Buckets:
| # 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 | |
| --- | |
| ### 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) | |
| --- | |
| ## 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](LICENSE) file for details. | |
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