Larry Green's Calculus Videos

Sequences and Series

• Sequences
  • Simplifying a Quotient Involving Factorials
  • Determining if a Sequence Converges by Taking a Limit
  • Determining if a Sequence that Involves Factorials Converges by Taking a Limit
    
    
• Series
  • Using the n^th Term Test to Show that a Series Diverges
  • Finding the Sum of a Telescoping Series
  • Determining if a Geometric Series Converges and then Finding what it Converges to
  • Find the Values of x that Make a Geometric Series Converge
    
    
• The Integral Test
  • Using the Integral Test to Show that a Series Converges
    
  • Using the Integral Test to Show that a Series Diverges
  • Using the p-Series Test to Show that a Series Diverges.
    
    
• The Comparison Tests
  • Using the Direct Comparison Test to Show that a Series Converges
  • Using the Direct Comparison Test to Show that a Series Diverges
  • Using the Limit Comparison Test to Show that a Series Converges
  • Using the Limit Comparison Test to Show that a Series Diverges
    
    
• Alternating Series
  • Showing that an Alternating Series Converges Absolutely
  • Showing that an Alternating Series Diverges
  • Showing that an Alternating Series Converges Conditionally
  • Finding N such that the Error in Approximating a Series is Less Than 0.001
  
  
• The Ratio and Root Tests
  • Using the Ratio Test to Show that a Series Converges
  • Using the Ratio Test to Show that a Series Diverges
  • Shifting the Index of Summation from n=2 to n=0
  • Using the Root Test to Show that a Series Converges
  • Using the Root Test to Show that a Series Diverges
    
    
• Taylor and Mclaurin Polynomials
  • Finding a Mclaurin Polynomial
  • Finding a Third Degree Taylor Polynomial and Using it to Approximate a Value
  • Using Taylor's Remainder Theorem to Find an Upper Bound for the Error
  • Determining the degree of the Mclaurin polynomial needed to approximate e.
    
    
• Power Series
  • Finding the Interval of Convergence
  • Finding the Interval of Convergence (involves factorials and an infinite radius of convergence)
  • Finding the Interval of Convergence (involves (3)(5)(7)...(2n-1) and a zero radius of convergence)
  • Verifying that a Power Series is a Solution to a Differential Equation
    
    
• Geometric Power Series
  • Writing a Function as a Geometric Power Series Centered at c = 0
  • Writing a Function as a Geometric Power Series Centered at c = 3
  • Using a Geometric Power Series to Approximate an Integral
  • Using a Well-known Function's Power Series to Evaluate a Power Series
    
    
• Taylor and Mclaurin Series
  • Use the Definition to Find the Taylor Series of a Function Centered at c = -2
  • Use the Binomial Series Formula to Find a Mclaurin Series
  • Using the Known Mclaurin Series for cos x to Find the Mclaurin Series for a Related Function
  • Finding a Mclaurin Series of a Product by Multiplying Two Mclaurin Series Together
  • Use a Mclaurin Series to Find a Limit
  • Use a Mclaurin Series to Find an Integral that Represents a Probability (Normal Distribution)

Conics, Parametric Equations, and Polar Equations

• Conics and Calculus
  • Finding the Equation of the Tangent Line to the Hyperbola
  • Finding the Area of an Ellipse
    
    
• Parametric Equations
  • Finding Parametric Equations for y = f(x)
  • Finding Parametric Equations of a Line
  • Finding Parametric Equations of a Circle
  • Eliminating the Parameter and using the Pythagorean Trig Identity
  • Eliminating the Parameter to Sketch a Graph
    
    
    
• Parametric Equations
  • Finding the First and Second Derivative for Parametric Equations
  • Finding the Equation of the Tangent Lines Where a Curve Intersects Itself
  • Finding Points Where There are Horizontal and Vertical Tangent Lines
  • Finding the Arc Length of a Curve
  • Finding the Surface Area of Revolution about the x-axis and the y-axis
    
    
• Polar Coordinates
  • Converting From a Rectangular Equation to Polar Form
  • Converting From a Polar Equation to Rectangular Form
  • Finding the Slope of the Tangent Line (Polar Form)
  • Find the Horizontal and Vertical Tangent Lines to a Polar Graph
    
    
• Area and Arc Length in Polar Coordinates
  • Finding the Intersection of Two Polar Curves
  • Finding the Area of a Polar Region
  • Finding the Arc Length of a Polar Curve
  • Finding the Surface Area of Revolution of a Polar Curve

Vectors

• Plane Vectors
  • Finding the Unit Vector in the Direction of Another Vector
  • Vector Addition and Scalar Multiplication and the Geometric Interpretation
  • Using Vectors to Find the Airspeed of an Airplane
    
    
• 3 Dimensional Vectors
  • Plotting a Point in the xyz-Space
  • Determine if a Triangle is Right, Isosceles, or Neither
  • Determine if Three Points are Collinear
  • Describing a Solid that is the Outside of a Sphere
    
    
• The Dot Product
  • Finding the Angle Between Two Vectors
  • Finding Vectors that are Orthogonal to a Given Vector
  • Determining if a Triangle is Acute, Obtuse, or Right
  • Finding the Projection of u Onto v and the Component of u Orthogonal to v
  • Finding the Work Done on and Object
  • Proving the Diagonals of a Rhombus are Perpendicular
    
    
• The Cross Product
  • Finding the Area of a Parallelogram
  • Finding the Volume of a Parallelepiped
  • Calculating the Torque
    
    
• Lines and Planes
  • Finding the Equation of a Line that is Parallel to a Given Line
  • Finding the Point of Intersection of Two Lines
  • Finding the Equation of a Plane that Passes Through Three Given Points
  • Sketching a Plane
  • Finding the Distance Between a Point and a Plane
    
    
• Surfaces
  • Sketching a Cylinder
  • Sketching an Ellipsoid
  • Sketching a Paraboloid
  • Finding the Equation of a Surface of Revolution
    
    
• Cylindrical and Spherical Coordinates
  • Converting a Rectangular Equation to Cylindrical and Spherical Coordinates
  • Converting an Equation From Cylindrical Coordinates to Rectangular Coordinates
  • Converting an Equation From Spherical Coordinates to Rectangular Coordinates

Functions of Several Variables

• Introduction to Functions of Several Variables
  • Finding the Domain and Range of a Function of Two Variables
  • Sketching Level Curves for a Contour Diagram and Describing a Surface
    
    
• Limits
  • Showing a Limit Does Not Exist
  • Using Polar Coordinates to Find a Limit that Exists
  • Discussing the Continuity of a Function:  Removable Discontinuity
    
    
• Partial Derivatives
  • Finding the First Partial Derivatives of a Function
  • Using the Limit Definition to Find a Partial Derivative With Respect to y
  • Verifying that a Function is a Solution to a Partial Differential Equation (Laplace's Equation)
    
    
• Differentials
  • Approximating the Propagated Error
  • Using Differentials to Approximate the Percent Change
    
    
• The Chain Rule
  • The Chain Rule an Polar Coordinates
  • Using the Chain Rule for a Second Derivative
  • Differentiating a Function of Four Variables Implicitly
    
    
• Directional Derivatives and the Gradient
  • Finding the Directional Derivative
  • Using the Gradient Vector to Find a Normal Vector to a Level Curve
  • Finding the Path of a Heat Seeking Particle
    
    
• Tangent Planes and Normal Lines
  • Finding the Equation of the Tangent Plane to a Surface
  • Finding Symmetric Equations to the Normal Line to a Surface
  • Finding the Equation of the Tangent Line to the Curve of Intersection of Two Surfaces
    
    
• Relative and Absolute Extrema
  • Locating and Classifying Relative Extrema Using the Second Partials Test
  • Finding the Absolute Extrema Over a Triangle
    
    
• Applications of Relative Extrema
  • Finding the Dimensions that Maximize the Volume of a Rectangular Building
  • Using Least Squares Regression
    
    
• Lagrange Multipliers
  • Minimizing a Distance
  • Finding a Maximum (2 Variables)
  • Locating Extrema for a Function of 3 Variables Given 2 Constraints

Full Collection of Calculus Videos

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