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Calculus 3 Lecture 12.3/12.5: TNB (Frenet-Serret) Frames, Curvature, and Torsion: Focus on how to compute the TNB Frames as simply as possible and use the results to find the Curvature, Osculating circle, osculating plane, normal plane, and radius of curvature. Formulas are also given including how to perform vector encapsulation for 2-D functions.

Calculus 3 Lecture 12.4: Velocity and Acceleration of Vector Functions: How to find the Velocity and Acceleration of a particle when the particular motion is described by a vector function (space curve). How to integrate to find a position function from acceleration or velocity. How to define acceleration as "T" and "N". A look at Projectile Motion.

Calculus 3 Lecture 14.3: Double Integrals over POLAR REGIONS: How to perform Double Integrals over regions using Polar Coordinates/Equations. How to translate Rectangular Double integrals into Polar Double integrals.

Calculus 3 Lecture 13.5: The Chain Rule for Multivariable Functions: How to find derivatives of Multivariable Functions involving Parametrics and/or Compositions. Focus will be on deriving the Chain Rule and practice of examples.

Calculus 3 Lecture 13.9: Constrained Optimization with LaGrange Multipliers: How to use the Gradient and LaGrange Multipliers to perform Optimization, with constraints, on Multivariable Functions.

Calculus 3 Lecture 13.7: Finding Tangent Planes and Normal Lines to Surfaces: How to find a tangent plane and/or a normal line to any surface (multivariable function) at a point. This is based on the ability to find the gradient of a function.

Calculus 3 Lecture 13.3: Partial Derivatives (Derivatives of Multivariable Functions): How to find the slope of a tangent line to a surface in the X-Direction and Y-Direction. Focus is on the concept of a partial derivative and several examples. Also included is implicit differentiation and higher order partial derivatives.