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

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

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

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

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 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

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

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

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

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

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 V1Finding the directional derivative to a function of two variables at a given point and direction

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 V4Using the gradient vector to find the maximum rate of change and the direction it occurs

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

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

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

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

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) 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Calculus Exam Review (Derivatives and Approximate Profit): MATH 142Examples of finding derivatives and calculating approximate profit

Calculus Exam Review (Average Cost): MATH 142Using the derivative to calculate the average cost of an item

Calculus Exam Review (Derivative Applications): MATH 142Finding a tangent line and approximating marginal cost

Calculus Exam Review (Marginal Revenue): MATH 142Finding marginal revenue and approximating the cost of the next item

Business Applications of the Derivative (Revenue, Profit, Cost, Demand): MATH 142Marginal Analysis and Marginal Average Functions

Business Applications of the Derivative (Revenue, Profit, Cost, Demand): MATH 142Marginal Analysis and Marginal Average Functions

Vectors and Derivatives: MATH 171 Problems 1-3Using the limit definition to find derivatives of functions and vector functions

Derivatives and Applications: MATH 151 Problems 9-15Tangent lines to parametric equations and related rates examples

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15Review of limits and derivatives of inverse trigonometric functions

Review for the Common Exam: MATH 151 Exam 2 Review Problems 10-15Implicit differentiation and physics applications of derivatives

Review for the Common Exam: MATH 151 Exam 2 Review Problems 16-20Derivatives of parametric equations and tangent lines

Review for the Common Exam: MATH 151 Exam 2 Review Problems 1-9Reviewing the chain rule and the derivatives and limits of trigonometric functions

Review for the Common Exam: MATH 151 Exam 2 Review Problems 21-29Related rates problems, differentials, linear and quadratic approximations

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40Review of derivatives and tangent lines to functions and vector equations

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15Review of limits and derivatives of inverse trigonometric functions

Approximations and Exponentials: MATH 151 Problems 7-14Approximation and Newton's Method, and limits and derivatives of exponential functions

Limits and Asymptotes: MATH 151 Problems 7-11Limits at infinity and asymptotes, along with physics applications

Derivatives and Rates of Change: MATH 171 Problems 1-3Using the limit definition to find derivatives of functions and vector functions

The Derivative as a Function: MATH 171 Problems 1-3Using the limit definition to find derivatives of functions and vector functions

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40Review of derivatives and tangent lines to functions and vector equations

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40Review of derivatives and tangent lines to functions and vector equations

Approximations and Exponentials: MATH 151 Problems 7-14Approximation and Newton's Method, and limits and derivatives of exponential functions

Differentiation and Applications: MATH 151 Problems 1-8Derivatives of exponential and logarithmic functions and the exponential model

Derivatives and Applications: MATH 151 Problems 9-15Tangent lines to parametric equations and related rates examples

Riemann Sums and Definite Integrals: MATH 151 Problems 6-12Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 Problems 6-12Using Reimann sums and the Fundamental Theorem of Calculus

Trapezoid Rule: MATH 172 Problems 1 & 2 Covering the Trapezoid Rule for approximating the value of an integral

Derivatives and Applications: MATH 151 Problems 9-15Tangent lines to parametric equations and related rates examples

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15Review of limits and derivatives of inverse trigonometric functions

Review for the Common Exam: MATH 151 Exam 2 Review Problems 10-15Implicit differentiation and physics applications of derivatives

Review for the Common Exam: MATH 151 Exam 2 Review Problems 16-20Derivatives of parametric equations and tangent lines

Review for the Common Exam: MATH 151 Exam 2 Review Problems 1-9Reviewing the chain rule and the derivatives and limits of trigonometric functions

Review for the Common Exam: MATH 151 Exam 2 Review Problems 21-29Related rates problems, differentials, linear and quadratic approximations

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40Review of derivatives and tangent lines to functions and vector equations

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15Review of limits and derivatives of inverse trigonometric functions

Approximations and Exponentials: MATH 151 Problems 7-14Approximation and Newton's Method, and limits and derivatives of exponential functions

Limits and Asymptotes: MATH 151 Problems 7-11Limits at infinity and asymptotes, along with physics applications

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40Review of derivatives and tangent lines to functions and vector equations

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35Review of the limit definition of a derivative and calculating the derivative

Approximations and Exponentials: MATH 151 Problems 7-14Approximation and Newton's Method, and limits and derivatives of exponential functions

Differentiation and Applications: MATH 151 Problems 1-8Derivatives of exponential and logarithmic functions and the exponential model

Differentiation and Applications: MATH 151 Problems 1-8Derivatives of exponential and logarithmic functions and the exponential model

Derivatives and Applications: MATH 151 Problems 9-15Tangent lines to parametric equations and related rates examples

Riemann Sums and Definite Integrals: MATH 151 Problems 6-12Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 Problems 6-12Using Reimann sums and the Fundamental Theorem of Calculus

MLC WIR 20B M151 week5 #10Finding the points on a parametric curve where the tangent line is horizontal or vertical

MLC WIR 20B M151 week6 #8Finding the point when the tangent line to a function has a particular slope

MLC WIR 20B M151 week6 #13Finding where the tangent line is horizontal or vertical for a parametric equation

MLC WIR 20B M151 week10 #13Finding when the tangent line to a parametric curve is vertical or horizontal

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 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 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

Finding and Graphing Tangent Lines to a Curve in PythonUsing Python to find the equation of the tangent line to a curve and graphing the result

Finding Horizontal Tangent Lines in PythonFinding when the tangent line to a function is horizontal in Python

Implicit Plots and Implicit Differentiation in PythonUsing Python to plot an implicit curve and find a tangent line using implicit differentiation

MATH 140 5.5 #2Finding the piecewise-defined function for a given graph along with its domain and range