Ivan Li

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)

Chapter 12 - Vectors and the Geometry of Space

• 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

Chapter 13 - Vector-Valued Functions and Motion in Space

• 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

Chapter 14 - Partial Derivatives

• 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
  • Addendum - A Slight Mistake in the Algebra

Chapter 15 - Multiple Integrals

• 15.1: Intro to Double Integrals
• 15.2: Sketching Regions and Finding Boundaries
• 15.2: Switching the Order of Integration
  • Addendum - Another Switching the Order of Integration Example
• 15.3: Area by Double Integration
• 15.4: Setting up Polar Integrals
• 15.4: Converting Cartesian Integrals to Polar
  • Addendum - Hints from the Integral Bounds to Convert 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
  • Cone Example cont.
• 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

Chapter 16 - Integrals and Vector Fields

• 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
  • Addendum - Correcting the Spherical Parameterization
• 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
  • Addendum - Deciphering the Wording of a Problem - Bounded (lid) or Hollow (no lid)?
• 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?