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281 Lecture Graphs

12.1 - 3D Coordinates


Example 3 - Distance between two coordinates

https://ggbm.at/zTa5Twyq

Example 4 - Parabola with z=3

https://ggbm.at/F2yWEhHC

Example 7 - 3D inequalities and systems

https://ggbm.at/ahnDAvRX


Example 8 - Volume inside cube but outside sphere







12.2 - Vectors

Example 1 - Equal vectors from separate starting points

https://ggbm.at/h6vfu99p


12.3 - The Dot Product


Example 3 - Angle between two vectors

https://ggbm.at/uXtXzct6


Example 5 - Direction cosines and direction angles

https://ggbm.at/n4zA85sC



12.4 - The Cross Product


Example 5 - Scalar triple product and the volume of a parallelepiped

https://ggbm.at/eBKChcAg



12.5 - Equations of 3D Lines and Planes

Example 1 - 3D line based on direction vector and starting point

https://ggbm.at/u3Vr3pXt


Example 7 - Line of intersection between planes and the angle between planes

https://ggbm.at/nC3HBts7


12.6 - Quadric Surfaces

Example Overload! All quadric surface examples from lecture in one.

https://ggbm.at/SZh2k5mR


13.1 - Vector Functions and Space Curves

Example 4 - Space curve of intersection between surfaces

https://ggbm.at/TWG6Bh97

Example 5 - Trefoil Knot


https://ggbm.at/xzjeSJ9R


Example 6 - Motion of Charged Particle in Electric/Magnetic Field


https://ggbm.at/zBQb8vTd



13.2 - Calculus of Space Curves

Example 2 - Tangent line to a space curve

https://www.geogebra.org/m/N5MVasGa




13.3 - Arc Length and Curvature


Example 1,2,4,6,7 - Helix space curve, TNB frame, Osculating Plane, etc.

https://ggbm.at/HUZBZJuB


13.4 - Motion in Space - Velocity and Acceleration

Just For Fun - Home Run or Not? Adjust Initial Velocity and Elevation Angle


https://ggbm.at/HxFnJTpj




14.1 - Functions in Several Variables


Example 5 - Comparing Graph in R^3 to Contour Map on R^2


https://ggbm.at/KMrFBWkS


14.3 - Partial Derivatives


Example 8/9 - Solutions to Laplace's equation and the Wave equation.

https://ggbm.at/V4Ypqk4E


14.4 - Tangent Planes and Linear Approximations


Example 2 - Tangent plane to the elliptic paraboloid


https://ggbm.at/XT2Srh3U



14.6 - Directional Derivatives


Example 2 - Graph of the tangent plane and tangent lines given by the partial derivatives and directional derivatives.


https://ggbm.at/cWgukKnM



14.7 - Minimum and Maximum Values


Examples 1-4: Second Derivative Test


https://ggbm.at/kePymbVh



15.1 - Double Integrals over Rectangles

Example 2 - Using Iterated Integrals to calculate volume


https://ggbm.at/jV3qy4n2



15.6 - Triple Integrals


Example 4 - Using Triple Integral to calculate volume


https://ggbm.at/n44hfRVQ


15.7 - Triple Integrals in Cylindrical Coordinates


Example 2 - Using triple integral to calculate volume



https://ggbm.at/hpERcW9C


16.1 - Vector Fields


Example 1 - Gravitational Field, A Conservative Vector Field


https://ggbm.at/gmRz9Eyg


16.2 - Line Integrals

Example 1 - Evaluating a Line Integral


https://ggbm.at/fEY6FWqq



16.6 - Parametric Surfaces and Their Areas

Example 2 - Graph Parametric Surfaces in GeoGebra

https://ggbm.at/zbCYeuGM



16.6 - Parametric Surfaces and Their Areas

Example 6 - Tangent Plane to Paraboloid

https://ggbm.at/TzvVSsvJ



16.8 - Stokes' Theorem

Example 1 - Evaluating a line integral using a surface integral


https://ggbm.at/KxkEEyRQ






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