Version: 1.0 Developer: Priyanshu (prxcode) Domain: Mathematics / Computer Science

Math Solver Studio is an interactive Python application that allows users to:

• Solve Ordinary Differential Equations (ODEs) using symbolic methods (Laplace Transform or Classical methods).
• Compute Fourier Series of any given function over a specified interval.
• Plot solution graphs for ODEs and Fourier Series approximations.
• Compare original functions with their Fourier Series approximation visually.

This tool is ideal for learning Mathematics III topics like Laplace Transform, Fourier Series, and ODEs interactively.

• Enter ODEs using sympy syntax (e.g., Derivative(y(t),(t,2)) + 3*Derivative(y(t),t) + 2*y(t) - exp(-t)).
• Provide initial conditions (e.g., y(0)=0, y'(0)=1).
• Solve symbolically using sympy.dsolve.
• Plot the solution graph.

• Enter a function ( f(x) ) in sympy format (e.g., x**2).
• Specify the interval [a,b] (e.g., -pi, pi) and number of terms N.
• Compute Fourier coefficients ( a_n ) and ( b_n ) automatically.
• Plot the Fourier series approximation alongside the original function.

• Tabs for Laplace/ODE and Fourier Series.
• Text areas for solution display.
• Buttons for computing solutions and plotting graphs.

git clone https://github.com/prxcode/math-solver-studio.git
cd math-solver-studio

python -m venv venv

Activate the environment:

• Windows: venv\Scripts\activate
• Linux / macOS: source venv/bin/activate

Dependencies are listed in requirements.txt. Use pip to install:

pip install -r requirements.txt

requirements.txt

sympy==1.12
matplotlib==3.7.2
numpy==1.25.0

Note: Tkinter is included with most Python distributions. On Linux, you may need:

sudo apt-get install python3-tk

After installing dependencies, run the main program:

python main.py

• The GUI window will open.
• Use the Laplace / ODE tab to solve differential equations.
• Use the Fourier Series tab to compute series and plot approximations.

• Enter the differential equation in sympy syntax.
• Input initial conditions.
• Click Solve ODE to compute the solution.
• Click Plot Solution to visualize ( y(t) ).

• Enter the function ( f(x) ) in sympy syntax.
• Enter the interval [a,b] (e.g., -pi, pi).
• Enter the number of terms N.
• Click Compute Fourier Series to calculate coefficients.
• Click Plot Fourier Series to visualize the approximation against the original function.

• Python 3.8+
• SymPy (symbolic computation)
• NumPy (numerical operations)
• Matplotlib (graph plotting)
• Tkinter (GUI toolkit, usually included with Python)