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