*[https://www.youtube.com/watch?v=HxRG_phgGUw&t=10831s How to Solve Double/Repeated/Iterated Integrals ] Video by Professor Leonar
* [https://www.youtube.com/watch?v=NETmfwOAKpQ Double Integrals - Changing Order of Integration - Full Ex. ] Video by patrickJMT
*[https://www.youtube.com/watch?v=k7ND70gFTLU Calculating Double Integrals over General Regions] Video by patrickJMT
*[https://www.youtube.com/watch?v=DYsv6L-VcsQ Calculating a Double Integral ] Video by -patrickJMT

Double Integrals over General Regions

2020-10-27T03:47:00Z

Vu.nguyen:

2020-10-26T02:26:46Z

Vu.nguyen: Created page with "Lagrange Multipliers"

Lagrange Multipliers

MAT2214

2020-09-26T17:11:13Z

Vu.nguyen: /* Topics List */

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes

|-

|Week 1

||

<div style="text-align: center;">1.1</div>

||

[[Polar Coordinates]]

||

* [[Trigonometric Functions: Unit Circle Approach]] 
* [[The inverse Sine, Cosine and Tangent functions]] 

||

* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa

|-

|Week 1

||

<div style="text-align: center;">1.2</div>

||

[[Three-Dimensional Coordinate Systems]]

||

* [[Bases and Linear Independence| Two-dimensional coordinate systems]] 
* [[Solving Equations| Algebraic Expressions]] 

||

* Three-dimensional coordinate systems
* Distance Formula in R<sup>3</sup>
* Standard Equation for a Sphere

|-

|Weeks 1/2

||

<div style="text-align: center;">2.1</div>

||

[[Vectors in The Plane]]

||

* [[Linear Equations|Line Segments]] 
* [[Distance Formula| Distance Formula]] 

||

* Vector Algebra Operations
* The Magnitude of a vector
* Unit Vectors
* The Midpoint of a Line Segment
* The Vector projection

|-

|Week 2

||

<div style="text-align: center;">2.2</div>

||

[[Vectors in Space]]

||

* [[Vectors in the Plane ]]
* [[Distance Formula]] 

||

* Vector Algebra Operations
* The Magnitude of a vector
* Unit Vectors
* The Midpoint of a Line Segment
* The Vector projection

|-

|Week 2

||

<div style="text-align: center;">2.3</div>

||

[[The Dot Product]]

||

* [[Trig. Functions|Basic Trig Functions]] 
* [[Vectors]]  

||
* Definition of Dot Product
* Properties of Dot Product
* Angle between vectors
* Orthogonal vectors

|-

|Week 2

||

<div style="text-align: center;">2.4</div>

||

[[The Cross Product]]

||

* [[Trig. Functions|Basic Trig Functions]] 
* [[Determinants]] 
* [[Vectors]]

||

* Definition of Cross Product
* Properties of the cross product
* Area of a parallelogram
* Cross product as a determinant

||

|-

|Week 3

||

<div style="text-align: center;">2.5</div>

||

[[Equations of Lines, Planes and Surfaces in Space]]

||

* [[The Dot Product]] 
* [[The Cross Product]]
* [[Quadratic Functions]] 
* [[Parametric Equations]] 

||

* Write the vector, parametric equation of a line through a given point in a given direction, and a line through two given points.
* Find the distance from a point to a given line.
* Write the equation of a plane through a given point with a given normal, and a plane through three given points.
* Find the distance from a point to a given plane.

||

|-

|Week 3

||

<div style="text-align: center;">2.6</div>

||

[[Cylinders and Quadratic Surfaces]]

||

* [[Quadratic Functions]] 
* [[Parametric Equations]] 
* '''[[Conics]]''' 

||

* Find equations for cylinders that are generated by rotating lines that are parallel to a plane
* Understand basic quadratic surfaces
* Understand general quadratic surfaces

||

|-

|Weeks 3/4

||

<div style="text-align: center;">3.1, 3.2</div>

||

[[Curves in Space and Vector-Valued Functions]]

||

* [[Parametric Equations]] 
* [[Vectors]]  
* [[The Derivative as a Function]] 
* [[The Limit of a Function]] 
* [[Continuity of a function]] 
* [[The Dot Product]] 
* [[The Cross Product]] 

||

* Vector functions
* Limits of vector functions
* Continuity of vector functions
* Differentiation rules for vector functions
* Curves and paths in space

||

|-

|Week 4

||

<div style="text-align: center;">3.3</div>

||

[[Arc Length]]

||

* '''[[Distance Formula| The Length of a Line Segment]]''' 
* [[Curves in Space and Vector Functions|Vector Functions]] 
* [[Integrals of Vector Functions]] 

||

* The arc Length of a vector function
* Arc length parameterization
||

|-

|Weeks 4/5

||

<div style="text-align: center;">3.4</div>

||

[[Motion in Space]]

||
* [[Vectors]] 
* [[Parametric Equations]] 
* [[The Cross Product]] 
* [[Derivatives of Vector Functions]] 
||
* The Unit tangent vector
* The curvature
* The Principal Unit Normal Vector
* The Binormal Vector
* The tangential and normal components of acceleration
* The Torsion
||

|-

|Week 5/6

||

<div style="text-align: center;">4.1</div>

||

[[Functions of Several Variables]]

||

* [[Domain of a Function]] 
* [[Range of a Function]] 
* [[Solving Inequalities]] 
* [[Graphs| Graphing a Function]] 

||
* Functions of two variables
* Functions of three variables
* Domain and range of multivariable functions
* Bounded regions
* Graphs and level curves of two variable functions
* Level surfaces of three variable functions
|-

|Week 6

||

<div style="text-align: center;">4.2</div>

||

[[Limit and Continuity of Function of Several Variables]]

||

* [[The Limit and Continuity of a Function]] 
* [[The Limit Laws for Functions]] 
* [[Composition of Functions]] 
* [[The Dot Product]] 

||

* Limits of functions of two variables
* Limits of functions of more than two variables
* Properties of limits of functions of several variables
* Two path test of non-existing of a limit
* Continuity for functions of several variables
* Continuity of composition
* Extreme values on closed and bounded domains
|-

|Week 6

||

<div style="text-align: center;">4.3</div>

||

[[Partial Derivatives]]

||

* [[The derivative and second derivative of a function ]] 
* [[The limit and continuity for a function of several variables]] 

||
* Partial derivatives for functions of two variables
* Partial derivatives for functions of more than two variables
* Partial derivatives and continuity
* Second order partial derivatives
* Mixed derivative theorem
|-

|Week 7

||

<div style="text-align: center;">4.4</div>

||

[[Directional Derivatives and Gradient Vectors]]

||
* [[Trigonometric Functions]] 
* [[Vectors, Unit Vectors]]  
* [[Partial Derivatives]] 
* Gradients
* [[The Dot Product]] 
||
* Directional derivatives for functions of two variables
* Gradients
* Properties of directional derivatives
* Tangents to level curves
* Directional derivatives for functions of three variables
|-

|Week 7

||

<div style="text-align: center;">4.5</div>

||
[[Tangent Plane]]
[[Differentiability]]

||
* [[Partial Derivatives]] 
* [[Parametric Equations of Lines]]
* [[Equations of Planes]]

||
* Determine the equation of a plane tangent to a given surface at a point
* Determine the parametric equation of a normal line to a given surface at a point
* The linear approximation of a function of two variables at a point
* The definition of differentiability for a function of two variables
* Differentiability implies Continuity
* Continuity of First Partial Derivatives implies Differentiability
* The definition of total differentiability for a function of two variables
* Use the total differential to approximate the change in a function of two variables
|-

|Week 7

||

<div style="text-align: center;">4.6</div>

||

[[The Chain Rule for Functions of more than One Variable]]

||
* [[Differentiation Rules of Functions]] 
* [[The Chain Rule of Functions]] 
* [[Partial Derivatives]] 

||
* Chain rule for functions of one independent variable and several intermediate variables.
* Chain rule for functions of two independent variable and several intermediate variables.
* Method for implicit differentiation.
* The general chain rule for functions of several independent variables
|-
|Week 8

||

<div style="text-align: center;">4.7</div>

||

[[Maxima and Minima Problems]]

||
* [[Limit and Continuity for a Function of several variables|Extreme values on closed and bounded domains]] 
* [[Partial Derivatives]] 
* [[Maxima, Minima and Critical Points of a Function]] 
* [[Continuity of functions with two variables]] 

||
* The derivative test for local extreme values
* Extreme values on closed and bounded domains
* Critical points and saddle points for functions of two variables
* Second derivative test for local extreme values
* Absolute maxima and minima on closed and bounded regions
|-
|Week 9

||

<div style="text-align: center;">4.8</div>

||

[[Lagrange Multipliers]]

||

* [[Partial Derivatives]] 
* [[Critical Points of a Function]] 

||
* Lagrange Multipliers with One Constraint
* Lagrange Multipliers with Two Constraints
|-

|Week 9/10

||

<div style="text-align: center;">Chapter 5</div>

||

[[Double and Iterated Integrals over Rectangles]]

||

* [[Approximating Areas]] 
* [[The Definite Integral|Limits of Riemann Sums]] 

||

* Double Integrals
* Fubini's Theorem (part 1)

|-

|Week 10

||

<div style="text-align: center;">Chapter 5</div>

||

[[Double Integrals over General Regions]]

||

* [[Continuity]] 
* [[Determining Volumes by Slicing]] 
* [[Double and Iterated Integrals over Rectangles]] 

||

* Double integrals over bounded, nonrectangular regions
* Volumes of solid regions
* Fubini's theorem (part 2)
* Finding the limits of integration for regions in the plane
* Properties of double Integrals

|-

|Week 11

||

<div style="text-align: center;">Chapter 5</div>

||

[[Double Integrals in Polar Coordinates]]

||

* [[Double Integrals over General Regions]] 
* [[Parametric Equations| Polar Coordinates]] 

||

* Integrals in Polar Form
* Finding limits of integration for polar coordinates
* Changing Cartesian Integrals into Polar Integrals

|-

|Week 11

||

<div style="text-align: center;">Chapter 5</div>

||

[[Applications of Double Integrals]]

||

* [[Moments and Center of Mass]] 
* [[Triple Integrals in Rectangular Coordinates]] 
* [[Partial Derivatives]] 

||

* Masses and First moments
* Moments of Inertia

|-

|Week 11

||

<div style="text-align: center;">Chapter 5</div>

||

[[Triple Integrals in Rectangular Coordinates]]

||

* [[Double and Iterated Integrals over Rectangles]] 
* [[Area by Double Integration]] 
* '''[[Change of Variables]]''' 

||

* Triple Integrals
* Volume of a region in space
* Finding the limits of integration for triple integrals
* Average value of a function in space

|-

|Week 12

||

<div style="text-align: center;">Chapter 5</div>

||

[[Triple Integrals in Cylindrical and Spherical Coordinates]]

||

* [[Double Integrals in Polar Form]] 
* [[Parametric Equations| Polar Form]] 
* [[Triple Integrals in Rectangular Coordinates]] 

||

* Integration in Cylindrical Coordinates
* Equations relating rectangular and cylindrical coordinates
* Spherical coordinates and integrations
* Equations relating spherical coordinates to Cartesian and cylindrical coordinates

|-

|Week 12

||

<div style="text-align: center;">Chapter 5</div>

||

[[Applications of Triple Integrals]]

||

* [[Moments and Center of Mass]] 
* [[Triple Integrals in Rectangular Coordinates]] 
* [[Partial Derivatives]] 

||

* Masses and First moments
* Moments of Inertia

|-

|Week 14

||

<div style="text-align: center;">Chapter 6</div>

||

[[Line Integrals of Scalar Functions]]

||

* [[Parametric Equations]] 
* [[Curves in Space and Vector Functions]] 
* [[Arc Length]] 

||

* Evaluating a Line Integral
* Additivity of Line Integrals
* Mass and Moments
* Line Integrals in the plane

|-

|Week 14

||

<div style="text-align: center;">Chapter 6</div>

||

[[Vector Fields]]

||

* [[The Dot Product]] 
* [[Directional Derivatives and Gradient Vectors]] 
* [[Parametric Equations]] 
* [[Line Integrals of Scalar Functions]] 

||

* Vector Fields
* Gradient Fields
* Line Integrals of vector fields
* Line integrals with respect to each components direction
* Work done by a force over a curve in space
* Flow integrals and circulation for velocity fields
* Flux across a simple closed plane curve

|-

|Week 14

||

<div style="text-align: center;">Chapter 6</div>

||

[[Conservation Fields]]

||

* [[Vector Fields and Line Integrals]] 
* [[Partial Derivatives]] 
* [[Vector Fields and Line Integrals|Gradient Fields]] 
* [[Tangent Planes and Differentials]] 

||

* Path Independence
* Piecewise smooth curves and connected domains in open regions
* Line integrals in Conservation fields
* Finding potentials for conservative fields
* Exact Differential forms

|-

|Weeks 14/15

||

<div style="text-align: center;">Chapter 6</div>

||

[[Green's Theorem]]

||

* [[Vector Fields and Line Integrals]] 
* [[Partial Derivatives]] 
* [[Dot Product]] 
* [[Path Independence and Conservation Fields]] 

||

* Circulation Density
* Divergence (flux density) of a vector field
* The two forms of Green's theorem (Tangential and Normal forms)
* Green's theorem for evaluating line integrals

|-

MAT2214

2020-09-26T17:05:58Z

Vu.nguyen: /* Topics List */

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes

|-

|Week 1

||

<div style="text-align: center;">1.1</div>

||

[[Polar Coordinates]]

||

* [[Trigonometric Functions: Unit Circle Approach]] 
* [[The inverse Sine, Cosine and Tangent functions]] 

||

* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa

|-

|Week 1

||

<div style="text-align: center;">1.2</div>

||

[[Three-Dimensional Coordinate Systems]]

||

* [[Bases and Linear Independence| Two-dimensional coordinate systems]] 
* [[Solving Equations| Algebraic Expressions]] 

||

* Three-dimensional coordinate systems
* Distance Formula in R<sup>3</sup>
* Standard Equation for a Sphere

|-

|Weeks 1/2

||

<div style="text-align: center;">2.1</div>

||

[[Vectors in The Plane]]

||

* [[Linear Equations|Line Segments]] 
* [[Distance Formula| Distance Formula]] 

||

* Vector Algebra Operations
* The Magnitude of a vector
* Unit Vectors
* The Midpoint of a Line Segment
* The Vector projection

|-

|Week 2

||

<div style="text-align: center;">2.2</div>

||

[[Vectors in Space]]

||

* [[Vectors in the Plane ]]
* [[Distance Formula]] 

||

* Vector Algebra Operations
* The Magnitude of a vector
* Unit Vectors
* The Midpoint of a Line Segment
* The Vector projection

|-

|Week 2

||

<div style="text-align: center;">2.3</div>

||

[[The Dot Product]]

||

* [[Trig. Functions|Basic Trig Functions]] 
* [[Vectors]]  

||
* Definition of Dot Product
* Properties of Dot Product
* Angle between vectors
* Orthogonal vectors

|-

|Week 2

||

<div style="text-align: center;">2.4</div>

||

[[The Cross Product]]

||

* [[Trig. Functions|Basic Trig Functions]] 
* [[Determinants]] 
* [[Vectors]]

||

* Definition of Cross Product
* Properties of the cross product
* Area of a parallelogram
* Cross product as a determinant

||

|-

|Week 3

||

<div style="text-align: center;">2.5</div>

||

[[Equations of Lines, Planes and Surfaces in Space]]

||

* [[The Dot Product]] 
* [[The Cross Product]]
* [[Quadratic Functions]] 
* [[Parametric Equations]] 

||

* Write the vector, parametric equation of a line through a given point in a given direction, and a line through two given points.
* Find the distance from a point to a given line.
* Write the equation of a plane through a given point with a given normal, and a plane through three given points.
* Find the distance from a point to a given plane.

||

|-

|Week 3

||

<div style="text-align: center;">2.6</div>

||

[[Cylinders and Quadratic Surfaces]]

||

* [[Quadratic Functions]] 
* [[Parametric Equations]] 
* '''[[Conics]]''' 

||

* Find equations for cylinders that are generated by rotating lines that are parallel to a plane
* Understand basic quadratic surfaces
* Understand general quadratic surfaces

||

|-

|Weeks 3/4

||

<div style="text-align: center;">3.1, 3.2</div>

||

[[Curves in Space and Vector-Valued Functions]]

||

* [[Parametric Equations]] 
* [[Vectors]]  
* [[The Derivative as a Function]] 
* [[The Limit of a Function]] 
* [[Continuity of a function]] 
* [[The Dot Product]] 
* [[The Cross Product]] 

||

* Vector functions
* Limits of vector functions
* Continuity of vector functions
* Differentiation rules for vector functions
* Curves and paths in space

||

|-

|Week 4

||

<div style="text-align: center;">3.3</div>

||

[[Arc Length]]

||

* '''[[Distance Formula| The Length of a Line Segment]]''' 
* [[Curves in Space and Vector Functions|Vector Functions]] 
* [[Integrals of Vector Functions]] 

||

* The arc Length of a vector function
* Arc length parameterization
||

|-

|Weeks 4/5

||

<div style="text-align: center;">3.4</div>

||

[[Motion in Space]]

||
* [[Vectors]] 
* [[Parametric Equations]] 
* [[The Cross Product]] 
* [[Derivatives of Vector Functions]] 
||
* The Unit tangent vector
* The curvature
* The Principal Unit Normal Vector
* The Binormal Vector
* The tangential and normal components of acceleration
* The Torsion
||

|-

|Week 5/6

||

<div style="text-align: center;">4.1</div>

||

[[Functions of Several Variables]]

||

* [[Domain of a Function]] 
* [[Range of a Function]] 
* [[Solving Inequalities]] 
* [[Graphs| Graphing a Function]] 

||
* Functions of two variables
* Functions of three variables
* Domain and range of multivariable functions
* Bounded regions
* Graphs and level curves of two variable functions
* Level surfaces of three variable functions
|-

|Week 6

||

<div style="text-align: center;">4.2</div>

||

[[Limit and Continuity of Function of Several Variables]]

||

* [[The Limit and Continuity of a Function]] 
* [[The Limit Laws for Functions]] 
* [[Composition of Functions]] 
* [[The Dot Product]] 

||

* Limits of functions of two variables
* Limits of functions of more than two variables
* Properties of limits of functions of several variables
* Two path test of non-existing of a limit
* Continuity for functions of several variables
* Continuity of composition
* Extreme values on closed and bounded domains
|-

|Week 6

||

<div style="text-align: center;">4.3</div>

||

[[Partial Derivatives]]

||

* [[The derivative and second derivative of a function ]] 
* [[The limit and continuity for a function of several variables]] 

||
* Partial derivatives for functions of two variables
* Partial derivatives for functions of more than two variables
* Partial derivatives and continuity
* Second order partial derivatives
* Mixed derivative theorem
|-

|Week 7

||

<div style="text-align: center;">4.4</div>

||

[[Directional Derivatives and Gradient Vectors]]

||
* [[Trigonometric Functions]] 
* [[Vectors, Unit Vectors]]  
* [[Partial Derivatives]] 
* Gradients
* [[The Dot Product]] 
||
* Directional derivatives for functions of two variables
* Gradients
* Properties of directional derivatives
* Tangents to level curves
* Directional derivatives for functions of three variables
|-

|Week 7

||

<div style="text-align: center;">4.5</div>

||
[[Tangent Plane]]
[[Differentiability]]

||
* [[Partial Derivatives]] 
* [[Parametric Equations of Lines]]
* [[Equations of Planes]]

||
* Determine the equation of a plane tangent to a given surface at a point
* Determine the parametric equation of a normal line to a given surface at a point
* The linear approximation of a function of two variables at a point
* The definition of differentiability for a function of two variables
* Differentiability implies Continuity
* Continuity of First Partial Derivatives implies Differentiability
* The definition of total differentiability for a function of two variables
* Use the total differential to approximate the change in a function of two variables
|-

|Week 7

||

<div style="text-align: center;">4.6</div>

||

[[The Chain Rule for Functions of more than One Variable]]

||
* [[Differentiation Rules of Functions]] 
* [[The Chain Rule of Functions]] 
* [[Partial Derivatives]] 

||
* Chain rule for functions of one independent variable and several intermediate variables.
* Chain rule for functions of two independent variable and several intermediate variables.
* Method for implicit differentiation.
* The general chain rule for functions of several independent variables
|-
|Week 8

||

<div style="text-align: center;">4.7</div>

||

[[Maxima and Minima Problems]]

||
* [[Limit and Continuity for a Function of several variables|Extreme values on closed and bounded domains]] 
* [[Partial Derivatives]] 
* [[Maxima, Minima and Critical Points of a Function]] 
* [[Continuity of functions with two variables]] 

||
* The derivative test for local extreme values
* Extreme values on closed and bounded domains
* Critical points and saddle points for functions of two variables
* Second derivative test for local extreme values
* Absolute maxima and minima on closed and bounded regions
|-
|Week 9

||

<div style="text-align: center;">4.8</div>

||

[[Lagrange Multiplires]]

||

* [[Partial Derivatives]] 
* [[Critical Points of a Function]] 

||
* Lagrange Multipliers with One Constraint
* Lagrange Multipliers with Two Constraints
|-

|Week 9/10

||

<div style="text-align: center;">Chapter 5</div>

||

[[Double and Iterated Integrals over Rectangles]]

||

* [[Approximating Areas]] 
* [[The Definite Integral|Limits of Riemann Sums]] 

||

* Double Integrals
* Fubini's Theorem (part 1)

|-

|Week 10

||

<div style="text-align: center;">Chapter 5</div>

||

[[Double Integrals over General Regions]]

||

* [[Continuity]] 
* [[Determining Volumes by Slicing]] 
* [[Double and Iterated Integrals over Rectangles]] 

||

* Double integrals over bounded, nonrectangular regions
* Volumes of solid regions
* Fubini's theorem (part 2)
* Finding the limits of integration for regions in the plane
* Properties of double Integrals

|-

|Week 11

||

<div style="text-align: center;">Chapter 5</div>

||

[[Double Integrals in Polar Coordinates]]

||

* [[Double Integrals over General Regions]] 
* [[Parametric Equations| Polar Coordinates]] 

||

* Integrals in Polar Form
* Finding limits of integration for polar coordinates
* Changing Cartesian Integrals into Polar Integrals

|-

|Week 11

||

<div style="text-align: center;">Chapter 5</div>

||

[[Applications of Double Integrals]]

||

* [[Moments and Center of Mass]] 
* [[Triple Integrals in Rectangular Coordinates]] 
* [[Partial Derivatives]] 

||

* Masses and First moments
* Moments of Inertia

|-

|Week 11

||

<div style="text-align: center;">Chapter 5</div>

||

[[Triple Integrals in Rectangular Coordinates]]

||

* [[Double and Iterated Integrals over Rectangles]] 
* [[Area by Double Integration]] 
* '''[[Change of Variables]]''' 

||

* Triple Integrals
* Volume of a region in space
* Finding the limits of integration for triple integrals
* Average value of a function in space

|-

|Week 12

||

<div style="text-align: center;">Chapter 5</div>

||

[[Triple Integrals in Cylindrical and Spherical Coordinates]]

||

* [[Double Integrals in Polar Form]] 
* [[Parametric Equations| Polar Form]] 
* [[Triple Integrals in Rectangular Coordinates]] 

||

* Integration in Cylindrical Coordinates
* Equations relating rectangular and cylindrical coordinates
* Spherical coordinates and integrations
* Equations relating spherical coordinates to Cartesian and cylindrical coordinates

|-

|Week 12

||

<div style="text-align: center;">Chapter 5</div>

||

[[Applications of Triple Integrals]]

||

* [[Moments and Center of Mass]] 
* [[Triple Integrals in Rectangular Coordinates]] 
* [[Partial Derivatives]] 

||

* Masses and First moments
* Moments of Inertia

|-

|Week 14

||

<div style="text-align: center;">Chapter 6</div>

||

[[Line Integrals of Scalar Functions]]

||

* [[Parametric Equations]] 
* [[Curves in Space and Vector Functions]] 
* [[Arc Length]] 

||

* Evaluating a Line Integral
* Additivity of Line Integrals
* Mass and Moments
* Line Integrals in the plane

|-

|Week 14

||

<div style="text-align: center;">Chapter 6</div>

||

[[Vector Fields]]

||

* [[The Dot Product]] 
* [[Directional Derivatives and Gradient Vectors]] 
* [[Parametric Equations]] 
* [[Line Integrals of Scalar Functions]] 

||

* Vector Fields
* Gradient Fields
* Line Integrals of vector fields
* Line integrals with respect to each components direction
* Work done by a force over a curve in space
* Flow integrals and circulation for velocity fields
* Flux across a simple closed plane curve

|-

|Week 14

||

<div style="text-align: center;">Chapter 6</div>

||

[[Conservation Fields]]

||

* [[Vector Fields and Line Integrals]] 
* [[Partial Derivatives]] 
* [[Vector Fields and Line Integrals|Gradient Fields]] 
* [[Tangent Planes and Differentials]] 

||

* Path Independence
* Piecewise smooth curves and connected domains in open regions
* Line integrals in Conservation fields
* Finding potentials for conservative fields
* Exact Differential forms

|-

|Weeks 14/15

||

<div style="text-align: center;">Chapter 6</div>

||

[[Green's Theorem]]

||

* [[Vector Fields and Line Integrals]] 
* [[Partial Derivatives]] 
* [[Dot Product]] 
* [[Path Independence and Conservation Fields]] 

||

* Circulation Density
* Divergence (flux density) of a vector field
* The two forms of Green's theorem (Tangential and Normal forms)
* Green's theorem for evaluating line integrals

|-