The Implicit Function Theorem is a result in multivariable calculus that provides conditions for the existence of implicit functions and information about their partial derivatives.

Parametric equations represent points using one or more independent parameters, making them useful for describing curves and surfaces that are difficult to represent using Cartesian coordinates alone.

A Riemann sum is a mathematical technique used to approximate the definite integral of a function over a specified interval, providing an estimate of the area under a curve using a series of rectangles.

A total derivative is a concept in multivariable calculus that generalizes the derivative of a single-variable function to a function of multiple variables, capturing the rate of change of the dependent variable with respect to an independent variable.

Arc length is the length of a curve or a segment of a curve in a plane or space, used to measure the distance along a curve, such as the path of a particle moving through space or the contour of a geometric shape.

The Method of Least Squares is a statistical technique used to find the best-fitting line or curve to a set of data points, minimizing the sum of squared residuals.

Continuity is a fundamental concept in calculus, describing the smoothness of a function, which is crucial for many theorems and techniques in calculus.

Homogeneous differential equations have terms of the same order and can be transformed into separable form. Discover how to solve these equations and their applications.

Euler’s method and Improved Euler’s method are numerical techniques for solving first-order initial value problems, with Improved Euler’s method providing better accuracy.

Numerical integration is used to approximate definite integrals when analytical solutions are difficult or impossible. Learn about different techniques and their applications.