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