Differential Operators Module
Overview
The Differential Operators module allows you to calculate various differential operators in arbitrary coordinate systems. This includes gradient, divergence, curl, laplacian, and covariant derivatives.
Using tensor calculus fundamentals, this module handles the complexities of coordinate transformations and metric tensors to provide accurate calculations in any coordinate system.
Available Operators
- Gradient - Calculates the gradient of a scalar field
- Divergence - Calculates the divergence of a vector field
- Curl - Calculates the curl of a vector field (in 3D)
- Laplacian - Calculates the Laplacian of a scalar field
- Covariant Derivative - Calculates the covariant derivative of a vector or tensor field
Applications
General Relativity
Calculate covariant derivatives and other differential operators needed for Einstein's equations and geodesic motion.
Electromagnetism
Compute curl, divergence, and other operators for electromagnetic fields in various coordinate systems.
Fluid Dynamics
Apply differential operators to fluid velocity fields, pressure gradients, and other fluid properties.
Quantum Mechanics
Use the Laplacian operator for Schrödinger's equation and other quantum mechanical calculations.