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 a partial derivative
The derivative of a multivariable function with respect to one variable while keeping others constant.
Define limit
The value that a function approaches as the input approaches some value.
Define implicit differentiation
Finding the derivative of a function defined by an equation.
Define a PDE (Partial Differential Equation)
An equation involving partial derivatives of a function of several variables.
Define the ratio test for series convergence
A test that uses the ratio of successive terms to determine a series' convergence.
Define a Maclaurin Series
A Taylor Series centered at zero.
Define curl in vector analysis
A measure of the rotation of a vector field.
Define a parametric equation
An equation where the variables are expressed as functions of a parameter.
Define a Riemann Sum
An approximation of the integral of a function using finite sums.
Define the disk method for volume calculation
A method to find the volume of a solid of revolution using disks.
Define Euler's Method
A numerical method to approximate solutions of differential equations.
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 surface integral
The integral of a scalar field over a surface.
Define a vector field
An assignment of a vector to each point in a subset of space.
Define the concept of a gradient field
A vector field representing the gradient of a scalar function.
Define a differential
An infinitesimally small change in a function, related to the derivative.
Define the concept of optimization
The process of finding the maximum or minimum values of a function.
Define a derivative at a point
The slope of the tangent line to a function at that point.
Define a conservative vector field
A vector field where the line integral from one point to another is independent of the path.
Define definite integral
The integral of a function over a specified interval.
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.
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 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.