Difference between revisions of "MAT2214"

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(Added content to the table(16.5))
(Altered the table to match the new list of Topics (several large changes to contents))
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|-   
 
|-   
 +
 +
 +
|Week 1
 +
 +
||
 +
 +
<div style="text-align: center;">Chapter 1</div>
 +
 +
||
 +
       
 +
[[Polar Coordinates]]
 +
 +
||
 +
 +
* [[Trigonometric Functions: Unit Circle Approach]] <!-- 1093-2.2 -->
 +
* [[The inverse Sine, Cosine and Tangent functions]] <!-- 1093-3.1 -->
 +
 +
||
 +
 +
* 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&nbsp;1
 
|Week&nbsp;1
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||
 
||
  
<div style="text-align: center;">12.1</div>
+
<div style="text-align: center;">Chapter 1</div>
  
 
||
 
||
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|Week&nbsp;1/2   
+
|Weeks&nbsp;1/2   
  
 
||
 
||
  
<div style="text-align: center;">12.2</div>
+
<div style="text-align: center;">Chapter 2</div>
  
 
||
 
||
 
    
 
    
  
[[Vectors]]  
+
[[Vectors in The Plane and in Three Dimensions]]  
  
 
||
 
||
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* Midpoint of a Line Segment
 
* Midpoint of a Line Segment
 
* Angle between vectors
 
* Angle between vectors
* Definition of Dot product
 
 
* Orthogonal vectors
 
* Orthogonal vectors
 
* Vector projection
 
* Vector projection
  
 
|-
 
|-
 +
 +
 +
|Week&nbsp;2 
 +
 +
||
 +
 +
<div style="text-align: center;">Chapter 2</div>
 +
 +
||
 +
 
 +
 +
[[Vectors in Space]]
 +
 +
||
 +
 +
* [[Vecotors in the Plane and in Three Dimensions]]
 +
* [[Distance Formula]] <!-- DNE (recommend pairing with discussion of absolute value function) -->
 +
 +
||
 +
 +
* Vector Algebra Operations
 +
* Magnitude of a vector
 +
* Unit Vectors
 +
* Midpoint of a Line Segment
 +
* Angle between vectors
 +
* Orthogonal vectors
 +
* Vector projection
 +
 +
|-
 +
  
  
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||
 
||
  
<div style="text-align: center;">12.3</div>
+
<div style="text-align: center;">Chapter 2</div>
  
 
||
 
||
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|Week&nbsp;2/3 
+
|Week&nbsp;2
  
 
||
 
||
  
<div style="text-align: center;">12.4</div>
+
<div style="text-align: center;">Chapter 2</div>
  
 
||
 
||
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||
 
||
  
<div style="text-align: center;">12.5</div>
+
<div style="text-align: center;">Chapter 2</div>
  
 
||
 
||
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|Week&nbsp;3/4
+
 
 +
|Weeks&nbsp;3/4
  
 
||
 
||
  
<div style="text-align: center;">13.1</div>
+
<div style="text-align: center;">Chapters 2 and 3</div>
  
||
+
||  
 
 
  
 
[[Curves in Space and Vector Functions]]  
 
[[Curves in Space and Vector Functions]]  
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|-
 
|-
  
 
|Week&nbsp;4
 
 
||
 
 
<div style="text-align: center;">13.2</div>
 
 
||
 
 
 
[[Integrals of Vector Functions]]
 
 
||
 
 
* [[Antiderivatives| Initial Value Problems]] <!-- 1214-4.10 -->
 
* [[The Definite Integral|Solving Basic Integrals]] <!-- 1214-5.2 -->
 
* [[Parametric Equations]] <!-- 1224-7.1 -->
 
* [[Curves in Space and Vector Functions|Vector Functions]] <!-- 1224-7.1 -->
 
 
||
 
 
* Indefinite integrals of vector functions
 
* Definite integrals of vector functions
 
* Vector and parametric equations for ideal projectile motion
 
 
||
 
 
 
|-
 
  
  
|Week&nbsp;4/5
+
|Week&nbsp;4
  
 
||
 
||
  
<div style="text-align: center;">13.3</div>
+
<div style="text-align: center;">Chapter 3</div>
  
 
||
 
||
 
    
 
    
 
+
[[Vector-Valued Functions: Arc Length]]
[[Arc Length]]
 
  
 
||
 
||
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||
 
||
 +
  
  
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|Week&nbsp;5
+
 
 +
|Weeks&nbsp;4/5
  
 
||
 
||
  
<div style="text-align: center;">13.4</div>
+
<div style="text-align: center;">Chapter 3</div>
  
 
||
 
||
 
    
 
    
 
 
[[Curvature and Normal Vectors]]
 
[[Curvature and Normal Vectors]]
  
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|Week&nbsp;5/6
+
|Weeks&nbsp;4/5
  
 
||
 
||
  
<div style="text-align: center;">13.5</div>
+
<div style="text-align: center;">Chapter 3</div>
 
||
 
||
 
    
 
    
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|Week&nbsp;7  
+
 
 +
|Week&nbsp;6  
  
 
||
 
||
  
<div style="text-align: center;">14.1</div>
+
<div style="text-align: center;">Chapter 4</div>
  
 
||
 
||
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|Week&nbsp;7/8
+
|Week&nbsp;6
  
 
||
 
||
  
<div style="text-align: center;">14.2</div>
+
<div style="text-align: center;">Chapter 4</div>
  
 
||
 
||
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|Week&nbsp;8
+
|Week&nbsp;6
  
 
||
 
||
  
<div style="text-align: center;">14.3</div>
+
<div style="text-align: center;">Chapter 4</div>
  
 
||   
 
||   
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|Week&nbsp;8/9 
+
|Week&nbsp;7
  
 
||
 
||
  
<div style="text-align: center;">14.4</div>
+
<div style="text-align: center;">Chapter 4</div>
  
 
||   
 
||   
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|Week&nbsp;9   
+
|Week&nbsp;
  
 
||
 
||
  
<div style="text-align: center;">14.5</div>
+
<div style="text-align: center;">Chapter 4</div>
  
 
||   
 
||   
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|Week&nbsp;9/10 
+
|Week&nbsp;7
  
 
||
 
||
  
<div style="text-align: center;">14.6</div>
+
<div style="text-align: center;">Chapter 4</div>
  
 
||   
 
||   
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|Week&nbsp;10 
+
|Week&nbsp;8
  
 
||
 
||
  
<div style="text-align: center;">14.7</div>
+
<div style="text-align: center;">Chapter 4</div>
  
 
||   
 
||   
  
[[Extreme Values and Saddle Points]]
+
[[Maxima and Minima Problems]]
  
 
||
 
||
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|-
 
|-
|Week&nbsp;10/11
 
 
||
 
 
<div style="text-align: center;">14.8</div>
 
 
|| 
 
 
[[Lagrange Multipliers]]
 
 
||
 
 
* [[Extreme Values and Saddle Points]] <!-- 2214-14.7 -->
 
* [[Cylinders and Quadratic Surfaces]] <!-- 2214-12.5 -->
 
* [[Directional Derivatives and Gradient Vectors]] <!-- 2214-14.5 -->
 
 
||
 
 
* Define the convergence or divergence of an infinite series.
 
* Find the sum of a geometric or telescoping series.
 
 
|-
 
 
 
 
|Week&nbsp;12 
 
 
||
 
 
<div style="text-align: center;">14.9</div>
 
 
|| 
 
 
[[Taylors formula for Two Variables]]
 
 
||
 
 
* [[Taylor and Maclaurin Series]] <!-- 1224-6.3-->
 
* [[Partial Derivatives]]  <!-- 1214-14.3 -->
 
* [[Limits and Continuity in Higher Dimensions]] <!-- 2214-14.2 -->
 
 
||
 
 
* The derivation of the second derivative test
 
* Taylor's formula for functions of two variables
 
  
 
|-
 
  
  
|Week&nbsp;12/13
+
|Week&nbsp;10
  
 
||
 
||
  
<div style="text-align: center;">15.1</div>
+
<div style="text-align: center;">Chapter 5</div>
  
 
||   
 
||   
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* Double Integrals
 
* Double Integrals
 
* Fubini's Theorem (part 1)
 
* Fubini's Theorem (part 1)
 +
 +
  
 
|-
 
|-
  
  
|Week&nbsp;14
+
|Week&nbsp;10
  
 
||
 
||
  
<div style="text-align: center;">15.2</div>
+
<div style="text-align: center;">Chapter 5</div>
  
 
||   
 
||   
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|Week&nbsp;14/15 
+
 
 +
|Week&nbsp;11   
  
 
||
 
||
  
<div style="text-align: center;">15.3</div>
+
<div style="text-align: center;">Chapter 5</div>
  
||  
+
||
  
[[Area by Double Intgration]]
+
[[Double Integrals in Polar Coordinates]]
  
 
||
 
||
  
 
* [[Double Integrals over General Regions]] <!-- 2214-15.2 -->
 
* [[Double Integrals over General Regions]] <!-- 2214-15.2 -->
* [[The Definite Integral| Average value of a fucntion]] <!-- 1214-5.2 -->
+
* [[Parametric Equations| Polar Coordinates]] <!-- 1093-5.1 -->
* '''[[Conics]]''' <!-- DNE (recommend 1093) -->
 
  
 
||
 
||
  
* Areas of bounded regions in the plane
+
* Integrals in Polar Form
* Average value for functions of two or more variables
+
* Finding limits of integration for polar coordinates
 +
* Changing Cartesian Integrals into Polar Integrals
  
  
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|Week&nbsp;15   
+
 
 +
|Week&nbsp;11 
  
 
||
 
||
  
<div style="text-align: center;">15.4</div>
+
<div style="text-align: center;">Chapter 5</div>
  
||
+
||
 
+
 
[[Double Integrals in Polar Form]]
+
[[Applications of Double Integrals]]
  
 
||
 
||
  
* [[Double Integrals over General Regions]] <!-- 2214-15.2 -->
+
* [[Moments and Center of Mass]] <!-- 1224-2.6 -->
* [[Parametric Equations| Polar Coordinates]] <!-- 1093-5.1 -->
+
* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
 +
* [[Partial Derivatives]] <!-- 1214-14.3 -->
  
 
||
 
||
  
* Integrals in Polar Form
+
* Masses and First moments
* Finding limits of integration for polar coordinates
+
* Moments of Inertia
* Changing Cartesian Integrals into Polar Integrals
+
 
  
  
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|Week&nbsp;15/16 
+
 
 +
|Week&nbsp;11
  
 
||
 
||
  
<div style="text-align: center;">15.5</div>
+
<div style="text-align: center;">Chapter 5</div>
  
 
||  
 
||  
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|-
 
|-
  
|Week&nbsp;16 
+
 
 +
 
 +
|Week&nbsp;12
  
 
||
 
||
  
<div style="text-align: center;">15.6</div>
+
<div style="text-align: center;">Chapter 5</div>
 +
 
 +
||
  
||
+
[[Triple Integrals in Cylindrical and Spherical Coordinates]]
 
 
[[Applications of Double and Triple Integrals]]
 
  
 
||
 
||
  
* [[Moments and Center of Mass]] <!-- 1224-2.6 -->
+
* [[Double Integrals in Polar Form]] <!-- 2214-15.4 -->
 +
* [[Parametric Equations| Polar Form]] <!-- 1093-5.1 -->
 
* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
 
* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
* [[Partial Derivatives]] <!-- 1214-14.3 -->
 
  
 
||
 
||
  
* Masses and First moments
+
* Integration in Cylindrical Coordinates
* Moments of Inertia
+
* Equations relating rectangular and cylindrical coordinates
 
+
* Spherical coordinates and integrations
 +
* Equations relating spherical coordinates to Cartesian and cylindrical coordinates
  
  
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|Week&nbsp;16/17
+
|Week&nbsp;12 
  
 
||
 
||
  
<div style="text-align: center;">15.7</div>
+
<div style="text-align: center;">Chapter 5</div>
  
||  
+
||
 
+
 
[[Triple Integrals in Cylindrical and Spherical Coordinates]]
+
[[Applications of Triple Integrals]]
  
 
||
 
||
  
* [[Double Integrals in Polar Form]] <!-- 2214-15.4 -->
+
* [[Moments and Center of Mass]] <!-- 1224-2.6 -->
* [[Parametric Equations| Polar Form]] <!-- 1093-5.1 -->
 
 
* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
 
* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
 +
* [[Partial Derivatives]] <!-- 1214-14.3 -->
  
 
||
 
||
  
* Integration in Cylindrical Coordinates
+
* Masses and First moments
* Equations relating rectangular and cylindrical coordinates
+
* Moments of Inertia
* Spherical coordinates and integrations
 
* Equations relating spherical coordinates to Cartesian and cylindrical coordinates
 
 
 
  
  
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|Week&nbsp;17
+
|Week&nbsp;14
  
 
||
 
||
  
<div style="text-align: center;">16.1</div>
+
<div style="text-align: center;">Chapter 6</div>
  
 
||   
 
||   
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|Week&nbsp;18 
+
 
 +
|Week&nbsp;14
  
 
||
 
||
  
<div style="text-align: center;">16.2</div>
+
<div style="text-align: center;">Chapter 6</div>
  
 
||
 
||
  
[[Vector Fields and Line Integrals]]
+
[[Vector Fields]]
  
 
||
 
||
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+
|Week&nbsp;14  
|Week&nbsp;18/19  
 
  
 
||
 
||
  
<div style="text-align: center;">16.3</div>
+
<div style="text-align: center;">Chapter 6</div>
  
 
||
 
||
  
[[Path Independence and Conservation Fields]]
+
[[Conservation Fields]]
  
 
||
 
||
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|Week&nbsp;20  
+
|Weeks&nbsp;14/15  
  
 
||
 
||
  
<div style="text-align: center;">16.4</div>
+
<div style="text-align: center;">Chapter 6</div>
  
 
||
 
||
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|-
 
|-
 
 
|Week&nbsp;21
 
 
||
 
 
<div style="text-align: center;">16.5</div>
 
 
||
 
 
[[Surfaces and Area]]
 
 
||
 
 
* [[Vector Fields and Line Integrals]] <!-- 2214-16.2 -->
 
* [[Partial Derivatives]]  <!-- 1214-14.3 -->
 
* [[The Cross Product]] <!-- 2214-16.3 -->
 
* [[Parametric Equations]] <!-- 1224-7.1 -->
 
* [[The Definite Integral|Integration Techniques]] <!-- 1214-5.2 -->
 
* [[Double Integrals over General Regions]] <!-- 1214-15.2 -->
 
 
||
 
 
* Parameterizations of Surfaces
 
* Surface Area
 
* Surface Area Differential for a Parameterized Surface
 
* Implicit Surfaces
 

Revision as of 19:10, 12 August 2020

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1
Chapter 1

Polar Coordinates

  • 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
Chapter 1

Three-Dimensional Coordinate Systems


  • Three-dimensional coordinate systems
  • Distance Formula in R3
  • Standard Equation for a Sphere


Weeks 1/2
Chapter 2


Vectors in The Plane and in Three Dimensions

  • Vector Algebra Operations
  • Magnitude of a vector
  • Unit Vectors
  • Midpoint of a Line Segment
  • Angle between vectors
  • Orthogonal vectors
  • Vector projection
Week 2
Chapter 2


Vectors in Space

  • Vector Algebra Operations
  • Magnitude of a vector
  • Unit Vectors
  • Midpoint of a Line Segment
  • Angle between vectors
  • Orthogonal vectors
  • Vector projection
Week 2
Chapter 2

The Dot Product


  • Find the area of plane regions bounded by the graphs of functions.
Week 2
Chapter 2

The Cross Product

  • Define the cross product
  • Properties of the cross product
  • Area of a parallelogram
  • Cross product as a determinant


Week 3
Chapter 2


Cylinders and Quadratic Surfaces

  • 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
Chapters 2 and 3

Curves in Space and Vector Functions

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


Week 4
Chapter 3

Vector-Valued Functions: Arc Length

  • Length of a curve in R3
  • General arc length formula
  • Arc length for parameterized curves
  • The Unit tangent vector


Weeks 4/5
Chapter 3

Curvature and Normal Vectors

  • Curvature in R2
  • Formula for curvature
  • Definition of Principal unit normal
  • Curvature and normal vectors for higher dimensions.


Weeks 4/5
Chapter 3


Tangential and Normal Components of Acceleration

  • Binormal Vectors
  • Definition of tangential and normal components of acceleration
  • Torsion


Week 6
Chapter 4


Functions of Several Variables


  • Domain and range of multivariable functions
  • Functions with two variables
  • Bounded regions
  • Graphs and level curves of two variable functions
  • Functions of three variables
  • Level surfaces


Week 6
Chapter 4


Limits and Continuity in Higher Dimensions

  • Limits of functions of two variables
  • Properties of limits of functions of two variables
  • Continuity for functions of two variables
  • Continuity of composition
  • Functions of more than two variables
  • Extreme values on closed and bounded sets


Week 6
Chapter 4

Partial Derivatives

  • 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
  • Define the derivative for functions of two variables


Week 7
Chapter 4

The Chain Rule for Functions of more than One Variable

  • Chain rule for functions of one independent variable and two intermediate variables.
  • Chain rule for functions of one independent variable and three intermediate variables.
  • Chain rule for functions of two independent variable and two intermediate variables.
  • Additional method for implicit differentiation.
  • The general chain rule
Week 7
Chapter 4

Directional Derivatives and Gradient Vectors

  • Direction Derivatives in the plane
  • Gradients
  • Properties of directional derivatives
  • Tangents to level curves
  • Directional derivatives for functions of three variables
  • The chain rule for paths


Week 7
Chapter 4

Tangent Planes and Differentials

  • Tangent Planes and Normal lines
  • The plane tangent to a surface
  • How to linearize a function of two variables
  • Differentials for functions of two variables
  • Linearization and differentials for functions of more than two variables


Week 8
Chapter 4

Maxima and Minima Problems

  • The derivative test for local extreme values
  • 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 10
Chapter 5

Double and Iterated Integrals over Rectangles

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


Week 10
Chapter 5

Double Integrals over General Regions

  • 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
Chapter 5

Double Integrals in Polar Coordinates

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


Week 11
Chapter 5

Applications of Double Integrals

  • Masses and First moments
  • Moments of Inertia


Week 11
Chapter 5

Triple Integrals in Rectangular Coordinates

  • 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
Chapter 5

Triple Integrals in Cylindrical and Spherical 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
Chapter 5

Applications of Triple Integrals

  • Masses and First moments
  • Moments of Inertia


Week 14
Chapter 6

Line Integrals of Scalar Functions

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


Week 14
Chapter 6

Vector Fields

  • 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
Chapter 6

Conservation Fields

  • 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
Chapter 6

Green's Theorem

  • 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