Calculus 3

Introduction to Points in 3 Dimensional Space.
Distance Formula and Equation of a Sphere in 3D With Examples.
Distance from a Point to the y-axis in 3D Space..
Find a Unit Vector in the Same Direction as the Given Vector.
Are the two Vectors Parallel? :: How to Determine if Vectors are Parallel.
Magnitude and Angle of the Resultant Force :: Cartesian Components of Vectors.
Find the Tension in Cables Attached to a Hanging Mass:: Vectors :: Static Equillibrium.
Dot Product of Two Vectors.
How to Find the Angle Between Two Vectors :: Why Cosine and Dot Product Explained.
Find Unit Vector Perpendicular to Two Vectors :: Using Dot Product!.
Find Force Needed to Supply 100 Nm of Torque.
Acute Angle Between a Line and a Plane.
Angle Between two Intersecting Lines :: 3D Vectors :: First Show Intersection.
Planes Parallel, Orthogonal, or Neither, Angle Between Planes Approach.
Find the Limit of a Vector Function.
Vector Function for the Curve of Intersection of Two Surfaces.
Derivative of a Vector Function.
Derivative of the Vector Function :: r(t) = ta x (tb +t^2 c).
Find the Unit Tangent and Unit Normal Vectors.
Integral of a Vector Function.
Arc Length of the Curve :: Two Examples :: Calculus 3.
Both Curvature Formulas Derivation :: Vector Calculus.
Contour Plots || Contour Maps || Multivariable Functions || Calculus 3.
Domain of Multivariable Functions || Two Examples!.
Multivariable Limits Polar Coordinates.
Multivariable Limits :: Show the Limit Does Not Exist :: TWO WAYS! :: Polar Coordinates.
What The Heck are Partial Derivatives?? With Visualization, Examples and Clairaut's Theorem!!.
Partial Derivative Examples Advanced (Including Derivative of an Integral).
Find the Linear Approximation of f(x,y) = 1-xycos(pi y) at the Point (1,1).
Use Differentials to Estimate the Amount of Metal in a Cylindrical Can.
Use the Chain Rule to find the Partial Derivatives.
Use the Chain Rule to Find the Partial Derivatives of z = tan(u/v), u-2s+3t, v=3s-2t.
Find the Directional Derivative of f(x,y,z) = xy+yz+xz at (1,-1,3) in the direction of (2,4,5).
Find all points at which the direction of fastest change of the function is i+j.
Local Extrema and Saddle Points of a Multivariable Function. 2nd Derivative Test.
Use Lagrange Multipliers to Find the Maximum and Minimum Values of f(x,y) = x^3y^5.
Midpoint Rule Double Integrals Using Level Curves!.
Evaluate by Reversing the Order of Integration :: integral bounds include ln(x)!!.
Double Integrals in Polar Coordinates.
Graphing Polar Curves by Changing the Parameter.
Double Integral to find Area Enclosed by a Cardioid r=2-2cos(t).
Find the Centroid of the Triangular Region Given the Vertices :: Double Integrals.
Moments of Inertia :: Double Integrals :: Polar Coordinates.
Evaluate by Changing to Cylindrical Coordinates :: 2 Ways!!!.
Triple Integral to find Volume Cylindrical and Spherical Coordinates :: Inside Sphere Outside Cone.
Evaluate By Changing to Spherical Coordinates :: Above Cone Between Two Spheres.
Triple Integral in Spherical Coordinates to find Volume :: Under Sphere Between Two Cones..
Change of Variables in Multiple Integrals (Find the Jacobian).
Line Integrals of Scalar Functions: Evaluate Line Integrals : Contour Integrals.
Line Integral of a Vector Field :: F(x,y,z) = sin(x) i + cos(y) j + xz k.
Fundamental Theorem for Line Integrals :: Conservative Vector Field Line Integral.
Green's Theorem Examples.
Scalar Surface Integral ∫∫ x^2yz dS where S is part of the plane z=1+2x+3y.
Scalar Surface Integral ∫∫xy dS, S is the triangular region (1,0,0), (0,2,0), (0,0,2).
Evaluate the Surface Integral over the Helicoid r(u,v) = ucos v i + usin v j + v k.
Find the Flux of the Vector Field F = x i + y j + z^4 k Through the Cone with Downward Orientation.
Use Stokes' Theorem to Evaluate the Surface Integral.
Divergence Theorem:: Find the flux of F = ( cos(z) + xy^2, xexp(-z), sin(y)+x^2z ).
Multivariable Limit Using the Definition.
What Angle Equalizes Horiz. Range and Vertical Distance? || Projectile Motion.