WIR4 20B M251 V11Using the method of Lagrange multipliers to find the extreme values of a function subject to a constraint

WIR8 20B M251 V11Using the Fundamental Theorem of Line Integrals to evaluate a line integral of a vector field

WIR8 20B M251 V12Using the Fundamental Theorem of Line Integrals to evaluate a line integral of a vector field

Directional Derivatives and The Gradient Vector Conceptual V2Explaining the gradient vector for functions of two derivatives and its properties

Directional Derivatives and The Gradient Vector Exercise V3Finding a directional derivative and gradient vector for a function of two variables

Directional Derivatives and The Gradient Vector Exercise V5Finding the directional derivative to a function of two variables at a given point and direction

Lagrange Multipliers Exercise V1Using Lagrange Multipliers to find the extreme values of a function subject to a constraint

Lagrange Multipliers Exercise V2Using Lagrange Multipliers to find the extreme values of a function subject to a constraint

WIR3 20B M251 V13Use the linearization of a function of two variables to approximate the value of the function

WIR3 20B M251 V15Using the differential of a function of two variables to estimate the maximum error in calculating the volume of a cone

WIR4 20B M251 V1Finding the rate a volume is changing using the Chain Rule for functions of more than one variable

WIR4 20B M251 V5Finding the maximum rate of change and the direction it occurs for a function of two variables

WIR4 20B M251 V9Finding the absolute maximum and minimum values of a function of two variables on a rectangle

WIR4 20B M251 V10Finding the absolute maximum and minimum values of a function of two variables on a triangular region

WIR8 20B M251 V13Using the Fundamental Theorem of Line Integrals to evaluate a line integral of a vector field

WIR9 20B M251 V10Using a double integral to find the surface area of a given plane in the first octant

Lagrange Multipliers Exercise V3Using Lagrange Multipliers to find the minimum values of a function subject to a constraint

Lagrange Multipliers Exercise V4Using Lagrange Multipliers to find the largest box that can be inscribed in an ellipsoid

Maximum and Minimum Value (multivariable) Exercise V1Finding all local extrema and saddle points for a function of two variables

Maximum and Minimum Value (multivariable) Exercise V2Finding all local extrema and saddle points for a function of two variables

Maximum and Minimum Value (multivariable) Exercise V3Finding the minimum surface area for a box by minimizing a function of two variables

Maximum and Minimum Value (multivariable) Conceptual V2Explaining the Second Derivative Test for Local Extrema for functions of two variables

Maximum and Minimum Value (multivariable) Exercise V4Finding the absolute extrema of a function of two variables on a closed region

Maximum and Minimum Value (multivariable) Exercise V5Finding the absolute extrema of a function of two variables on a closed region

Lagrange Multipliers Conceptual V1Explaining how to use Lagrange Multipliers to find absolute extrema subject to a constraint

Directional Derivatives and The Gradient Vector Exercise V1Finding the directional derivative to a function of two variables at a given point and direction

The Chain Rule (multivariable) Exercise V3Using the Chain Rule for multivariable functions to find the rate a volume is changing

Directional Derivatives and The Gradient Vector Conceptual V1Explaining directional derivatives for functions of two variables

The Chain Rule (multivariable) Exercise V1Using the Chain Rule for functions of several variables to find a derivative

Partial Derivatives Exercise V3Example of finding a partial derivative of a function with two variables

Partial Derivatives Exercise V4Finding all higher order partial derivatives of a function with two variables

Tangent Planes and Linear Approximations Conceptual V1.1Explaining tangent planes for functions of two variables and how to calculate them

Tangent Planes and Linear Approximations Exercise V1Using differentials for a function of two variables to approximate a value

Tangent Planes and Linear Approximations Exercise V2Using differentials for a function of two variables to estimate the maximum error in an area

Tangent Planes and Linear Approximations Exercise V3.1Finding the tangent plane through a point for a function of two variables

WIR4 20B M251 V2Using the Chain Rule for functions of more than one variable to find partial derivatives

WIR5 20B M251 V11Setting up double integrals of Type I and II to give the volume of a solid under a surface

WIR6 20B M251 V5Writing an iterated integral in polar coordinates that gives the volume of the solid that lies below a paraboloid

WIR6 20B M251 V6Writing an iterated integral in polar coordinates that gives the volume of the solid bounded by a cone

WIR8 20B M251 V8Using a line integral to find the work done by a force field moving a particle along a curve

WIR9 20B M251 V4Using Green's Theorem to calculate the work done as a particle moves through a force field

WIR10 20B M251 V5Using Stokes' Theorem to evaluate a line integral of a vector field over a boundary curve

WIR10 20B M251 V6Using Stokes' Theorem to evaluate a line integral of a vector field over a boundary curve

Tangent Planes and Linear Approximations Exercise V4Finding the differential of a function of two variables and using it to approximate the change in the function

The Chain Rule (multivariable) Exercise V2Using the Chain Rule for functions of several variables to find partial derivatives

Directional Derivatives and The Gradient Vector Exercise V2Finding the directional derivative to a function of two variables at a given point and direction

Maximum and Minimum Value (multivariable) Conceptual V3Explaining the Extreme Value Theorem for functions of two variables and how to find the absolute maximum and minimum on a closed bounded region

Maximum and Minimum Value (multivariable) Conceptual V1Explaining local and absolute maximum and minimum values for multivariable functions

The Chain Rule (multivariable) Exercise V4Using the Chain Rule for multivariable functions to find a partial derivative

Functions of Several Variables Conceptual V1Introducing functions of several variables and level curves

Functions of Several Variables Exercise V1Evaluating and then finding and sketching the domain of a function of two variables

Functions of Several Variables Exercise V2Finding and sketching the domain of a function of two variables

Partial Derivatives Conceptual V1.2Explanation of partial derivatives for functions with more than one variable

WIR1 20B M251 V8Calculating the dot product for three-dimensional vectors given the vectors' lengths and the angle between them

WIR1 20B M251 V11Finding the scalar and vector projection of one three-dimensional vector onto another

WIR1 20B M251 V13Using the cross product to find a vector orthogonal to the plane defined by three points

WIR1 20B M251 V14Using the cross product to find the area of a parallelogram in three-dimensional space

WIR1 20B M251 V15Calculating the length of the cross product of two vectors given information about the vectors

WIR2 20B M251 V3Finding an equation of the plane containing two given lines in three-dimensional space

WIR2 20B M251 V8Finding a vector equation for the tangent line to a three-dimensional vector function

WIR7 20B M251 V5Evaluating a triple integral for a given solid by writing an iterated integral in spherical coordinates

WIR7 20B M251 V7Using a given transformation to write a double integral as an iterated integral with changed variables

WIR10 20B M251 V7Using Stokes' Theorem to express a surface integral of the curl of a vector field as a single integral