Difference between revisions of "MAT2214"

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|Weeks 1 and 2
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|Week 1
  
 
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[[Vectors and the Geometry of Space]]  
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[[Three-Dimensional Coordinate Systems]]  
  
 
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* One-dimensional coordinate system.
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* [[Graphs|One-dimensional coordinate systems]] <!-- 1073-Mod R -->
* Two-dimensional coordinate systems.
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* [[Bases and Linear Independence| Two-dimensional coordinate systems]] <!-- 2233-3.3 -->
* Algebraic equations.
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* [[Solving Equations| Algebraic Expressions]] <!-- 1073-Mod R -->
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* [[Solving Inequalities]] <!-- 1073-Mod R -->
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* '''[[Distance Formula for R<sup>2</sup> ]]''' <!-- DNE (recommend pairing with discussion of absolute value function) -->
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* Three-dimensional coordinate systems
 
* Three-dimensional coordinate systems
* Vectors
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* Distance Formula in R<sup>3</sup>
* Linear operations
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* Standard Equation for a Sphere
* The dot product
 
* The cross product
 
* Lines and planes in space
 
* Cylinders and quadratic surfaces
 
  
  
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|Week&nbsp;3  
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|Week&nbsp;1 and 2  
  
 
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<div style="text-align: center;">1.5</div>
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<div style="text-align: center;">12.2</div>
  
 
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[[Vector-valued Functions and Motion in Space]]  
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[[Vectors and the Dot product]]  
  
 
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* [[Trig. Functions|Basic Trig Functions]] <!-- 1093-2.2 -->
 
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* [[Inverse Trigonometric Functions|Customary domain restrictions for Trigonometric Functions]] <!-- 1093-3.1 -->
* [[The Limit of a Function]] <!-- 1214-2.2 -->
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* '''[[Midpoint formula]]''' <!-- Grades 6-12 -->
* [[Continuity]] <!-- 1214-3.5 -->
 
* [[The Derivative of a Function]] <!-- 1214-2.1 -->
 
* [[The Definite Integral|Solving Basic Integrals]] <!-- 1214-5.2 -->
 
* [[Trigonometric Integrals]] <!-- 1224-3.2 -->
 
* [[Integration by Parts]] <!-- 1224-3.1 -->
 
* [[Integration by Substitution]] <!-- 1224-1.5 -->
 
 
 
  
 
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* Determine limits and continuity of vector-valued functions.
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* Vector Algebra Operations
* Determine derivatives and integrals of vector-valued functions.
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* Magnitude of a vector
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* Unit Vectors
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* Midpoint of a Line Segment
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* Angle between vectors
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* Definition of Dot product
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* Orthogonal vectors
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* Vector projection
  
 
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[[Area between Curves]]  
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[[]]  
  
  
 
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* [[Toolkit Functions|Graphs of elementary functions, including points of intersection.]] <!-- 1073-Mod 1.2 -->
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* [[The Limit of a Function]] <!-- 1214-2.2 -->
* [[Antiderivatives]] <!-- 1214-4.10 -->  
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* [[Continuity]] <!-- 1214-3.5 -->
 +
* [[The Derivative of a Function]] <!-- 1214-2.1 -->
 +
* [[The Definite Integral|Solving Basic Integrals]] <!-- 1214-5.2 -->
 +
* [[Trigonometric Integrals]] <!-- 1224-3.2 -->
 +
* [[Integration by Parts]] <!-- 1224-3.1 -->
 +
* [[Integration by Substitution]] <!-- 1224-1.5 -->
  
 
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Revision as of 11:53, 28 June 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 and the Dot product

  • 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
1.2

[[]]


  • Find the area of plane regions bounded by the graphs of functions.
Week 3/4
2.2

Determining Volumes by Slicing

  • Find the volume of solid regions with a known cross-sectional area.


Week 4
2.3


The Shell Method

  • Find the volume of solid regions obtained by revolving a plane region about a line.


Week 4/5
2.4


Arc Length and Surface Area

  • Find the arc length of a plane curve
  • The area of the surface obtained by revolving a curve about one of the coordinate axes.


Week 5/6
2.5


Physical Applications

  • Find the mass of an object with a given density function.
  • Find the work done by a variable force
  • Find the work done in pumping fluid from a tank
  • Find the hydrostatic force on a vertical plate.


Week 6/7
2.6


Moments and Center of Mass

  • Find the moments and center of mass of a thin plate of uniform density.


Week 6
3.1


Integration by Parts

  • Integrate products of certain functions.
  • Integrate logarithmic and inverse trigonometric functions.


Week 7
3.2


Trigonometric Integrals

  • Integrate products of powers of sin(x) and cos(x) as well as sec(x) and tan(x).


Week 7/8
3.3


Trigonometric Substitution


  • Integrate the square root of a sum or difference of squares.


Week 6/7
3.8


Partial Fractions

  • Integrate rational functions whose denominator is a product of linear and quadratic polynomials.


Week 7
3.7

Improper Integrals

  • Recognize improper integrals and determine their convergence or divergence.


Week 8
4.1

Basics of Differential Equations

  • Classify an Ordinary Differential Equation according to order and linearity.
  • Verify that a function is a solution of an Ordinary Differential Equation or an initial value problem.


Week 8/9
4.2

Direction Fields and Numerical Methods

  • Sketch the direction field of a first-order ODE(Ordinary Differential Equation) by hand
  • Using direction field, find equilibria of an autonomous ODE.
  • Determine the stability of equilibria using a phase line diagram.


Week 9
4.3

Separable Equations

  • Recognize and solve separable differential equations
  • Develop and analyze elementary mathematical models.


Week 10/11
4.4

Exponential Growth and Decay, The Logistic Equation

  • Solve the exponential growth/decay equations and the logistic equation.
  • Describe the differences between these two models for population growth.


Week 11
5.1

Sequences

  • Find the formula for the general term of a sequence.
  • Discuss the convergence or divergence of a sequence.
  • Find the limit of a convergent sequence.
  • Determine whether a sequence is monotone.


Week 11/12
5.2

Series

  • Define the convergence or divergence of an infinite series.
  • Find the sum of a geometric or telescoping series.
Week 12
5.3

The Divergence and Integral Tests

  • Determine the convergence or divergence of a series using the Divergence or Integral Tests.
  • Estimate the sum of a series using the Remainder Estimate Theorem.


Week 13/14
5.4

Comparison Tests

  • Determine the convergence or divergence of a series using the Direct or Limit Comparison Tests.


Week 14
5.5

Alternating Series

  • Determine the convergence or divergence of alternating series.
  • Estimate the sum of an alternating series.
  • Describe the difference between conditional and absolute convergence.


Week 15
5.6

Ratio and Root Tests


  • Determine the convergence or divergence of infinite series using the ratio and root tests..


Week 15/16
6.1

Power Series and Functions

  • Recognize a power series.
  • Find its interval and radius of convergence.
  • Represent certain functions as power series.


Week 16
6.2

Properties of Power Series

  • Differentiate and integrate power series term-by-term.
  • Recognize certain continuous functions as power series on their radius of convergence.



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