A Windows desktop application for symbolic calculus with step-by-step solutions and interactive features.

🎓 Comprehensive calculus toolkit supporting single and multivariate calculus operations with symbolic computation and real-time visualization.

1. Differentiation (d/dx) - Find derivatives with step-by-step solutions
2. Indefinite Integration (∫ f(x) dx) - Find antiderivatives + C
3. Definite Integration (∫[a,b] f(x) dx) - Calculate area under curve
4. Limits (lim f(x)) - Calculate limits with step-by-step evaluation
5. Matrix Multiplication - Multiply matrices with custom dimensions
6. Partial Derivatives (∂f/∂x, ∂f/∂y) - Compute partial derivatives for multivariate functions
7. Double Integration (∫∫ f(x,y) dy dx) - Calculate double integrals over rectangular regions

• Custom Equation Input: Type your own equations interactively
• Step-by-Step Solutions: View detailed calculations with mathematical notation
• UTF-8 Support: Full Unicode support for Greek letters (∂, π, α) and math symbols (⋅, √, ∫)
• Interactive Menu: Choose operation at startup
• Multiple Examples: Pre-loaded expressions for each mode
• OpenGL Plotting: Real-time graphs for all modes:
  • Differentiation: f(x) and f'(x) curves
  • Indefinite: f(x) and F(x) antiderivative curves
  • Definite: f(x) with shaded area between bounds
• Bounds Input: Set custom integration bounds for definite integrals

• C++17
• SDL2 + SDL2_ttf for windowing and UTF-8 text rendering
• OpenGL for plotting and graphics
• GLEW for OpenGL extension loading
• CMake for cross-platform building

Download and install MSYS2 from https://www.msys2.org/

Open MSYS2 MinGW64 terminal and run:

# Update package database
pacman -Syu

# Install compiler and build tools
pacman -S mingw-w64-x86_64-gcc mingw-w64-x86_64-cmake mingw-w64-x86_64-make

# Install SDL2 and graphics libraries
pacman -S mingw-w64-x86_64-SDL2 mingw-w64-x86_64-SDL2_ttf
pacman -S mingw-w64-x86_64-glew mingw-w64-x86_64-glm

cd Mathh
mkdir build
cd build

g++ -std=c++17     -I/mingw64/include -I../src     ../src/main.cpp     ../src/engine/parser.cpp     ../src/engine/differentiator.cpp     ../src/engine/integrator.cpp     ../src/engine/simplifier.cpp     ../src/engine/limit_calculator.cpp     ../src/engine/matrix_operations.cpp     ../src/engine/latex_exporter.cpp     ../src/engine/partial_derivative.cpp     ../src/engine/multivariate_integrator.cpp     ../src/ui/renderer.cpp     ../src/ui/text_renderer.cpp     ../src/ui/plotter.cpp     -L/mingw64/lib     -o MathEngineUTF8.exe     -lmingw32 -lSDL2main -lSDL2 -lSDL2_ttf     -lfreetype -lharfbuzz -lgraphite2 -ldwrite -lole32     -lbz2 -lz -lglew32 -lopengl32     -mconsole -O2 -Wall

cd Mathh
mkdir build
cd build

# Generate build files
cmake -G "MinGW Makefiles" ..

# Compile
cmake --build .

./math_engine.exe

MathEngineUTF8 now supports native Linux builds 🎉
Follow the steps below to compile and run it easily.

Make sure you have all required development tools and libraries:

sudo apt update
sudo apt install build-essential pkg-config libsdl2-dev libsdl2-ttf-dev libglew-dev libgl1-mesa-dev

git clone https://github.com/shubhu121/Mathh.git
cd Mathh

Run the included Linux build script:

./build/build_linux.sh

This script will:

1. Compile all source files using g++ -std=c++17

2. Use pkg-config to link against SDL2, SDL2_ttf, GLEW, and OpenGL

3. Output the executable MathEngineUTF8 inside the build/ directory

./build/MathEngineUTF8

you should see output like :

+===================================+
|  Mathematics Engine - Calculus    |
+===================================+

• The Linux build script is located at: build/build_linux.sh
• You can edit it if you use a different compiler or custom flags.
• The script won’t affect Windows or other build systems.

1. Launch: See main menu with 7 operations
2. Select Mode: Press 1-7 or use UP/DOWN arrows + ENTER
3. Custom Input: Press ENTER and type equation
4. View Results: See step-by-step solution
5. Advanced Features: Press B for bounds, L/P for limit config, X for LaTeX export
6. Return: Press ESC to go back to menu

• Addition: x + 2
• Subtraction: x - 3
• Multiplication: x * 5 or 5x
• Division: x / 2
• Exponentiation: x^3

• sin(x), cos(x), tan(x)

• exp(x) - Exponential
• ln(x) - Natural logarithm
• sqrt(x) - Square root

Differentiation:

sin(x^2)            → Chain rule
x^3 + 2*x           → Power rule
(x^3 + 2*x)*cos(x)  → Product rule

Integration:

x^2                 → Power rule (first/second degree)
sin(x)              → Trigonometric
exp(x)              → Exponential

Definite Integration:

x^2 from [0, 3]     → Area = 9.0
sin(x) from [0, π]  → Area = 2.0

Partial Derivatives:

x^2 + y^2           → ∂f/∂x = 2*x, ∂f/∂y = 2*y
x*y                 → ∂f/∂x = y, ∂f/∂y = x
sin(x)*cos(y)       → ∂f/∂x = cos(x)*cos(y), ∂f/∂y = -sin(x)*sin(y)

Double Integration:

x*y over [0,1]×[0,1]      → Result = 0.25
x^2 + y^2 over [0,2]×[0,2] → Numerical result

MathEngine/
├── CMakeLists.txt           # Build configuration
├── README.md                # This file
├── src/
│   ├── main.cpp            # Application entry point
│   ├── engine/
│   │   ├── ast.h/.cpp                    # Abstract Syntax Tree definitions
│   │   ├── parser.h/.cpp                 # Expression parser
│   │   ├── differentiator.h/.cpp         # Symbolic differentiation
│   │   ├── integrator.h/.cpp             # Symbolic integration
│   │   ├── simplifier.h/.cpp             # Expression simplification
│   │   ├── limit_calculator.h/.cpp       # Limit evaluation
│   │   ├── matrix_operations.h/.cpp      # Matrix operations
│   │   ├── latex_exporter.h/.cpp         # LaTeX export
│   │   ├── partial_derivative.h/.cpp     # Partial derivatives
│   │   └── multivariate_integrator.h/.cpp # Double integration
│   └── ui/
│       ├── renderer.h/.cpp        # SDL2/OpenGL renderer
│       ├── text_renderer.h/.cpp   # UTF-8 text rendering
│       └── plotter.h/.cpp         # Function plotting
└── assets/
    └── fonts/
        └── NotoSans-Regular.ttf   # UTF-8 compatible font

• Input expression is tokenized and converted to Abstract Syntax Tree (AST)
• Supports operator precedence and parentheses
• Handles implicit multiplication (e.g., 2x → 2 * x)

• Applies calculus rules:
  • Power Rule: d/dx(xⁿ) = n·xⁿ⁻¹
  • Chain Rule: d/dx(f(g(x))) = f'(g(x))·g'(x)
  • Product Rule: d/dx(f·g) = f'·g + f·g'
  • Quotient Rule: d/dx(f/g) = (f'·g - f·g')/g²
• Records each step with description and expression

• Applies integration rules:
  • Power Rule: ∫ xⁿ dx = xⁿ⁺¹/(n+1) + C
  • Constant Multiple: ∫ c·f(x) dx = c·∫ f(x) dx
  • Sum Rule: ∫ (f + g) dx = ∫ f dx + ∫ g dx
  • Trigonometric: ∫ sin(x) dx = -cos(x) + C
• For definite: applies Fundamental Theorem (F(b) - F(a))
• Records each step with description

• Eliminates redundant operations:
  • x + 0 → x
  • x * 1 → x
  • x * 0 → 0
  • x^1 → x
• Constant folding: evaluates numeric expressions

• Text: SDL2_ttf renders UTF-8 strings to OpenGL textures
• Plotting: OpenGL draws function graphs by sampling x values
• UI: Orthographic projection for 2D interface
• Menu System: Interactive mode selection

Edit src/main.cpp:

textRenderer.init("assets/fonts/NotoSans-Regular.ttf", 24); // Change 24 to desired size

1. Add function to UnaryFunc enum in src/engine/ast.h
2. Implement derivative in src/engine/differentiator.cpp
3. Add parser support in src/engine/parser.cpp

Edit src/main.cpp:

plotter.setViewport(-5, 5, -5, 5); // xMin, xMax, yMin, yMax

Ensure NotoSans-Regular.ttf is in build/assets/fonts/

Copy these from MinGW64 bin to build directory:

• SDL2.dll
• SDL2_ttf.dll
• libfreetype-6.dll
• glew32.dll
• libgcc_s_seh-1.dll
• libstdc++-6.dll
• libwinpthread-1.dll

Update graphics drivers to support OpenGL 2.1+

• Multiple variable support (partial derivatives, double integration)
• Limits with L'Hôpital's rule
• Matrix operations
• LaTeX export
• Triple integration
• Gradient and divergence
• Taylor series expansion
• Visual AST tree representation
• ImGui-based UI for expression input
• Syntax highlighting in input field
• Symbol palette (∫, π, ∑, etc.)
• Equation solver

We welcome contributions! Please see CONTRIBUTING.md for guidelines.

1. Fork the repository
2. Create a feature branch: git checkout -b feature/your-feature
3. Make your changes and test thoroughly
4. Commit with clear messages: git commit -m "feat: add new feature"
5. Push and create a pull request

• 🐛 Bug fixes and testing
• 📚 Documentation improvements
• ✨ New mathematical operations
• 🎨 UI/UX enhancements
• ⚡ Performance optimizations

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

TL;DR: Feel free to use, modify, and distribute this software. Attribution is appreciated but not required.

Created by: Shubh (@positronx_)

Contributors: See contributors list

Built with ❤️ using SDL2, OpenGL, and C++17 for Windows 10/11 (MSYS2 MinGW64)

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