EM/README.md

Engineering Mathematics Projects (University of Tehran)

Overview

This repository contains two MATLAB projects completed as part of the Engineering Mathematics course at the University of Tehran . The projects focus on the application of Fourier Analysis and Partial Differential Equations (PDEs) in solving engineering-related problems.

Project 1: Fourier Analysis

This project introduces the use of Fourier Series and Fourier Transforms to analyze and solve functions in both the time and frequency domains. Key elements include:

• Introduction to MATLAB : Basic commands for plotting and working with matrices.
• Fourier Series Calculation : Implementing MATLAB functions to compute the Fourier series of a given function and comparing the result with the original function.
• Fourier Transform : Applying Fourier transforms to functions and analyzing the frequency domain representation.
• Sampling Frequency : Understanding the concept of sampling frequency through an audio signal analysis task.

Key Topics:

• Plotting functions in MATLAB
• Computing Fourier Series and Fourier Transform
• Harmonic Analysis in Fourier Series
• Audio signal processing

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Project 2: Partial Differential Equations (PDEs)

This project focuses on solving Partial Differential Equations (PDEs) such as the Heat Equation and the Helmholtz Equation using MATLAB. Key steps include:

• Solving the Heat Equation : Implementing MATLAB functions to solve the heat equation for a one-dimensional rod with specific boundary and initial conditions.
• Solving the Helmholtz Equation : Analyzing and solving the Helmholtz equation in a specific region and visualizing the results using MATLAB’s PDE Modeler.

Key Topics:

• Solving PDEs using MATLAB
• Boundary and initial conditions for PDEs
• Visualization of solutions (2D and 3D plots)

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Structure

The repository is structured as follows:

• EXTRA/ : Contains additional files related to the projects.
• Projects/ : Contains the MATLAB scripts and functions for both projects.
• README.md : Documentation for the projects.

How to Run the Projects

1. Clone the repository.
2. Open MATLAB and navigate to the project directory.
3. Run the corresponding scripts for each project:
   • For Fourier Analysis , open and run the script: fourier_analysis.m.
   • For PDEs , open and run the script: heat_equation_solver.m or helmholtz_solver.m.

License

This project is licensed under the MIT License - see the LICENSE file for details.