Multivariable Calculus/Differential Equations

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Multivariable Calculus

Equation of a Parabola 1

Equation of Parabola 2

Equation of an Ellipse 1

Equation of an Ellipse 2

Equation of a Hyperbola 1

Equation of Hyperbola 2

Example of Equation of a Sphere

Equation of a Sphere Given Diameter

Equation of Sphere Given Tangent Plane 1

Equation of Sphere Given Tangent Plane 2

Equation of Sphere Given Tangent Plane 3

Angle Between Two Vectors Using Dot Product

Vector Decomposition of (2,2,1) Along (1,1,1)

Unit Vector Perpendicular to Two Vectors

Area of Parallelogram in Three Space

Volume of a Parallelepiped

Diagonal Lengths of a Parallelepiped

Example of Symmetric Equations of a Line

Equation of a Parallel Line

Example of Intersecting Lines

Angle Between Two Planes

Equation of a Plane Containing a Point and a Line

Equation of a Plane Through Three Points

Planes: Parallel, Equal, or Intersecting?

Line of Intersection of Two Planes

Example of Plane Line Intersections

Domain of a Vector-Valued Function

Limit and Derivative of Vector Function

Example of Position, Velocity and Acceleration in Three Space

Tangent Line to a Parametrized Curve

Angle of Intersection Between Two Curves

Unit Tangent and Normal Vectors for a Helix

Sketch/Area of Polar Curve r = sin(3O)

Arc Length along Polar Curve r = e^{-O}

Showing a Limit Does Not Exist

Contour Map of f(x,y) = 1/(x^2 + y^2)

Sketch of an Ellipsoid

Sketch of a One-Sheeted Hyperboloid

Sketch of a Double-Napped Cone

Gradient of f(x,y) = yx^2 + cos(xy)

Example of Implicit Differentiation with Several Variables

Tangent Plane to x^2 - xy - y^2 -z = 0

Lagrange Multiplier: Single Constraint

Optimization on Ellipse in R^3 1: Parametrization Method

Optimization on Ellipse in R^3 2: Lagrange Multipliers with Two Constraints

Example of Chain Rule for Partial Derivatives

Second Partials Test for f(x,y) = x^3 + 3xy + y^3

Directional Derivative of f(x,y,z) = xz + yz

Linear Approximation to f(x,y) = x^2y^2 + x

Taylor Polynomial of f(x,y) = ycos(x+y)

Conversion From Rectangular Coordinates

Conversion From Cylindrical Coordinates

Conversion from Spherical Coordinates

Examples of Double and Triple Integrals

Center of Mass for a Rectangle of Variable Density

Interchange of Limits of Integration

Integral in Polar Coordinates

Area Between Polar Curves r = 2/cos(O) and r = 4cos(O)

Integral of exp(-x^2) (HD Version)

Surface area of z = (x^2+y2)^1/2

Mass of Solid as a Triple integral in Rectangular Coordinates

Volume of Truncated Paraboloid in Cylindrical Coordinates

Volume of a Snow Cone in Cylindrical and Spherical Coordinates

Example of Vector Field

Example of Arc Length Along a Parametrized Curve

Sketching A Parametrized Curve

Line Integral of xy^3 over Unit Circle in Q1