About Me
As a lifelong math enthusiast, I have a deep passion for tackling complex problems. From diving into the intricacies of partial differential equations to unraveling the mysteries of numerical analysis, I thrive on the challenge of unlocking mathematical conundrums.
With proficiency in cutting-edge tools like Desmos and Python, I'm driven to push the boundaries of what's possible in the realm of mathematics. Whether I'm visualizing complex functions or automating tedious calculations, my goal is to leverage technology to unlock new insights and solutions.
Through my mathematical journey, I've honed a relentless problem-solving mindset, always seeking new ways to approach challenging concepts. I find immense satisfaction in the "aha" moments that come from unraveling a particularly intricate mathematical puzzle.
Modeling Linear ODES
1
Problem Definition
Define a linear Ordinary Differential Equation (ODE) with initial conditions.
2
Solution Approach
Apply analytical methods such as integrating factors or Laplace transforms to find the general solution.
3
Numerical Verification
Verify the analytical solution using numerical methods like Euler's method or Runge-Kutta methods in Python.
Linear ODEs are fundamental in modeling various physical phenomena, providing insights into system behavior.
Modeling PDE Equation
1
Heat Equation
Simulating heat distribution in a solid object using finite difference methods. Learn more
2
Wave Equation
Modeling wave propagation through a medium, showcasing reflection and refraction. Learn more
Simulation on Fourier Series
Decomposition of Functions
Fourier series allow us to decompose periodic functions into a sum of simple sine and cosine functions. This decomposition is fundamental in signal processing and physics.
- Express complex periodic functions
- Analyze frequency components
- Solve differential equations
Project: Audio Signal Analysis
In this project, I visualise how 3B1B use fourier series to analyze audio signals, identifying key frequency components and filtering out noise. This involved decomposing the audio signal into its constituent frequencies, allowing for targeted manipulation and enhancement.
Applications
Fourier series have a wide range of applications, including:
- Signal processing
- Image analysis
- Solving PDEs
- Data compression
The ability to represent functions as a sum of sines and cosines opens up powerful analytical tools for understanding complex systems.
Skills & Expertise
Core Competencies
- Finite Element Analysis
- Spectral Methods
- Dynamical Systems
Programming Languages
- Python (NumPy, SciPy, Matplotlib)
- MATLAB
Software Tools
- Desmos
- Spline
