Table of Contents
Introduction
Review
Multiple Integrals
Partial Derivatives I
Vectors I
Partial Derivatives II
Vectors II
Extra
Introduction
Warmup
Prerequisite Ideas
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
(
SGA
)
Surfaces
(Lecture)
Contour Maps
(Lecture)
The Park
(
SGA
)
The Heater
(
SGA
)
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)
The Cake
(
SGA
)
Multiple Integrals
Double Integrals
Double Integrals
(Lecture)
Chocolate
(Lecture)
Constant limits
(SWBQ: ConcepTest)
Chop, Multiply, and Add
Activity: chop (single integrals)
Wrap up: chop (double integrals)
Integration
(
SGA
)
The Triangle
(
SGA
)
Order of Integration
(Lecture)
Match region to limits
(SWBQ: ConcepTest)
Non-constant limits
(Lecture)
Example: Computation
Reverse order of integration
(
SGA
)
Activity: Chop (Mass)
Triple Integrals
(Lecture)
Mass
(Lecture)
Questions for integrals
(Lecture)
Polar and Curvilinear Coordinates
The Area of a Circle
(SWBQ: 10 min)
Polar Coordinates
Curvilinear Coordinates
Area and Volume Elements
(
SGA
)
The Cone
(
SGA
: 1 hour)
Integrals in Polar Coordinates
(Lecture)
Integrals in Curvilinear Coordinates
(Lecture)
Partial Derivatives I
Differentials and Derivatives
Derivatives?
(SWBQ)
Representations of Derivatives
(Lecture)
The Heater II
(
SGA
)
The Hot Plate
(
SGA
)
Representations of Partial Derivatives
(Lecture)
Differentials
(Lecture)
Computing Partial Derivatives
(Lecture)
Drill
(
SGA
)
Second-Order Partial Derivatives
(Lecture)
Chain Rule
Chain Rule
(SWBQ)
Chain Rule
(Lecture)
Tree Diagrams
(Lecture)
Chain Rule
(
SGA
)
Summary and Examples
(Lecture)
Resistors
(
SGA
)
Chain Rule Measurements
(
SGA
)
Vectors I
Introduction
Vectors
(SWBQ)
Vectors
(Lecture)
Dot Product
The Dot Product
(SWBQ)
The Dot Product
(Lecture)
Geometry and Algebra
(Lecture)
Partial Derivatives II
Gradient and Directional Derivatives
The Hillside
(
SGA
)
The Master Formula
(Lecture)
The Gradient
(Lecture)
Properties of the Gradient
(Lecture)
Directional Derivatives
(
SGA
)
Directional Derivatives
(Lecture)
The Puddle
(
SGA
)
Optimization
Maxima and Minima
(SQBQ)
The Second-Derivative Test
(SWBQ)
Max/min
(Lecture)
Second-Derivative Test
(Lecture)
The Gold Mine
(
SGA
)
The Water Table
(
SGA
)
The Roller Coaster
(
SGA
)
Lagrange multipliers
(Lecture)
Optimization
(
SGA
)
Vectors II
Applications
The Cross Product
(Lecture)
Cross Product
(
SGA
)
The Cube
(
SGA
)
Curves
(Lecture)
Parametric Curves
(Lecture)
Arclength
(Lecture)
Change of Variables
(Lecture)
Change of Variables
(
SGA
)
Extra
Learning Outcomes
Differentiation
(SWBQ: 10 min)