MTH 2130 - Calculus III

• Analyze and sketch common surfaces in three dimensions
• Find parametric equations of a line in space
• Find equations for planes in space
• Solve geometric problems involving lines and planes in space
• Parameterize lines and simple curves in space as a vector-valued functions
• Analyze a vector-valued function and the corresponding two or three-dimensional curve
• Find limits, derivatives, and integrals of a vector-valued function and interpret the results in terms of rectilinear motion (position, velocity, acceleration)
• Determine if a vector-valued function smoothly parameterizes a curve
• Find arc length and an arc-length parameterization of a oriented curve
• Find and interpret the directions of unit tangent and principal unit normal vectors
• Find curvature of a smooth curve
• Determine the domain of a function of several variables
• Find first and higher-order partial derivatives of a function
• Use implicit differentiation to find partial derivatives
• Interpret partial derivatives as rates of change in applications
• Find the total differential of a function of more than one variable, use it to estimate change
• Estimate error propagation using the total differential
• Construct the correct form of multivariate chain rule and use it to find a derivative
• Solve related rates problems using the multivariate chain rule
• Find the gradient of a function and interpret its direction
• Find directional derivatives of a function and interpret the result
• Determine the maximum, minimum, and saddle points on a surface
• Set up and evaluate double integrals using rectangular and polar coordinates
• Find areas and volumes using double integrals
• Convert equations and coordinates of points between rectangular, cylindrical, and spherical coordinates
• Set up and evaluate triple integrals in rectangular, cylindrical, or spherical coordinates
• Use multiple integration to find mass, centroids, and moments
• Find and interpret the divergence and curl of a vector field
• Determine if a vector field is conservative on a region and, if so, find a scalar potential function
• Evaluate line integrals by parameterization of the path
• Find the work done by a vector field along a curve
• Evaluate line integrals in conservative fields using the fundamental theorem
• Demonstrate that line integrals in conservative fields are path independent
• Find circulation or associated integrals using Green’s theorem
• Analyze a two-parameter vector-valued function and the corresponding surface
• Evaluate surface areas and surface integrals
• Find outward flux or associated integrals using the divergence theorem
• Find circulation or associated integrals using Stokes’ theorem
• Use the operator del to find the gradient, curl, and divergence
• Prove identities involving the operator del

• Limits, derivatives, and integrals of algebraic and transcendental functions of one variable
• Polar coordinates

• Vectors, lines, planes
• Vector-valued functions
• Functions of several variables 
• Partial derivatives 
• Extrema of functions of two variables 
• Double integrals, area, volume, and moments
• Triple integrals, volume, moments, cylindrical and spherical coordinates
• Vector fields
• Line integrals
• Surface integrals
• Green’s, divergence and Stokes’ theorems