Larry Green's Calculus Videos

Vector Valued Functions

• Vector Valued Functions (Definitions)
  • Finding the Domain of a Vector Valued Function
  • Sketching the Graph Represented by a Vector Valued Function (Helix)
  • Determining Whether Curves Intersect or Collide
    
    
• Derivatives and Integrals of Vector Valued Functions
  • Verifying a Property Involving Derivatives and Dot Products
  • Finding Where a Curve is Smooth
  • Finding an Indefinite Integral
  • Find r(t) Given r''(t) and r'(0) and r(0)
  • Proving a Property About Vector Valued Functions
    
    
• Velocity and Acceleration
  • Finding the Velocity and Acceleration
  • Finding the Minimal Angle Required to Hit a Home Run
  • Finding an Initial Speed and a Maximal Height
    
    
• Unit Tangent and Unit Normal Vectors
  • Finding the Velocity, Acceleration, Unit Tangent, and Unit Normal Vectors (2D)
  • Finding the Unit Tangent and Unit Normal Vectors an the Tangential and Normal Components of Acceleration (3D)
    
    
• Arc Length and Curvature
  • Finding the Arc Length of a Space Curve
  • Parameterizing a Curve by Arc Length
  • Finding the Curvature of a Curve Parameterized by Arc Length
  • Finding the Curvature of a Curve Given  by a General Vector Valued Function
  • Finding the Point Where a Curve has Maximum Curvature (y = e^x)

Multiple Integration

• Double Integrals and Area
  • Using a Double Integral to Find the Area Bounded by Two Curves
  • Switching the Order of Integration
  • Integrating by Switching the Order of Integration
  • Splitting the Region Into Two Regions and Using Two Double Integrals
    
    
• Double Integrals and Volume
  • Using a Formula From Geometry to Evaluate a Double Integral
  • Using a Double Integral to Find Volume
  • Showing a Function is a Joint Density Function and then Finding a Probability
    
    
• Double Integrals in Polar Coordinates
  • Using Polar Coordinates to Evaluate a Double Integral
  • Combining Two Messy Integrals into One Nice Integral in Polar Coordinates
  • Finding the Area that is Inside a Cardioid and Outside a Circle
    
    
• Center of Mass and Moment of Inertia
  • Finding the Center of Mass of a Lamina
  • Finding the Moments of Inertia and Radii of Gyration
  • Finding the Moment of Inertia of a Lamina About the Line x=2
    
    
• Surface Area
  • Finding the Surface Area Over a Triangle
  • Finding the Surface Area of the Part of a Sphere that Lies Over a Circle
    
    
• Triple Integrals
  • Sketching a Solid and Switching the Order of Integration
  • Using a Triple Integral to Find a Volume
  • Finding the Moment of Inertia (Assumes Constant Density 1)
    
    
• Triple Integrals in Cylindrical and Spherical Coordinates
  • Using Cylindrical Coordinates to Find the Mass of a Solid
  • Using Spherical Coordinates to Find the Volume in a Sphere and a Cone
    
    
• Jacobians
  • Using the Jacobian for a Parallelogram Region
  • Using the Jacobian for a Curvy Region
  • Finding the Volume of an Ellipsoid Using Jacobians

Vector Calculus

• Vector Fields
  • Sketching a Vector Field
  • Determining if Vector Fields are Conservative and Finding a Potential Function (Two Variables)
  • Determining if Vector Fields are Conservative (Three Variables)
  • Finding a Potential Function (Three Variables)
  • Finding the Divergence of a Vector Field at a Point
    
    
• Line Integrals
  • Evaluating a Line Integral (ds) over a line segment
  • Finding the Mass of a Wire Defined as a Piecewise Curve
  • Finding the Work Done by a Particle Against a Force Field Around a Circle
  • Using the Graph to Determine if Work is Positive, Negative, or Zero
    
    
• The Fundamental Theorem of Line Integrals and Independence of Path
  • Applying the Fundamental Theorem of Line Integrals
  • Finding a Line Integral Over a Conservative Vector Field Using Independence of Path
  • Applying the Fundamental Theorem of Line Integrals (3D)
  • Finding the Work Done by a Conservative Force Field on a Particle Moving Along a Closed Curve
    
    
• Green's Theorem
  • Using Green's Theorem
  • Using Green's Theorem in Polar Coordinates
  • Splitting a Non-Simple Curve Into Two Simple Curves
  • Using Green's Theorem to Find the Area of an Ellipse
    
    
• Parametric Surfaces
  • Eliminating the Parameter
  • Eliminating the Parameter (for a Cylinder)
  • Finding a Vector Valued Function Given a Rectangular Equation that is a Function z = f(x,y)
  • Finding a Vector Valued Function for an Ellipsoid
  • Finding Parametric Equations for a Surface of Revolution about the y-axis
  • Finding a Tangent Plane Given a Parameterized Surface
  • Finding the Surface Area of a Parameterized Surface
    
    
• Surface Integrals
  • Finding the Mass of a Surface Defined by a Function of x and y
  • Finding the Surface Integral Over a Parameterized Surface
  • Finding the Flux Through a Surface
    
    
• The Divergence Theorem
  • Applying the Divergence Theorem
  • Showing that the Surface Integral of CurlF ^. N dS Equals 0
    
    
• Stoke's Theorem
  • Using Stoke's Theorem to Evaluate a Line Integral Over a Triangle
  • Verifying Stoke's Theorem by Computing Both the Line Integral and the Surface Integral

Entire Collection of Calculus Videos

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