Multivariable Calculus/Differential Equations

Multivariable Calculus
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
Diagonal Lengths of a Parallelepiped
Example of Symmetric Equations of a Line
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 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
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 Arc Length Along a Parametrized Curve
Differential Equations
General Solution of y' + xy = 0
Verifying the Solution of an ODE
The Logistic Function 1: Solving The ODE
The Logistic Function 2: Sketching The S-Curve
General Solution to y' - 3y = b(x)
Example of Population Growth 1
Example of Population Growth 2
Example of Radioactive Decay 1
Example of Radioactive Decay 2
General Solution to y'' - 6y' + 9y = 0
Complex Numbers for ODEs (1 of 4)
Complex Numbers for ODEs (2 of 4)
Complex Numbers for ODEs (3 of 4)
Complex Numbers for ODEs (4 of 4)
General Solution to y'' - 6y' +25y = 0
Antiderivative of e^{3x} cos(4x) (ODE Solution)
Antiderivative of x^2 e^x (ODE Solution)
General Solution of y'''-4y''+5y'-2y=0
Wronskian for {e^{3x}, e^{-x}, 2}
Linear Dependence of {x^2-1, x^2+x, x+1}
Annihilator Method 1: Real Linear Factors
Example of Annihilator Method: y''-y = sin(2x)
Power Series Solution for y''-2y'+y=x, y(0)=0, y'(0)=1
Mass-Spring Systems 1: Free, Undamped Motion
Mass-Spring Systems 2: Free, Underdamped Motion
Mass-Spring Systems 3: Critically Damped Motion
Laplace Transform of f(t) = 2t-1
Laplace Transform of f(t) = sin(2t)
Laplace Transform of f(t) = t sin(2t)
Laplace Transform of f(t) = e^{3t}cos(4t)
Laplace Transform of f(t) = t^2 e^{2t} cos(3t)
Inverse Laplace Transform of (s-1)/s^2(s^2+4)
Laplace Transform Solution of y'-3y=e^{2t}, y(0)=2
Laplace Transform Solution of y''-2y'-3y=e^t, y(0) = 0, y'(0) = 1
Laplace Transform of f(t) = 2 on the Interval (1,2)
Second Shift Formula for a Piecewise-defined Function
Laplace Transform Solution of y'-y=f(t) (Piecewise-Defined)
Example of Convolution Theorem: f(t)=t, g(t)=sin(t)
Convolution Theorem for y'-2y=e^t, y(0)=0