma function (Γ(z)) calculates factorial values for non-integer arguments, and the beta function (B(x, y)) computes probabilities. They have special properties relevant in many mathematical applications.

Radius of Curvature

• MATLAB can determine the radius of curvature for various curves given by equations or parametric equations.