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