Calculus III Video Library (Multivariable Calculus)

Introduction to Functions of Several Variables Double Integrals Vector Fields

Introduction to Functions of Two Variables with Approximate the Volume of Pool With The Midpoint Rule Introduction to Vector Fields Applications Using a Table of Values The Divergence of a Vector Field Introduction to Functions of Two Variables Double Integral Approximation Using Midpoint Rule Using Ex 1: Determine the Divergence of a Vector Field Ex: Function Values of a Function of Two Variables Using a Level Curves Ex 2: Determine the Divergence of a Vector Field Table Ex: Double Integral Approximation Using Midpoint Rule - Ex: Determine the Sign of the Divergence from the Graph Ex: Evaluate a Function of Two Variables (Cobb-Douglas f(x,y)=ax+by of a Vector Field Production Function) Integrating Functions of Two Variables The Curl of a Vector Field Ex: Function Values of a Function of Two Variables Introduction to Double Integrals and Volume Ex 1: Determine the Curl of a Vector Field (Square Root) Double Integrals and Volume over a General Region - Part 1 Ex 2: Determine the Curl of a Vector Field Ex: Function Values of a Function of Two Variables Double Integrals and Volume over a General Region - Part 2 Ex 1: Determine the Curl of a Vector Field (2D) (Polynomial) Evaluating Double Integrals Ex 2: Determine the Curl of a Vector Field (2D) Ex: Function Values of a Function of Two Variables Ex: Double Integrals - Describe a Region of Integration Conservative Vector Fields (Fraction) (Triangle) Ex: Function Values of a Function of Two Variables Ex: Double Integrals - Describe a Region of Integration Line Integrals (Exponential) (Quadratic) Ex 1: Determine the Domain of a Function of Two Ex: Double Integrals - Describe a Region of Integration Defining a Smooth Parameterization of a Path Variables (Advanced) Ex 1A: Determine a Piecewise Smooth Parameterization Ex 2: Determine the Domain of a Function of Two Ex 1: Evaluate a Double Integral Over a Rectangular Region for a Curve (Triangle) Variables to Find a Volume - f(x,y)=c Ex 1B: Determine a Piecewise Smooth Parameterization Level Curves of Function of Two Variables Ex 2: Evaluate a Double Integral Over a Rectangular Region for a Curve (Triangle) Ex 1: Determine a Function Value Using a Contour Map to Find a Volume - f(x,y)=c Ex 2: Determine a Piecewise Smooth Parameterization Ex 2: Determine a Function Value Using a Contour Map Ex: Evaluate a Double Integral Over a Rectangular Region to for a Curve Ex: Determine if a Function is Increasing or Decreasing in Find a Volume - f(x,y)=ax Ex: Determine Parametric Equations for an Ellipse a Direction Using a Contour Map Ex: Evaluate a Double Integral Over a Rectangular Region - Line Integrals in R^2 f(x,y)=ax+by Line Integrals in R^3 Limits and Partial Derivatives of Functions of Two Ex: Evaluate a Double Integral to Determine Volume (Basic) Line Integral of Vector Fields Variables Ex: Evaluate a Double Integral to Determine Volume - Line Integrals in Differential Form Change Order of Integration Evaluate a Line Integral of y with Respect to Arc Length Limits of Functions of Two Variables Ex: Evaluate a Double Integral Over a Rectangular Region to (Area) Ex: Limit of a Function of Two Variables (Origin - DNE) Find a Volume - f(x,y)=x/y Evaluate a Line Integral of xy^2 with Respect to Arc Ex: Limit of a Function of Two Variables (Origin - Exist) Use a Double Integral to Find the Volume Under a Length C: Half Cirlce (Area) Ex: Limit of a Function of Two Variables (Not Origin - Exist Paraboloid Over a Rectangular Region Evaluate a Line Integral of xy with Respect to Arc Length - Direct Substitution) Evaluate a Double Integral Using Substitution Over a (Mass of Wire) Ex: Limit of a Function of Two Variables (Not Origin - DNE) Rectangular Region - f(x,y)=(xy^2)/(x^2+1) Evaluate a Line Integral of x^2+y^2+z^2 with Respect to First Order Partial Derivatives Evaluate a Double Integral Using Substitution Over a Arc Length(Mass of Wire) Ex: Estimate the Value of a Partial Derivative Using a Rectangular Region - f(x,y)=(ax+by)^n Evaluate a Line Integral of x^3y^2 with Respect to x Contour Map Evaluate a Double Integral Using Substitution Over a (Differential Form) Ex: Determine a Partial Derivative Function of an Rectangular Region - f(x,y)=xysin(x^2+y^2) Evaluate the Line Integral of x^2z Along a Line Segment Exponential Function of Two Variables Evaluate a Double Integral Over a General Region - in 3D Ex: Determine a Partial Derivative Function of an f(x,y)=ax+by Evaluate a Line Integral of in Differential Form Polynomial Function of Two Variables Evaluate a Double Integral Over a General Region - Evaluate a Line Integral of F*dr Ex: Find Partial Derivative Values for a Polynomial f(x,y)=xy^2 Line Integral Application - Work of a Charged Particle Function of Two Variables Evaluate a Double Integral Over a General Region with Determining the Potential Function of a Conservative Ex: Find Partial Derivative Values for a Square Root Substitution - f(x,y)=e^(x/y) Vector Field Function of Two Variables Average Value of a Function of Two Variables The Fundamental Theorem of Line Integrals - Part 1 Ex: Find the Partial Derivatives of the Cobb Douglas Fubini's Theorem The Fundamental Theorem of Line Integrals - Part 2 Production Function Setting up a Double Integral Using Both Orders of Fundamental Theorem of Line Integrals - Closed Ex: Find the Partial Derivative of a Function of Three Integration Path/Curve Variables (Square Root) Double Integrals: Changing the Order of Integration Ex 1: Fundamental Theorem of Line Integrals - Given Ex: Application of First Order Partial Derivative (Change in Double Integrals: Changing the Order of Integration - Vector Field in a Plane Production) Example 1 Ex 2: Fundamental Theorem of Line Integrals - Given Second Order Partial Derivatives Double Integrals: Changing the Order of Integration - Vector Field in a Plane (Not Conservative) Ex: Find First and Second Order Partial Derivatives Example 2 Ex 3: Fundamental Theorem of Line Integrals - Given Ex: Determine Second Order Partial Derivatives Vector Field in a Plane Differentials of Functions of Two Variables Ex 4: Fundamental Theorem of Line Integrals - Given Applications of Differentials of Functions of Several Double Integrals in Polar Coordinates Vector Field in Space Variables Green's Theorem - Part 1 Introduction to Double Integrals in Polar Coordinates Green's Theorem - Part 2 The Chain Rule and Directional Derivatives, and the Double Integrals in Polar Coordinates - Example 1 Ex: Use Green's Theorem to Evaluate a Line Integral Gradient Functions of Two Variables Double Integrals in Polar Coordinates - Example 2 (Rectangle) Area Using Double Integrals in Polar Coordinates - Example Ex: Use Green's Theorem to Evaluate a Line Integral The Chain Rule for Functions of Two Variables With One 1 (Polar) Independent Variable Area Using Double Integrals in Polar Coordinates - Example Ex: Use Green's Theorem to Evaluate a Line Integral The Chain Rule for Functions of Two Variables With Two 2 (Negative Orientation) Independent Variable Double Integrals in Polar Form - Volume of a Right Circular Ex: Use Green's Theorem to Determine Area of a Region Ex: Chain Rule - Function of Two Variables with One Cylinder (f(x,y) over a circle) Enclosed by a Curve Independent Variable Double Integrals in Polar Form - Volume of a Half Sphere Determining Area using Line Integrals Ex: Chain Rule - Function of Two Variables with Over a Circle Flux Form of Green's Theorem Two Independent Variable Evaluate a Double Integral in Polar Form - f(x,y)=ax+by Over Ex: Chain Rule - Function of Two Variables with a Half-Circle Surface Integrals Three Independent Variable Evaluate a Double Integral in Polar Form - Application of Chain Rule of a Function of Two Variables - f(x,y)=cos(x^2+y^2) Over a Ring Parameterized Surfaces Change of Volume Volume of a Drilled Sphere Using a Double Integral in Polar Area of a Parameterized Surface Implicit Differentiation of Functions in One Variable using Form Surface Integral with Explicit Surface Part 1 Partial Derivatives Double Integrals in Polar Form - Volume Bounded by Two Surface Integral with Explicit Surface Part 2 Partial Implicit Differentiation Paraboloids Ex: Surface Area of a Function of Two Variables (Surface Directional Derivatives Integral) The Gradient Applications of Double Integrals: Mass, Center of Mass, Surface Integrals with Parameterized Surface - Part 1 Ex: Find the Gradient of the Function f(x,y)=xy Jacobian Surface Integrals with Parameterized Surface - Part 2 Ex: Find the Gradient of the Function f(x,y)=e^(2x)sin(3y) Ex: Surface Area of a Parametric Surface (Surface Ex: Find the Gradient of the Function f(x,y)=5xsin(xy) Integral) Find the Gradient Vector Field of f(x,y)=x^3y^5 Double Integrals - Find the Mass of a Lamina Over a Region Surface Integral of a Vector Field - Part 1 Find the Gradient Vector Field of f(x,y)=ln(2x+5y) in the xy Plane Surface Integral of a Vector Field - Part 2 Ex: Use the Gradient to Find the Maximum Rate of Double Integrals - Find the Center Mass of a Lamina Over a Ex: Evaluate a Surface Integral (Parametric Surface - Increase of f(x,y)=(4y^5)/x from a Point Region Using Polar Coordinates Helicoid) Ex 1: Find a Value of a Directional Derivative - f(x,y)=xy Double Integrals - Find the Total Charge Over a Triangular Ex: Evaluate a Surface Integral (Basic Explicit Surface - Ex 2: Find a Value of a Directional Derivative - Region Plane Over Rectangle) f(x,y)=x^n*y^m Double Integrals - Find a Probability Using the Exponential Ex: Evaluate a Surface Integral Using Polar Coordinates- Ex 3: Find a Value of a Directional Derivative - Density Function: P(xNormal Vectors and Tangent Planes to Functions of Two Double Integrals - Surface Area over a Circle Using Polar Parametrically Variables Coordinates (Basic) Ex: Using a Flux Integral to Determine a Mass Flow Rate Double Integrals - Surface Area of a Vector Values Function Stoke's Theorem - Part 1 Determining a Unit Normal Vector to a Surface Over a Region Stoke's Theorem - Part 2 Verifying the Equation of a Tangent Plane to a Surface Find the Jacobian Given x=au+bv, y=u^2+cv Ex 1: Using Stoke's Theorem to Evaluate a Line Integral as Determining the Equation of a Tangent Plane Evaluate a Double Integral of ax+by Over Parallelogram a Surface Integral Ex 1: Find the Equation of a Tangent Plane to a Surface Given Transformation Equations (Jacobian) Ex 2: Using Stoke's Theorem to Evaluate a Line Integral as Ex 2: Find the Equation of a Tangent Plane to a Surface Evaluate a Double Integral of ax+by Over a Surface Integral (Exponential) Parallelogram (Jacobian) Ex 1: Using Stoke's Theorem to Evaluate a Surface Ex 3: Find the Equation of a Tangent Plane to a Surface Evaluate a Double Integral of x^2 Over an Ellipse Using a Integral as a Line Integral (Trigonometric) Change of Variables (Jacobian, Polar) Ex 2: Using Stoke's Theorem to Evaluate a Surface Find a Linear Approximation to a Function of Two Integral as a Line Integral Variables and Estimate a Function Value Triple Integrals The Divergence Theorem - Part 1 The Divergence Theorem - Part 2 Ex: Use the Divergence Theorem to Evaluate a Flux Relative Extrema and Applications to Functions of Two Introduction to Triple Integrals Integral (Rectangular Coordinates) Variables Evaluating Triple Integrals – Example Ex 1: Set Up and Evaluate a Triple Integral of z - Part 1: Ex: Use the Divergence Theorem to Evaluate a Flux Integral (Cylindrical Coordinates) Determining the Relative Extrema of a Function of Two Limits of Integration Ex: Use the Divergence Theorem to Evaluate a Flux Variables Ex 1: Set Up and Evaluate a Triple Integral of z - Part 2: Integral (Spherical Coordinates) Ex 1: Classify Critical Points as Extrema or Saddle Points - Evaluate the Triple Integral Function of Two Variables Ex 2: Set up and Evaluate a Triple Integral of 2xz Graphing Calculator Ex 2: Classify Critical Points as Extrema or Saddle Points - Ex 3: Set Up and Evaluate a Triple Integral of y - Part 1: Function of Two Variables Limits of Integration Ex: Determine Relative Extrema for a Function of Two Ex 3: Set Up and Evaluate a Triple Integral of y - Part 2: Determine the value of the derivative function on the Variables Evaluate the Triple Integral graphing calculator Absolute Extrema of Functions of Two Variables Ex 4: Set up and Evaluate a Triple Integral of x+y-4z Determining the value of a definite integral on the Applications of Extrema of Functions of Two Variables I Triple Integrals and Volume - Part 1 graphing calculator Applications of Extrema of Functions of Two Variables II Triple Integrals and Volume - Part 2 Sequences on the TI84 Graphing Calculator Applications of Extrema of Functions of Two Variables III Triple Integrals and Volume - Part 3 Sequences and Series on the TI84 Ex: Determine the Quantity to Maximize Revenue Set up a Triple Integral to Determine Volume (Rectangular Graph Partial Sums of an Infinite Series on the TI84 - Function of Two Variables Coordinates) Graphing Parametric Equations in the TI84 Ex: Minimize Cost to Make Open Top Box - Function of Determine Limits of Integration for a Triple Integral - Region Two Variables of Integration is a Tetrahedron Lagrange Multipliers - Part 1 Use a Triple Integral to Determine Volume Ex 1 (Rectangular Lagrange Multipliers - Part 2 Coordinates) Maximize a Cobb Douglas Production Function Using Use a Triple Integral to Determine Volume Ex 2 (Rectangular Lagrange Multipliers Coordinates) Maximize a Function of Two Variable Under a Constraint Triple Integrals: Find the Volume of a Tetrahedron Given Using Lagrange Multipliers - f(x,y)=x^2y the Vertices Minimize a Cost Function of Two Variable Under a Application of Triple Integrals: Mass Constraint Using Lagrange Multipliers Changing the Order of Triple Integrals Lagrange Multipliers: Find the Max and Min of a Function of Two Variables Triple Integrals in Cylindrical and Spherical Coordinates

Triple Integrals Using Cylindrical Coordinates Triple Integral and Volume Using Cylindrical Coordinates Rewrite Triple Integrals Using Cylindrical Coordinates Use a Triple Integral to Determine Volume Ex 1 (Cylindrical Coordinates) Introduction to Triple Integrals Using Spherical Coordinates Triple Integrals and Volume using Spherical Coordinates Evaluate a Triple Integral Using Cylindrical Coordinates - Triple Integral of e^z Evaluate a Triple Integral Using Spherical Coordinates - Triple Integral of 1/(x^2+y^2+z^2) Find the Moment of Inertia about the z-axis of a Solid Using Triple Integrals Find the Center of Mass of a Solid Using Triple Integrals A Change of Variables for a Double Integral: Jacobian Example of a Change of Variables for a Double Integral: Jacobian A Change of Variables for a Triple Integral: Jacobian