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Table of Contents
Introduction
Warmup
- Introduction
- Pretest and/or Skills Test (Pretest: 15 min)
- Differentiate (SWBQ: 10 min)
Representations of Multivariable Functions
- Surfaces (SWBQ: 10 min)
- Pizza and Cola (SWBQ: 10 min)
- Representations of surfaces (Lecture)
- Surfaces (Lecture)
- Contour Maps (Lecture)
Review
Review of Single Variable Integration
- Integration (SWBQ)
- Chop, Multiply, and Add (Lecture)
- Single Integrals (Lecture)
- The Cylinder (SGA: 10 min)
Review of Differentiation Rules
- Skills test (15 min)
- Derivative Rules (SWBQ)
- Derivative Rules from Differentials (Lecture: ?? min)
- Derivative and Integration rules (Lecture: ?? min)
Multiple Integrals
Double Integrals
- Double Integrals (Lecture)
- Chocolate (Lecture)
- Constant limits (SWBQ: ConcepTest)
- Activity: chop (single integrals)
- Wrap up: chop (double integrals)
- Order of Integration (Lecture)
- Match region to limits (SWBQ: ConcepTest)
- Non-constant limits (Lecture)
- Example: Computation
- Activity: Chop (Mass)
- Triple Integrals (Lecture)
- Mass (Lecture)
- Questions for integrals (Lecture)
Polar and Curvilinear Coordinates
- The Area of a Circle (SWBQ: 10 min)
- Integrals in Polar Coordinates (Lecture)
- Integrals in Curvilinear Coordinates (Lecture)
Partial Derivatives I
Differentials and Derivatives
- Derivatives? (SWBQ)
- Representations of Derivatives (Lecture)
- Representations of Partial Derivatives (Lecture)
- Differentials (Lecture)
- Computing Partial Derivatives (Lecture)
- Second-Order Partial Derivatives (Lecture)
Chain Rule
- Chain Rule (SWBQ)
- Chain Rule (Lecture)
- Tree Diagrams (Lecture)
- Summary and Examples (Lecture)
Vectors I
Introduction
Dot Product
- The Dot Product (SWBQ)
- The Dot Product (Lecture)
- Geometry and Algebra (Lecture)
Partial Derivatives II
Gradient and Directional Derivatives
- The Master Formula (Lecture)
- The Gradient (Lecture)
- Properties of the Gradient (Lecture)
- Directional Derivatives (Lecture)
Optimization
- Maxima and Minima (SQBQ)
- The Second-Derivative Test (SWBQ)
- Max/min (Lecture)
- Second-Derivative Test (Lecture)
- Lagrange multipliers (Lecture)
Vectors II
Applications
- The Cross Product (Lecture)
- Curves (Lecture)
- Parametric Curves (Lecture)
- Arclength (Lecture)
- Change of Variables (Lecture)
Extra
- Differentiation (SWBQ: 10 min)
