This toolkit is a Python-based library designed to help computations in multivariable calculus. It provides classes and methods for differentiating expressions, computing gradients, finding unit normal vectors, evaluating tangent planes, and calculating directional derivatives. This suite of tools is invaluable for students, educators, and professionals dealing with advanced mathematical concepts in fields like engineering, physics, data science, and more.

Features Differentiation: Automates the process of finding derivatives of algebraic expressions with respect to one or more variables. Gradient Computation: Offers functionality to calculate the gradient of a multivariable function, a fundamental concept in vector calculus. Unit Normal Vector Calculation: Computes the unit normal vectors to surfaces at given points, a crucial element in understanding geometric properties of surfaces. Tangent Plane Evaluation: Facilitates finding equations of tangent planes to surfaces at specified points, aiding in local approximations of surfaces. Directional Derivative Computation: Enables the calculation of directional derivatives, providing insight into the rate of change of functions in specified directions. Applications This toolkit is applicable in various scientific and engineering contexts, such as:

Optimization: In optimization problems, gradients can be used to find maxima and minima of functions. Physics: Used in fields like electromagnetism and fluid dynamics, where gradients, divergence, and curl are key concepts. Computer Graphics: Tangent planes and normal vectors are fundamental in rendering 3D graphics and animations. Data Science: Gradient descent algorithms in machine learning use concepts of gradients for minimizing loss functions.