Explain divergence in the context of a series

A series diverges if the sum does not approach a finite number as the number of terms increases.

Define the concept of a gradient field

A vector field representing the gradient of a scalar function.

Define implicit differentiation

Finding the derivative of a function defined by an equation.

Define the ratio test for series convergence

A test that uses the ratio of successive terms to determine a series' convergence.

Define a derivative at a point

The slope of the tangent line to a function at that point.

Define the concept of optimization

The process of finding the maximum or minimum values of a function.

Define the Mean Value Theorem

There exists at least one point where the function's derivative equals the function's average rate of change over an interval.

Define a Maclaurin Series

A Taylor Series centered at zero.

Define a Laplace transform

An integral transform that converts a function of a real variable into a function of a complex variable.

Define arc length

The length of a curve defined by a function.

Define a PDE (Partial Differential Equation)

An equation involving partial derivatives of a function of several variables.

Define a partial derivative

The derivative of a multivariable function with respect to one variable while keeping others constant.

Define the concept of a divergence of a vector field

A scalar representing the magnitude of a source or sink at a given point in a vector field.

Define limit

The value that a function approaches as the input approaches some value.

Define a surface integral

The integral of a scalar field over a surface.

Define definite integral

The integral of a function over a specified interval.

Define a vector field

An assignment of a vector to each point in a subset of space.

Define a differential

An infinitesimally small change in a function, related to the derivative.

Define convergence in the context of a series

A series converges if the sum approaches a finite number as the number of terms goes to infinity.

Define Euler's Method

A numerical method to approximate solutions of differential equations.

Define a Riemann Sum

An approximation of the integral of a function using finite sums.

Define a parametric equation

An equation where the variables are expressed as functions of a parameter.

Define the disk method for volume calculation

A method to find the volume of a solid of revolution using disks.

Define a conservative vector field

A vector field where the line integral from one point to another is independent of the path.

Define curl in vector analysis

A measure of the rotation of a vector field.