Difference between revisions of "MAT2214"

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(Added content to the table (15.1 -15.3))
(Added content to the table (15.4-15.7))
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[[Series]]
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[[EDIT]]
  
 
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<div style="text-align: center;">5.5</div>
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<div style="text-align: center;">15.4</div>
  
 
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[[Alternating Series]]
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[[Double Integrals in Polar Form]]
  
 
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* [[Toolkit Functions| Absolute Value Function]] <!-- 1073-Mod 1.2 -->
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* [[Double Integrals over General Regions]] <!-- 2214-15.2 -->
* ''' [[Increasing and Decreasing Functions]] <!-- DNE (recommend 1023-2.2) -->'''
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* '''[[Parametric Equations| Polar Form]]''' <!-- 1224-7.1 -->
* [[Limits at Infinity and Asymptotes | Infinite Limits]] <!-- 1214-4.6-->
 
  
 
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* Determine the convergence or divergence of alternating series.
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* Integrals in Polar Form
* Estimate the sum of an alternating series.
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* Finding limits of integration for polar coordinates
* Describe the difference between conditional and absolute convergence.
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* Changing Cartesian Integrals into Polar Integrals
  
  
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<div style="text-align: center;">5.6</div>
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<div style="text-align: center;">15.5</div>
  
 
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[[Ratio and Root Tests]]
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[[Triple Integrals in Rectangular Coordinates]]
  
 
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* '''[[Factorials]]''' <!-- Grades 6-12 -->
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* [[Double and Iterated Integrals over Rectangles]] <!-- 2214-15.1 -->
* [[Limits at Infinity and Asymptotes | Infinite Limits]] <!-- 1214-4.6-->
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* [[Area by Double Integration]] <!-- 2214-15.3 -->
* [[Toolkit Functions| Square root and Absolute value Functions]] <!-- 1073-Mod 1.2 -->
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* '''[[Change of Variables]]''' <!-- DNE (recommend 1073) -->
 
 
  
 
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* Determine the convergence or divergence of infinite series using the ratio and root tests..
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* Triple Integrals
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* Volume of a region in space
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* Finding the limits of integration for triple integrals
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* Average value of a function in space
  
  
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<div style="text-align: center;">6.1</div>
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<div style="text-align: center;">15.6</div>
  
 
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[[Power Series and Functions]]
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[[Applications of Double and Triple Integrals]]
  
 
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* [[Intro to Polynomial Functions| Polynomials]] <!-- 1073-Mod 2.1 -->
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* [[Moments and Center of Mass]] <!-- 1224-2.6 -->
* [[Continuity]] <!-- 1214-3.5 -->
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* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
* [[Series]] <!-- 1224-5.2 -->
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* [[Partial Derivatives]] <!-- 1214-14.3 -->
* [[Ratio and Root Tests]] <!-- 1224-5.6 -->
 
  
 
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* Recognize a power series.
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* Masses and First moments
* Find its interval and radius of convergence.
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* Moments of Inertia
* Represent certain functions as power series.
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<div style="text-align: center;">6.2</div>
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<div style="text-align: center;">15.7</div>
  
 
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[[Properties of Power Series]]
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[[Triple Integrals in Cylindrical and Spherical Coordinates]]
  
 
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* [[Antiderivatives|Indefinite integrals]]  <!-- 1214-4.10 -->
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* [[Double Integrals in Polar Form]]  <!-- 2214-15.4 -->
* [[The Limit Laws]] <!-- 1214-2.3 -->
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* '''[[Parametric Equations| Polar Form]]''' <!-- 1224-7.1 -->
* [[Power Series and Functions]] <!-- 1224-6.1 -->
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* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
  
 
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* Differentiate and integrate power series term-by-term.
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* Integration in Cylindrical Coordinates
* Recognize certain continuous functions as power series on their radius of convergence.
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* Equations relating rectangular and cylindrical coordinates
 +
* Spherical coordinates and integrations
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* Equations relating spherical coordinates to Cartesian and cylindrical coordinates
  
  

Revision as of 17:46, 2 July 2020

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1
1.3

Three-Dimensional Coordinate Systems


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


Week 1 and 2
12.2


Vectors

  • Vector Algebra Operations
  • Magnitude of a vector
  • Unit Vectors
  • Midpoint of a Line Segment
  • Angle between vectors
  • Definition of Dot product
  • Orthogonal vectors
  • Vector projection
Week 3
12.3

The Dot Product


  • Find the area of plane regions bounded by the graphs of functions.
Week 3/4
12.4

The Cross Product

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


Week 4
12.5


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


Week 4/5
13.1


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 5/6
13.2

Integrals of Vector Functions

  • Indefinite integrals of vector functions
  • Definite integrals of vector functions
  • Vector and parametric equations for ideal projectile motion


Week 6/7
13.3


Arc Length

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


Week 6
13.4


Curvature and Normal Vectors

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


Week 7
13.5


Tangential and Normal Components of Acceleration

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


Week 7/8
14.1


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 6/7
14.2


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 7
14.3

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 differentiability for functions of two variables


Week 8
14.4

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 8/9
14.5

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 9
14.6

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 10/11
14.7

Extreme Values and Saddle Points

  • 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 11/12
14.8

EDIT

  • Define the convergence or divergence of an infinite series.
  • Find the sum of a geometric or telescoping series.
Week 11
14.9

Taylors formula for Two Variables

  • The derivation of the second derivative test
  • Taylor's formula for functions of two variables


Week 11/12
15.1

Double and Iterated Integrals over Rectangles

  • Double Integrals
  • Fubini's Theorem (part 1)
Week 12
15.2

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 13/14
15.3

Area by Double Intgration

  • Areas of bounded regions in the plane
  • Average value for functions of two or more variables


Week 14
15.4

Double Integrals in Polar Form

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


Week 15
15.5

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 15/16
15.6

Applications of Double and Triple Integrals

  • Masses and First moments
  • Moments of Inertia



Week 16
15.7

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 17
6.3

Taylor and Maclaurin Series

  • Find the Taylor or Maclaurin series representation of a function.
  • Find the radius of convergence of a Taylor Series.
  • Estimate the remainder in a Taylor polynomial approximation.



Week 17/18
7.1

Parametric Equations

  • Sketch the graph of a parametric curve