## This Semester's Piazza

## The Plug and Chug Series Videos

- (UPDATED 2020) Introduction to the Math 114 Plug and Chug Series
- The Plug and Chug Series OneNote Notebook for Math 114 (download and open, must have OneNote)

- 12.3: Dot Product - Abstract Example
- 12.3: Dot Product - A General Example
- 12.3: Dot Product - Projection and and Forces on an Inclined Plane
- 12.3: Dot Product - Work
- 12.4: Cross Product - Area of a Triangle/Parallelogram
- 12.4: Cross Product - Torque
- 12.4: Cross Product - Triple Box Product/Volume of a Parallelepiped
- 12.5: Equations of Lines
- 12.5: Equations of Planes
- 12.5: Distance between a Point and a Line and a Point and a Plane
- 12.5: Intersecting Lines and Planes
- 12.5: Parallel and Skew Lines, Parallel Planes
- 12.5: Angles between Planes
- 13.1: Curves in Space and their Tangents
- 13.2: Projectile Motion
- 13.3: Arclength
- 13.4: Tangent and Normal Vectors, Curvature
- 13.5: The Binormal Vector and Torsion
- 13.5: Tangent and Normal Components of Acceleration
- 13.5: Normal, Rectifying, and Osculating Planes
- 14.1: Domain, Range, and Level Curves
- 14.2: Intro to Limits and Polar Coordinates
- 14.2: The Squeeze/Sandwich Theorem
- 14.2: Continuity at a Point
- 14.3: Partial Derivatives and Implicit Differentiation
- 14.4: Chain Rule and an Implicit Differentiation Shortcut
- 14.4: 14.4.45 - A Study of taking the Chain Rule Twice
- 14.5: Directional Derivatives
- 14.6: Tangent Planes
- 14.6: Linearization and Approximating Functions near a Point
- 14.7: Characterizing Critical Points on an Open Region
- 14.7: Finding Absolute Extrema on a Closed Region with Linear Boundaries
- 14.8: Lagrange Multipliers Part I - Absolute Extrema on Closed Region with Non-Linear Boundaries
- 14.8: Lagrange Multipliers Part II - Minimizing Distances over a Double Constraint
- 15.1: Intro to Double Integrals
- 15.2: Sketching Regions and Finding Boundaries
- 15.2: Switching the Order of Integration
- 15.3: Area by Double Integration
- 15.4: Setting up Polar Integrals
- 15.4: Converting Cartesian Integrals to Polar
- 15.5: Triple Integrals I - An Easy Example
- 15.5: Triple Integrals II - A Harder and Better Example
- 15.6: Moments and Center of Mass - 2D Center of Mass
- 15.7: Cylindrical Coordinates
- 15.7: Spherical Coordinates
- 15.7: A Cone Example
- 15.8: Change of Variables I - Given a Region (Explicitly)
- 15.8: Change of Variables II - Region is defined in the Bounds of the Integral
- 16.1: Intro to Line Integrals I - Line Integral of a Funtion
- 16.2: Intro to Line Integrals II - Line Integrals over a Vector Field
- 16.3: Line Integrals over Conservative Vector Fields (Path Independence)
- 16.4: Green's Theorem
- 16.4: Green's Theorem for Area
- 16.5: Intro to Surface Area Integrals - Key Formulas
- 16.5: Surface Area Integrals I - Cylindrical Parameterization of a Surface
- 16.5: Surface Area Integrals II - Spherical Parameterization of a Surface
- 16.5: Surface Area Integrals III - Implict and Explicit Formulas for Surface Area
- 16.6: Surface Integrals of Scalar Functions
- 16.6: Surface Integrals over Vector Fields I - Parameterized Surfaces
- 16.6: Surface Integrals over Vector Fields II - Implicitly Defined Surfaces
- 16.7: Stokes' Theorem I - Evaluating a Line Integral
- 16.7: Stokes' Theorem II - Finding the Flux of the Curl
- 16.8: Divergence Theorem I - Intro
- 16.8: Divergence Theorem II - What Happens when the Region is not Closed?