Define a parametric equation
An equation where the variables are expressed as functions of a parameter.
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.
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 a PDE (Partial Differential Equation)
An equation involving partial derivatives of a function of several variables.
Define implicit differentiation
Finding the derivative of a function defined by an equation.
Define a differential
An infinitesimally small change in a function, related to the derivative.
Define a Maclaurin Series
A Taylor Series centered at zero.
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 the concept of a gradient field
A vector field representing the gradient of a scalar function.
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 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 surface integral
The integral of a scalar field over a surface.
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 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 the ratio test for series convergence
A test that uses the ratio of successive terms to determine a series' convergence.
Define limit
The value that a function approaches as the input approaches some value.
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 vector field
An assignment of a vector to each point in a subset of space.
Define a conservative vector field
A vector field where the line integral from one point to another is independent of the path.
Define arc length
The length of a curve defined by a function.