View source for MAT2214

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


|Week&nbsp;1

||

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

||
        
[[Polar Coordinates]] 

||
* [[Trigonometric Functions: Unit Circle Approach]] <!-- 1093-2.2 -->
* [[Inverse Trigonometric 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

||

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

||
        
[[Three-Dimensional Coordinate Systems]] 

||

* [[Two-dimensional coordinate systems]] <!-- 2233-3.3 -->
* [[Solving Equations and Inequalities| Algebraic Expressions]] <!-- 1073-Mod R -->



||

* Three-dimensional coordinate systems.
* Distance Formula in Space. 
* Standard Equation for a Sphere.
|-


|Weeks&nbsp;1/2  

||

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

||
  

[[Vectors in The Plane, Space]] 

||

* [[Linear Equations|Line Segments]] <!-- 1073-Mod R -->
* [[Distance Formula| Distance Formula]] <!-- DNE (recommend pairing with discussion of absolute value function) -->

||

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



|Week&nbsp;2

||

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

||
  
[[The Dot Product]] 


||

* [[Trigonometric Functions|Basic Trig Functions]]  <!-- 1093-2.2 -->
* [[Vectors]]  <!-- 2214-12.2 -->  <!-- 2233-1.1 -->

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

|-


|Week&nbsp;2

||

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

||
  
[[The Cross Product]] 

||

* [[Trigonometric Functions|Basic Trig Functions]]  <!-- 1093-2.2 -->
* [[Determinants]] <!-- 2233-6.1,6.2 -->
* [[Vectors]]

||

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

||



|-



|Week&nbsp;3

||

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

||
  

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

||

* [[The Dot Product]] <!-- 2214-12.3 -->
* [[The Cross Product]] 
* [[Quadratic Functions]] <!-- 1073-Mod R -->
* [[Parametric Equations]] <!-- 1224-7.1 -->

||

* 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&nbsp;3

||

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

||
  

[[Equations of Lines, Planes and Surfaces in Space|Cylinders and Quadratic Surfaces]] 

||

* [[Quadratic Functions]] <!-- 1073-Mod R -->
* [[Parametric Equations]] <!-- 1224-7.1 -->
* '''[[Conics]]''' <!-- DNE (recommend 1093) -->

||

* 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&nbsp;3/4

||

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

|| 

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

||

* [[Parametric Equations]] <!-- 1224-7.1 -->
* [[Vectors]]  <!-- 2214-12.2 -->  <!-- 2233-1.1 -->
* [[The Derivative as a Function]] <!-- 1214-3.2 -->
* [[The Limit of a Function]] <!-- 1214-2.2 -->
* [[Continuity]] <!-- 1214-2.4 -->
* [[The Dot Product]] <!-- 2214-12.3 -->
* [[The Cross Product]] <!-- 2214-12.4 -->

||

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

||


|-



|Week&nbsp;4

||

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

||
  
[[Arc Length]]

||

* '''[[Distance Formula| The Length of a Line Segment]]''' <!-- DNE (recommend pairing with discussion of absolute value function) -->
* [[Curves in Space and Vector-Valued Functions|Vector Functions]] <!-- 1224-7.1 -->
* [[Integrals of Vector Functions]] <!-- 2214-13.2 -->

||

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



|-



|Weeks&nbsp;4/5

||

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

||
  
[[Motion in Space]]

||
* [[Vectors]] <!-- 1214-12.2 --> 
* [[Parametric Equations]] <!-- 1224-7.1 -->
* [[The Cross Product]] <!-- 2214-12.4 -->
* [[Derivatives of Vector Functions]] <!-- 1224-7.1 -->
||
* The Unit tangent vector
* The curvature
* The Principal Unit Normal Vector
* The Binormal Vector
* The tangential and normal components of acceleration
* The Torsion
||



|-



|Week&nbsp;5/6  

||

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

||
  

[[Functions of Several Variables]]

||

* [[Domain of a Function]] <!-- 1073-Mod 1.2 -->
* [[Range of a Function]] <!-- 1073-Mod 1.2 -->
* [[Solving Equations and Inequalities]] <!-- 1073-Mod R -->
* [[Graphs| Graphing a Function]] <!-- 1073-Mod R -->

||
* 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&nbsp;6

||

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

||
  

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

||

* [[Continuity]] <!-- 1214-2.2, 2.4 -->
* [[The Limit Laws]] <!-- 1214-2.3 -->
* [[Composition of Functions]] <!-- 1073-Mod 7.1 --> 
* [[The Dot Product]] <!-- 2214-12.3 -->

||

* 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&nbsp;6

||

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

||  

[[Partial Derivatives]]

||

* [[The Derivative as a Function|The first]] and [[The Second Derivative|second derivative]] of a function <!-- 1214-3.2 -->
* [[Limit and Continuity of Function of Several Variables]] <!-- 2214-14.2 -->


||
* 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&nbsp;7  

||

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

||  

[[Directional Derivatives and Gradient Vectors]]

||
* [[Trigonometric Functions]]  <!-- 1093-2.2 --> 
* [[Vectors, Unit Vectors]]  <!-- 2214-12.2 -->  <!-- 2233-1.1 -->
* [[Partial Derivatives]]  <!-- 1214-14.3 -->
* [[Gradients]]
* [[The Dot Product]] <!-- 2214-12.3 -->
||
* Directional derivatives for functions of two variables
* Gradients
* Properties of directional derivatives
* Tangents to level curves
* Directional derivatives for functions of three variables
|-


|Week&nbsp;7 

||

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

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


||
* [[Partial Derivatives]]  <!-- 1214-14.3 -->
* [[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&nbsp;7 

||

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

||  

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

||
* [[Differentiation Rules]] <!-- 1214-3.3 -->
* [[The Chain Rule]] <!-- 1214-3.6 -->
* [[Partial Derivatives]]  <!-- 1214-14.3 -->

||
* 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&nbsp;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]] <!-- 2214-14.2 -->
* [[Partial Derivatives]]  <!-- 1214-14.3 -->
* [[Maxima and Minima|Maxima, Minima and Critical Points of a Function]] <!-- 1214-4.3 -->
* [[Limit and Continuity of Function of Several Variables]] <!-- 2214-14.2 -->

||
* 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&nbsp;8/9 

||

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

||  

[[Lagrange Multipliers]]

||

* [[Partial Derivatives]]  <!-- 1214-14.3 -->
* [[Critical Points of a Function]] <!-- 1214-4.3 -->

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



|Week&nbsp;9/10

||

<div style="text-align: center;">5.1</div>

||  

[[Multiple Integrals|Double Integrals over Rectangular Regions]]

||

* [[Approximating Areas]] <!-- 1214-5.1 -->
* [[The Definite Integral|Limits of Riemann Sums]] <!-- 1214-5.2 -->

||
* Double Integral is the limit of Double Sums.
* Double Integrals over Rectangular Regions.
* Interated Integrals.
* Fubini's Theorem (part 1).
|-


|Week&nbsp;10

||

<div style="text-align: center;">5.2</div>

||  

[[Multiple Integrals|Double Integrals over General Regions]]

||

* [[Continuity]] <!-- 1214-3.5 -->
* [[Determining Volumes by Slicing]] <!-- 1224-2.2 -->
* [[Double and Iterated Integrals over Rectangular regions]] <!-- 2214-5.1 -->

||
* Double integrals over bounded, general regions.
* Properties of double Integrals. 
* Fubini's theorem (part 2) 
* Changing the order of Integration.
* Calculating Volumes, Areas and Average Values 
|-



|Week&nbsp;11    

||

<div style="text-align: center;">5.3</div>

||  

[[Multiple Integrals|Double Integrals in Polar Coordinates]]

||

* [[Multiple Integrals|Double Integrals over General Regions]] <!-- 2214-15.2 -->
* [[Parametric Equations| Polar Coordinates]] <!-- 1093-5.1 -->

||
* Double Integrals over rectangular polar  regions.
* Double Integrals over general polar regions.
* Changing Cartesian Integrals into Polar Integrals.
* Using Double Integrals in Polar Coordinates to find Volumes, Areas.
|-


|Week&nbsp;11 

||

<div style="text-align: center;"> 5.4</div>

|| 

[[Multiple Integrals|Triple Integrals in Rectangular Coordinates]]

||

* [Multiple Integrals|[Double Integrals]] <!-- 2214-5.1,  2214-5.2 -->
* [[Area by Double Integration]] <!-- 2214-15.3 -->
* '''[[Change of Variables]]''' <!-- DNE (recommend 1073) -->

||

* Triple Integrals over general bounded regions. 
* Finding Volumes by evaluating Triple Integrals.
* Average value of a function in space.
* Changing Integration Order and Coordinate systems.
|-



|Week&nbsp;12

||

<div style="text-align: center;">5.5</div>

|| 

[[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]]

||

* [[Multiple Integrals|Double Integrals in Polar Form]]  <!-- 2214-15.4 -->
* [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->

||

* Integrations  in Cylindrical Coordinates.
* Equations relating rectangular and cylindrical coordinates.
* Changing Cartesian integrations into Cylindrical integrations.
* Integrations in Spherical coordinates.
* Equations relating spherical coordinates to Cartesian and cylindrical coordinates.
* Changing Cartesian integrations into Cylindrical integrations.
|-


|Week&nbsp;13  

||

<div style="text-align: center;">5.6</div>

||
  
[[Multiple Integrals|Applications of Multiple Integrals]]

||

* [[Multiple Integrals|Double Integral]] <!-- 2214-5.2,2214-5.3  -->
* [[Multiple Integrals|Triple Integrals]] <!-- 2214-5.3,2214-5.4 -->

||

* Finding Masses, Moments, Centers of Masses, Moments of Inertia in Two Dimensions.
* Finding Masses, Moments, Centers of Masses, Moments of Inertia in Three Dimensions.
|-
|Week&nbsp;13/14  

||

<div style="text-align: center;">5.7</div>

||
  
[[Multiple Integrals|Change of Variables in Multiple Integrals]]

||

* [[Multiple Integrals|Double Integral]] <!-- 2214-5.2,2214-5.3  -->
* [[Multiple Integrals|Triple Integrals]] <!-- 2214-5.3,2214-5.4 -->

||

* Determine the image of a region under a given transformation of variables.
* Compute the Jacobian of a given transformation.
* Evaluate a double integral using a change of variables.
* Evaluate a triple integral using a change of variables.
|-
|Week&nbsp;14 

||

<div style="text-align: center;">6.1</div>

||

[[Vector Fields]]

||

* [[The Dot Product]] <!-- 2214-12.3 -->
* [[Directional Derivatives and Gradient Vectors]] <!-- 2214-14.5 --> 
||
* Vector Fields in a plane.
* Vector Fields in Space.
* Potential Functions.
* Gradient Fields, Conservative Vector Fields.
* The Cross-Partial Test for Conservative Vector Fields.
* Determining Whether a Vector Field is conservative. 
|-


|Week&nbsp;14 

||

<div style="text-align: center;">6.2</div>

||  

[[Line Integrals]]

||

* [[Parametric Equations]] <!-- 1224-7.1 -->
* [[Curves in Space and Vector Functions]] <!-- 2214-13.1 -->
* [[Arc Lengths]] <!-- 1224-13.3 -->

||
* Line Integrals of  functions a long a smooth curves in a planer or in space
* Line Integrals of  of vector fields along an oriented curves in a plane or space..
* Properties of Vector Line Integrals.
* Evaluating  Line Integrals.
* Applications of line integrals: Calculating Arc Length, the Mass of a wire, Work done by a force, Flux across a curve, Circulation of a force.
|-





|Week&nbsp;14/15  

||

<div style="text-align: center;">6.3</div>

||

[[Conservative Vector Fields]]

||

* [[Vector Fields and Line Integrals]] <!-- 2214-16.2 -->
* [[Partial Derivatives]]  <!-- 1214-14.3 -->

||
* Describe simple and closed curves
* Define connected and simply connected regions.
* Explain how to test a vector field to determine whether it is conservative.
* Find a potential function for a conservative vector field.
* Use the Fundamental Theorem for Line Integrals to evaluate a line integral of a vector field.
|-


|Weeks&nbsp;14/15  

||

<div style="text-align: center;">6.4</div>

||

[[Green's Theorem]]

||

* [[Vector Fields and Line Integrals]] <!-- 2214-16.2 -->
* [[Partial Derivatives]]  <!-- 1214-14.3 -->
* [[Dot Product]] <!-- 2214-16.3 -->
* [[Path Independence and Conservation Fields]]  <!-- 2214-16.3 -->

||

* Circulation form of Green's Theorem.
* Flux Form of Green’s Theorem.
* Applying Green's Theorem to find Work, Flux.
|-