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Calculus III Video Library (Multivariable Calculus)

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Calculus III Video Library (Multivariable Calculus) 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
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