Mathematics Engine - Calculus Toolkit

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.

🎯 Features

Seven Calculus Operations

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

Core Capabilities

• 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

🛠️ Technologies

• 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

📦 Windows/MSYS2 Setup

1. Install MSYS2 MinGW64

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

2. Install Dependencies

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

3. Build the Project

Option A: Using GCC Directly (Recommended)

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

Option B: Using CMake

cd Mathh
mkdir build
cd build

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

# Compile
cmake --build .

4. Run the Application

./math_engine.exe

🐧 Linux Build Instructions

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

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🧩 Prerequisites

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

⚙️ Building the Project

Clone the repository and switch into it:

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

Running the Program

./build/MathEngineUTF8

you should see output like :

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

💡 Notes

• 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.

🎮 Controls

Main Menu

Key	Action
1-7	Select operation (1=Diff, 2=Indefinite, 3=Definite, 4=Limits, 5=Matrix, 6=Partial, 7=Double)
UP/DOWN	Navigate menu
ENTER	Confirm selection
ESC	Quit

Calculus Modes (All)

Key	Action
ENTER	Type custom equation
SPACE	Next example
UP/DOWN	Scroll steps
ESC	Return to menu

Definite Integration

Key	Action
B	Change bounds
TAB	Switch between bounds

Limits

Key	Action
L or P	Open limit configuration
T	Quick toggle limit type (finite/+∞/-∞)
TAB	Switch fields in config

Matrix Multiplication

Key	Action
TAB	Switch between dimension fields
ENTER	Confirm and enter matrix values

Partial Derivatives

Key	Action
ENTER	Type custom equation f(x,y)
SPACE	Next example
X	Export to LaTeX

Double Integration

Key	Action
B	Set integration bounds (x and y)
TAB	Switch between bound fields
SPACE	Next example

How to Use

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

📚 Supported Functions

Basic Operations

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

Trigonometric Functions

• sin(x), cos(x), tan(x)

Other Functions

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

Example Expressions

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

🏗️ Project Structure

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

🧮 How It Works

1. Parsing

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

2. Differentiation

• 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

3. Integration

• 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

4. Simplification

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

5. Rendering

• 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

🔧 Customization

Change Font Size

Edit src/main.cpp:

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

Add New Functions

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

Adjust Plot Range

Edit src/main.cpp:

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

🐛 Troubleshooting

Font Not Found

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

Missing DLLs on Windows

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

OpenGL Errors

Update graphics drivers to support OpenGL 2.1+

🚀 Future Enhancements

• 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

🤝 Contributing

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

Quick Start for Contributors

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

Areas We Need Help

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

📝 License

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.

👥 Authors & Contributors

Created by: Shubh (@positronx_)

Contributors: See contributors list

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

☕ Support My Work

If you find this project helpful, consider supporting its development!

Your support helps me:

• 🚀 Build more open-source tools
• 📚 Create educational content
• 🔧 Maintain and improve existing projects
• ☕ Stay caffeinated while coding!

Buy me a coffee ☕

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