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Workbook for Stewart’s "Calculus"
Cory Wilson
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Front Matter
1
Functions and Limits
1.1
Four Ways to Represent a Function
1.1.1
Before Class
1.1.1.1
Functions
1.1.1.2
Representations of Functions
1.1.2
Pre-Class Activities
1.1.3
In Class
1.1.3.1
Piecewise Defined Functions
1.1.3.2
Symmetry
1.1.3.3
Increasing and Decreasing Functions
1.1.4
After Class Activities
1.1.5
Section 1.1 Additional Resources
1.1.5.1
Functions
1.1.5.2
Piecewise Functions
1.1.5.3
Symmetry
1.1.5.4
Difference Quotients
1.2
Mathematical Models: A Catalog of Essential Functions
1.2.1
Before Class
1.2.1.1
Linear Functions
1.2.1.2
Polynomials
1.2.1.3
Other Functions
1.2.2
Pre-Class Activities
1.2.3
In Class
1.2.3.1
Power Functions
1.2.3.2
Rational Functions
1.2.3.3
Algebraic Functions
1.2.3.4
Trigonometric Functions
1.2.4
After Class Activities
1.2.5
Section 1.2 Resources
1.2.5.1
Essential Functions
1.3
New Functions from Old Functions
1.3.1
Before Class
1.3.1.1
Combinations of Functions
1.3.1.2
Transformations of Functions
1.3.2
Pre-Class Activities
1.3.3
In Class
1.3.4
After Class Activities
1.3.5
Section 1.3 Resources
1.3.5.1
Function Operations
1.3.5.2
Graph Transformations
1.4
The Tangent and Velocity Problems
1.4.1
Before Class
1.4.1.1
Tangent Lines & Secant Lines
1.4.2
Pre-Class Activities
1.4.3
In Class
1.4.3.1
Velocity
1.4.4
After Class Activities
1.5
The Limit of a Function
1.5.1
Before Class
1.5.1.1
Motivating Example
1.5.1.2
The Limit
1.5.2
Pre-Class Activities
1.5.3
In Class
1.5.3.1
One-Sided Limits
1.5.3.2
Infinite Limits
1.5.4
After Class Activities
1.6
Calculating Limits Using Limit Laws
1.6.1
Before Class
1.6.1.1
Limit Laws
1.6.2
Pre-Class Activities
1.6.3
In Class
1.6.3.1
Two Theorems
1.6.4
After Class Activities
1.7
(X) The Precise Definition of a Limit
1.8
Continuity
1.8.1
Before Class
1.8.1.1
The Definition
1.8.2
Pre-Class Activities
1.8.3
In Class
1.8.3.1
Useful Results
1.8.3.2
The Intermediate Value Theorem
1.8.4
After Class Activities
2
Derivatives
2.1
Derivatives and Rates of Change
2.1.1
Before Class
2.1.1.1
2.1.1.2
Tangents & Velocities
2.1.1.3
Derivatives
2.1.2
Pre-Class Activities
2.1.3
In Class
2.1.3.1
Rates of Change
2.1.4
After Class Activities
2.2
The Derivative as a Function
2.2.1
Before Class
2.2.1.1
The Derivative as a Function
2.2.1.2
Differentiability & Non-Differentiability
2.2.1.3
Other Notations
2.2.2
Pre-Class Activities
2.2.3
In Class
2.2.3.1
Derivatives
2.2.3.2
Slope Graphs
2.2.3.3
Higher Derivatives
2.2.4
After Class Activities
2.3
Differentiation Formulas
2.3.1
Before Class
2.3.1.1
Constant Functions
2.3.1.2
Power Functions
2.3.1.3
New Derivatives from Old
2.3.2
Pre-Class Activities
2.3.3
In Class
2.3.4
After Class Activities
2.4
Derivatives of Trigonometric Functions
2.4.1
Before Class
2.4.1.1
Special Trig Limits
2.4.1.2
Derivative of Sine
2.4.1.3
Other Trig Derivatives
2.4.2
Pre-Class Activities
2.4.3
In Class
2.4.3.1
Trig Derivatives
2.4.4
After Class Activities
2.5
The Chain Rule
2.5.1
Before Class
2.5.1.1
Review: Composition of Functions
2.5.1.2
The Chain Rule
2.5.2
Pre-Class Activities
2.5.3
In Class
2.5.4
After Class Activities
2.6
Implicit Differentiation
2.6.1
Before Class
2.6.1.1
The Idea
2.6.2
Pre-Class Activities
2.6.3
In Class
2.6.4
After Class Activities
2.7
(X) Rates of Changes in the Natural and Social Sciences
2.8
Related Rates
2.8.1
Before Class
2.8.1.1
Functions of Time
2.8.2
Pre-Class Activities
2.8.3
In Class
2.8.3.1
Related Rates
2.8.4
After Class Activities
3
Applications of Differentiation
3.1
Maximum & Minimum Values
3.1.1
Before Class
3.1.1.1
Definitions
3.1.1.2
Important Results
3.1.2
Pre-Class Activities
3.1.3
In Class
3.1.3.1
Critical Numbers
3.1.3.2
Finding Absolute Maxima & Minima
3.1.4
After Class Activities
3.2
(X) The Mean Value Theorem
3.2.1
Before Class
3.2.1.1
Rolle’s Theorem
3.2.1.2
Mean Value Theorem
3.2.2
Pre-Class Activities
3.2.3
In Class
3.2.4
After Class Activities
3.3
How Derivatives Affect the Shape of a Graph
3.3.1
Before Class
3.3.1.1
Increasing/Decereasing Test
3.3.1.2
Local Extrema
3.3.1.3
Concavity
3.3.2
Pre-Class Activities
3.3.3
In Class
3.3.4
After Class Activities
3.4
Limits at Infinity & Horizontal Asymptotes
3.4.1
Before Class
3.4.1.1
The Ideas
3.4.2
Pre-Class Activities
3.4.3
In Class
3.4.3.1
Computing Limits at Infinity
3.4.4
After Class Activities
3.5
Summary of Curve Sketching
3.5.1
Before Class
3.5.1.1
Summary of Graphing
3.5.2
Pre-Class Activities
3.5.3
In Class
3.5.4
After Class Activities
3.6
(X) Graphing with Calculus and Calculators
3.7
Optimization
3.7.1
Before Class
3.7.1.1
Optimization
3.7.2
Pre-Class Activities
3.7.3
In Class
3.7.4
After Class Activities
3.8
(X) Newton’s Method
3.9
Antiderivatives
3.9.1
Before Class
3.9.1.1
Derivatives
3.9.1.2
The Antiderivative
3.9.2
Pre-Class Activities
3.9.3
In Class
3.9.4
After Class Activities
4
Integrals
4.1
Areas & Distance
4.1.1
Before Class
4.1.1.1
The Area Problem
4.1.1.2
Sigma Notation
4.1.2
Pre-Class Activities
4.1.3
In Class
4.1.3.1
The Distance Problem
4.1.4
After Class Activities
4.2
The Definite Integral
4.2.1
Before Class
4.2.1.1
Definition of the Definite Integral
4.2.2
Pre-Class Activities
4.2.3
In Class
4.2.3.1
Evaluating Integrals
4.2.3.2
The Midpoint Rule
4.2.3.3
Properties of the Definite Integral
4.2.4
After Class Activities
4.3
The Fundamental Theorem of Calculus
4.3.1
Before Class
4.3.1.1
The First Fundamental Theorem
4.3.2
Pre-Class Activities
4.3.3
In Class
4.3.3.1
The Second Fundamental Theorem
4.3.4
After Class Activities
4.4
Indefinite Integrals & the Net Change Theorem
4.4.1
Before Class
4.4.1.1
Indefinite Integrals
4.4.2
Pre-Class Activities
4.4.3
In Class
4.4.3.1
The Net Change Theorem
4.4.3.2
Practice
4.4.4
After Class Activities
4.5
The Substitution Rule
4.5.1
Before Class
4.5.1.1
The Rule for Indefinite & Definite Integrals
4.5.2
Pre-Class Activities
4.5.3
In Class
4.5.3.1
Examples
4.5.4
After Class Activities
5
Applications of Integration
5.1
Areas Between Curves
5.1.1
Before Class
5.1.1.1
Area
5.1.2
Pre-Class Activities
5.1.3
In Class
5.1.3.1
Examples
5.1.4
After Class Activities
5.2
Volumes
5.2.1
Before Class
5.2.1.1
Volumes by Cross-Sections
5.2.2
Pre-Class Activities
5.2.3
In Class
5.2.3.1
Disk Method
5.2.3.2
Washer Method
5.2.4
After Class Activities
5.3
Volumes by Cylindrical Shells
5.3.1
Before Class
5.3.1.1
Slicing with Cylinders
5.3.1.2
The Shell Method
5.3.2
Pre-Class Activities
5.3.3
In Class
5.3.4
After Class Activities
6
Inverse Functions
6.1
Inverse Functions
6.1.1
Before Class
6.1.1.1
Inverse Functions & Properties
6.1.2
Pre-Class Activities
6.1.3
In Class
6.1.3.1
Calculus of Inverse Functions
6.1.4
After Class Activities
6.2
Exponential Functions & Derivatives
6.2.1
Before Class
6.2.1.1
Exponential Functions
6.2.1.2
Calculus of Exponentials
6.2.2
Pre-Class Activities
6.2.3
In Class
6.2.3.1
Examples
6.2.4
After Class Activities
6.3
Logarithmic Functions
6.3.1
Before Class
6.3.1.1
Logarithmic Functions
6.3.2
Pre-Class Activities
6.3.3
In Class
6.3.3.1
The Natural Logarithm
6.3.4
After Class Activities
6.4
Derivatives of Logarithmic Functions
6.4.1
Before Class
6.4.1.1
The Natural Logarithm
6.4.2
Pre-Class Activities
6.4.3
In Class
6.4.3.1
General Logs and Exponentials
6.4.3.2
Logarithmic Differentiation
6.4.4
After Class Activities
6.5
(X) Exponential Growth and Decay
6.6
Inverse Trigonometric Functions
6.6.1
Before Class
6.6.1.1
Building Inverse Trig Functions
6.6.2
Pre-Class Activities
6.6.3
In Class
6.6.3.1
Derivatives of Inverse Trig Functions
6.6.3.2
Integrals of Inverse Trig Functions
6.6.4
After Class Activities
6.7
(X) Hyperbolic Functions
6.8
Indeterminate Forms & l’Hospital’s Rule
6.8.1
Before Class
6.8.1.1
l’Hospital’s Rule
6.8.2
Pre-Class Activities
6.8.3
In Class
6.8.3.1
Other Indeterminate Forms
6.8.3.2
Examples
6.8.4
After Class Activities
7
Techniques of Integration
7.1
Integration by Parts
7.1.1
Before Class
7.1.1.1
The Formula
7.1.2
Pre-Class Activities
7.1.3
In Class
7.1.3.1
Examples
7.1.4
After Class Activities
7.2
Trigonometric Integrals
7.2.1
Before Class
7.2.1.1
Trigonometric Identities
7.2.1.2
Trigonometric Integrals
7.2.2
Pre-Class Activities
7.2.3
In Class
7.2.3.1
Strategies for Trig Integrals
7.2.4
After Class Activities
7.3
Trigonometric Substitution
7.3.1
Before Class
7.3.1.1
The Substitutions
7.3.2
Pre-Class Activities
7.3.3
In Class
7.3.3.1
Examples
7.3.4
After Class Activities
7.4
Integration of Rational Functions by Partial Fractions
7.4.1
Before Class
7.4.1.1
Distinct Linear Factors
7.4.2
Pre-Class Activities
7.4.3
In Class
7.4.3.1
Repeated Linear Factors
7.4.3.2
Irreducible Quadratic Factors
7.4.3.3
Functions with Repeated Irreducible Quadratic Factors
7.4.4
After Class Activities
7.5
Strategy for Integration
7.5.1
Before Class
7.5.1.1
Integrals We Know
7.5.1.2
Strategies
7.5.2
Pre-Class Activities
7.5.3
In Class
7.5.3.1
Examples
7.5.4
After Class Activities
7.6
(X) Integration Using Tables and Computer Algebra Systems
7.7
(X) Approximate Integration
7.8
Improper Integrals
7.8.1
Before Class
7.8.1.1
Type 1 Integrals
7.8.2
Pre-Class Activities
7.8.3
In Class
7.8.3.1
Type 2 Integrals
7.8.4
After Class Activities
8
Further Applications of Integration
8.1
Arc Length
8.1.1
Before Class
8.1.1.1
The Formula
8.1.2
Pre-Class Activities
8.1.3
In Class
8.1.3.1
Some Examples
8.1.3.2
Arc Length Function
8.1.4
After Class Activities
8.2
(X) Area of a Surface of Revolution
8.3
(X) Applications to Physics and Engineering
8.4
(X) Applications to Economics and Biology
8.5
(X) Probability
9
Differential Equations
9.1
(X) Modeling with Differential Equations
9.2
(X) Direction Fields and Euler’s Method
9.3
(X) Separable Equations
9.4
(X) Models for Population Growth
9.5
(X) Linear Equations
9.6
(X) Predator-Prey Systems
10
Parametric Equations and Polar Coordinates
10.1
Curves Defined by Parametric Equations
10.1.1
Before Class
10.1.1.1
Parametric Equations
10.1.2
Pre-Class Activities
10.1.3
In Class
10.1.3.1
Examples
10.1.4
After Class Activities
10.2
Calculus with Parametric Curves
10.2.1
Before Class
10.2.1.1
Tangents
10.2.2
Pre-Class Activities
10.2.3
In Class
10.2.3.1
Areas
10.2.3.2
Arc Length
10.2.4
After Class Activities
10.3
Polar Coordinates
10.3.1
Before Class
10.3.1.1
The Polar Coordinate System
10.3.2
Pre-Class Activities
10.3.3
In Class
10.3.3.1
Polar Curves
10.3.3.2
Tangents to Polar Curves
10.3.4
After Class Activities
10.4
Calculus in Polar Coordinates
10.4.1
Before Class
10.4.1.1
Area
10.4.2
Pre-Class Activities
10.4.3
In Class
10.4.3.1
Arc Length
10.4.3.2
Tangents
10.4.4
After Class Activities
10.5
(X) Conic Sections
10.6
(X) Conic Sections in Polar Coordinates
11
Sequences, Series, and Power Series
11.1
Sequences
11.1.1
Before Class
11.1.1.1
Sequences
11.1.2
Pre-Class Activities
11.1.3
In Class
11.1.3.1
Working with Sequences
11.1.4
After Class Activities
11.2
Series
11.2.1
Before Class
11.2.1.1
Finite & Infinite Series
11.2.1.2
Geometric Series
11.2.2
Pre-Class Activities
11.2.3
In Class
11.2.3.1
Some Examples
11.2.3.2
Working with Infinite Series
11.2.4
After Class Activities
11.3
The Integral Test and Estimates of Sums
11.3.1
Before Class
11.3.1.1
The Integral Test
11.3.2
Pre-Class Activities
11.3.3
In Class
11.3.3.1
Some Examples
11.3.3.2
Estimating the Sum of a Series
11.3.4
After Class Activities
11.4
The Comparison Tests
11.4.1
Before Class
11.4.1.1
The Direct Comparison Test
11.4.2
Pre-Class Activities
11.4.3
In Class
11.4.3.1
Some Examples
11.4.3.2
The Limit Comparison Test
11.4.4
After Class Activities
11.5
Alternating Series and Absolute Convergence
11.5.1
Before Class
11.5.1.1
The Alternating Series Test
11.5.2
Pre-Class Activities
11.5.3
In Class
11.5.3.1
Some Examples
11.5.3.2
Absolute & Conditional Convergence
11.5.4
After Class Activities
11.6
The Ratio and Root Tests
11.6.1
Before Class
11.6.1.1
The Ratio Test
11.6.2
Pre-Class Activities
11.6.3
In Class
11.6.3.1
Some Examples
11.6.3.2
Absolute & Conditional Convergence
11.6.4
After Class Activities
11.7
Strategy for Testing Series
11.7.1
Before Class
11.7.1.1
Convergence Tests
11.7.1.2
Strategies
11.7.2
Pre-Class Activities
11.7.3
In Class
11.7.3.1
Some Examples
11.7.4
After Class Activities
11.8
Power Series
11.8.1
Before Class
11.8.1.1
Power Series
11.8.2
Pre-Class Activities
11.8.3
In Class
11.8.3.1
Radius & Interval of Convergence
11.8.4
After Class Activities
11.9
Representations of Functions as Power Series
11.9.1
Before Class
11.9.1.1
Functions as Power Series
11.9.2
Pre-Class Activities
11.9.3
In Class
11.9.3.1
Some Examples
11.9.3.2
Calculus & Power Series
11.9.4
After Class Activities
11.10
Taylor and Maclaurin Series
11.10.1
Before Class
11.10.1.1
The Idea
11.10.2
Pre-Class Activities
11.10.3
In Class
11.10.3.1
Taylor Polynomials
11.10.3.2
Useful Maclaurin Series
11.10.3.3
Multiplication/Division of Power Series
11.10.4
After Class Activities
11.11
Applications of Taylor Polynomials
11.11.1
Before Class
11.11.1.1
Approximating Functions by Polynomials
11.11.2
Pre-Class Activities
11.11.3
In Class
11.11.3.1
Examples and Applications
11.11.4
After Class Activities
12
Vectors and the Geometry of Space
12.1
Three-Dimensional Coordinate Systems
12.1.1
Before Class
12.1.1.1
3D Space
12.1.1.2
Surfaces
12.1.2
Pre-Class Activities
12.1.3
In Class
12.1.3.1
Distances and Spheres
12.1.4
After Class Activities
12.2
Vectors
12.2.1
Before Class
12.2.1.1
Vectors & Operations
12.2.1.2
Components
12.2.2
Pre-Class Activities
12.2.3
In Class
12.2.3.1
Properties of Vectors
12.2.3.2
Unit Vectors
12.2.3.3
Applications of Vectors
12.2.4
After Class Activities
12.3
The Dot Product
12.3.1
Before Class
12.3.1.1
The Dot Product
12.3.1.2
Properties of the Dot Product
12.3.2
Pre-Class Activities
12.3.3
In Class
12.3.3.1
Geometric Definition of the Dot Product
12.3.3.2
Direction Angles & Direction Cosines
12.3.3.3
Projections
12.3.4
After Class Activities
12.4
The Cross Product
12.4.1
Before Class
12.4.1.1
The Cross Product
12.4.2
Pre-Class Activities
12.4.3
In Class
12.4.3.1
Some Examples
12.4.3.2
Product of the Cross Product
12.4.3.3
Applications of the Cross Product
12.4.4
After Class Activities
12.5
Equations of Lines and Planes
12.5.1
Before Class
12.5.1.1
Lines
12.5.2
Pre-Class Activities
12.5.3
In Class
12.5.3.1
Planes
12.5.3.2
Distances
12.5.4
After Class Activities
12.6
(X) Cylinders and Quadric Surfaces
13
Vector Functions
13.1
Vector Functions and Space Curves
13.1.1
Before Class
13.1.1.1
Vector-Valued Functions
13.1.2
Pre-Class Activities
13.1.3
In Class
13.1.3.1
Limits & Continuity
13.1.3.2
Space Curves
13.1.4
After Class Activities
13.2
Derivatives and Integrals of Vector Functions
13.2.1
Before Class
13.2.1.1
Derivatives
13.2.1.2
Integrals
13.2.2
Pre-Class Activities
13.2.3
In Class
13.2.3.1
Examples
13.2.4
After Class Activities
13.3
Arc Length and Curvature
13.3.1
Before Class
13.3.1.1
Arc Length
13.3.2
Pre-Class Activities
13.3.3
In Class
13.3.3.1
Arc Length Function
13.3.3.2
Curvature
13.3.3.3
Normal and Binormal Vectors
13.3.3.4
Torsion
13.3.4
After Class Activities
13.4
Motion in Space: Velocity and Acceleration
13.4.1
Before Class
13.4.1.1
Velocity, Speed, Acceleration
13.4.2
Pre-Class Activities
13.4.3
In Class
13.4.3.1
Some Examples
13.4.3.2
Tangential and Normal Components of Acceleration
13.4.4
After Class Activities
14
Partial Derivatives
14.1
Functions of Several Variables
14.1.1
Before Class
14.1.1.1
Functions of Two Variables
14.1.1.2
Functions of Multiple Variables
14.1.2
Pre-Class Activities
14.1.3
In Class
14.1.3.1
Graphs
14.1.3.2
Level Curves and Contour Maps
14.1.4
After Class Activities
14.2
Limits and Continuity
14.2.1
Before Class
14.2.1.1
Limits of Functions of Two Variables
14.2.1.2
Limits of Functions of Multiple Variables
14.2.2
Pre-Class Activities
14.2.3
In Class
14.2.3.1
Some Examples
14.2.3.2
Properties of Limits
14.2.3.3
Continuity
14.2.4
After Class Activities
14.3
Partial Derivatives
14.3.1
Before Class
14.3.1.1
Partial Derivatives of Functions of Two Variables
14.3.2
Pre-Class Activities
14.3.3
In Class
14.3.3.1
Some Examples
14.3.3.2
Interpretations of Partial Derivatives
14.3.3.3
Higher-Order Partial Derivatives
14.3.4
After Class Activities
14.4
Tangent Planes and Linear Approximations
14.4.1
Before Class
14.4.1.1
Tangent Planes
14.4.2
Pre-Class Activities
14.4.3
In Class
14.4.3.1
Linear Approximations
14.4.4
After Class Activities
14.5
The Chain Rule
14.5.1
Before Class
14.5.1.1
Review: The Chain Rule
14.5.1.2
The Multivariate Chain Rule
14.5.2
Pre-Class Activities
14.5.3
In Class
14.5.3.1
Some Examples
14.5.3.2
The Multivariate Chain Rule: General Version
14.5.4
After Class Activities
14.6
Directional Derivatives and the Gradient Vector
14.6.1
Before Class
14.6.1.1
Directional Derivatives
14.6.2
Pre-Class Activities
14.6.3
In Class
14.6.3.1
The Gradient Vector
14.6.4
After Class Activities
14.7
Maximum and Minimum Values
14.7.1
Before Class
14.7.1.1
Review: Maximum/Minimum Values
14.7.1.2
Local Maximum/Minimum Values
14.7.2
Pre-Class Activities
14.7.3
In Class
14.7.3.1
Some Examples
14.7.3.2
Absolute Maximum/Minimum Values
14.7.4
After Class Activities
14.8
Lagrange Multipliers
14.8.1
Before Class
14.8.1.1
The Idea
14.8.1.2
One-Constraint Lagrange Multipliers
14.8.2
Pre-Class Activities
14.8.3
In Class
14.8.3.1
Some Examples
14.8.3.2
Two-Constraint Lagrange Multipliers
14.8.4
After Class Activities
15
Multiple Integrals
15.1
Double Integrals over Rectangles
15.1.1
Before Class
15.1.1.1
Review: The Definite Integral
15.1.1.2
The Double Integral
15.1.2
Pre-Class Activities
15.1.3
In Class
15.1.3.1
Midpoint Rule
15.1.3.2
Iterated Integrals
15.1.4
After Class Activities
15.2
Double Integrals over General Regions
15.2.1
Before Class
15.2.1.1
General Regions
15.2.1.2
Properties of Double Integrals
15.2.2
Pre-Class Activities
15.2.3
In Class
15.2.3.1
Some Examples
15.2.3.2
Changing the Order of Integration
15.2.4
After Class Activities
15.3
Double Integrals in Polar Coordinates
15.3.1
Before Class
15.3.1.1
Review: Polar Coordinates
15.3.1.2
Double Integrals in Polar Coordinates
15.3.2
Pre-Class Activities
15.3.3
In Class
15.3.3.1
Some Examples
15.3.4
After Class Activities
15.4
(X) Applications of Double Integrals
15.5
Surface Area
15.5.1
Before Class
15.5.1.1
Review: Surface Area
15.5.1.2
Surface Area
15.5.2
Pre-Class Activities
15.5.3
In Class
15.5.3.1
Some Examples
15.5.4
After Class Activities
15.6
Triple Integrals
15.6.1
Before Class
15.6.1.1
Triple Integrals
15.6.2
Pre-Class Activities
15.6.3
In Class
15.6.3.1
Some Examples
15.6.3.2
Triple Integrals over General Regions
15.6.3.3
Changing the Order of Integration
15.6.3.4
Applications of Triple Integrals
15.6.4
After Class Activities
15.7
Triple Integrals in Cylindrical Coordinates
15.7.1
Before Class
15.7.1.1
Cylindrical Coordinates
15.7.1.2
Triple Integrals in Cylindrical Coordinates
15.7.2
Pre-Class Activities
15.7.3
In Class
15.7.3.1
Examples
15.7.4
After Class Activities
15.8
Triple Integrals in Spherical Coordinates
15.8.1
Before Class
15.8.1.1
Spherical Coordinates
15.8.1.2
Triple Integrals in Spherical Coordinates
15.8.2
Pre-Class Activities
15.8.3
In Class
15.8.3.1
Examples
15.8.4
After Class Activities
15.9
Change of Variables in Multiple Integrals
15.9.1
Before Class
15.9.1.1
The Idea
15.9.1.2
Change of Variables in Double Integrals
15.9.2
Pre-Class Activities
15.9.3
In Class
15.9.3.1
Some Examples
15.9.3.2
Change of Variables in Triple Integrals
15.9.4
After Class Activities
16
Vector Calculus
16.1
Vector Fields
16.1.1
Before Class
16.1.1.1
Vector Fields in
\(\R^2\)
and
\(\R^3\)
16.1.2
Pre-Class Activities
16.1.3
In Class
16.1.3.1
Some Examples
16.1.3.2
Gradient Fields
16.1.4
After Class Activities
16.2
Line Integrals
16.2.1
Before Class
16.2.1.1
The Idea
16.2.1.2
Line Integrals in the Plane
16.2.2
Pre-Class Activities
16.2.3
In Class
16.2.3.1
Some Examples
16.2.3.2
Line Integrals in Space
16.2.3.3
Line Integrals of Vector Fields
16.2.4
After Class Activities
16.3
The Fundamental Theorem for Line Integrals
16.3.1
Before Class
16.3.1.1
The Fundamental Theorem for Line Integrals
16.3.2
Pre-Class Activities
16.3.3
In Class
16.3.3.1
Some Examples
16.3.3.2
Conservative Vector Fields and Potential Functions
16.3.4
After Class Activities
16.4
Green’s Theorem
16.4.1
Before Class
16.4.1.1
Green’s Theorem
16.4.2
Pre-Class Activities
16.4.3
In Class
16.4.3.1
Examples
16.4.4
After Class Activities
16.5
Curl and Divergence
16.5.1
Before Class
16.5.1.1
Curl
16.5.1.2
Divergence
16.5.2
Pre-Class Activities
16.5.3
In Class
16.5.3.1
Examples
16.5.3.2
Vector Forms of Green’s Theorem
16.5.4
After Class Activities
16.6
Parametric Surfaces and Their Areas
16.6.1
Before Class
16.6.1.1
Review: Parametric Equations
16.6.1.2
Parametric Surfaces
16.6.2
Pre-Class Activities
16.6.3
In Class
16.6.3.1
Some Examples
16.6.3.2
Surfaces of Revolution
16.6.3.3
Tangent Planes
16.6.3.4
Surface Area
16.6.4
After Class Activities
16.7
Surface Integrals
16.7.1
Before Class
16.7.1.1
Parametric Surfaces
16.7.1.2
Graphs of Functions
16.7.2
Pre-Class Activities
16.7.3
In Class
16.7.3.1
Some Examples
16.7.3.2
Oriented Surfaces
16.7.3.3
Surface Integrals of Vector Fields & Flux
16.7.4
After Class Activities
16.8
Stoke’s Theorem
16.8.1
Before Class
16.8.1.1
The Idea
16.8.1.2
Stoke’s Theorem
16.8.2
Pre-Class Activities
16.8.3
In Class
16.8.3.1
Examples
16.8.4
After Class Activities
16.9
The Divergence Theorem
16.9.1
Before Class
16.9.1.1
The Idea
16.9.1.2
The Divergence Theorem
16.9.2
Pre-Class Activities
16.9.3
In Class
16.9.3.1
Examples
16.9.4
After Class Activities
Section
2.7
(X) Rates of Changes in the Natural and Social Sciences
We don’t cover this section, but feel free to read it!
