Difference between revisions of "MAT2214"

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* [[Quadratic Functions]] <!-- 1073-Mod R -->
 
* [[Quadratic Functions]] <!-- 1073-Mod R -->
 
* [[Parametric Equations]] <!-- 1224-7.1 -->
 
* [[Parametric Equations]] <!-- 1224-7.1 -->
* [[Conics]] <!-- DNE (recommend 1093) -->
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* [['''Conics''']] <!-- DNE (recommend 1093) -->
  
 
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[[Curves in Space]]  
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[[Curves in Space and Vector Functions]]  
  
 
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<div style="text-align: center;">2.5</div>
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<div style="text-align: center;">13.2</div>
  
 
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[[Integrals of Vector Functions]]
[[Physical Applications]]
 
  
 
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* [[Antiderivatives| Initial Value Problems]] <!-- 1214-4.10 -->
 
* [[The Definite Integral|Solving Basic Integrals]] <!-- 1214-5.2 -->
 
* [[The Definite Integral|Solving Basic Integrals]] <!-- 1214-5.2 -->
* '''Knowledge of basic physics (e.g. mass, force, work).'''
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* [[Parametric Equations]] <!-- 1224-7.1 -->
 +
* [[Curves in Space and Vector Functions|Vector Functions]] <!-- 1224-7.1 -->
  
 
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* Find the mass of an object with a given density function.
+
* Indefinite integrals of vector functions
* Find the work done by a variable force
+
* Definite integrals of vector functions
* Find the work done in pumping fluid from a tank
+
* Vector and parametric equations for ideal projectile motion
* Find the hydrostatic force on a vertical plate.
 
  
 
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<div style="text-align: center;">2.6</div>
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<div style="text-align: center;">13.3</div>
  
 
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[[Moments and Center of Mass]]
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[[Arc Length]]
  
 
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* [[Toolkit Functions|Sketching Common Functions]] <!-- 1073-Mod 1.2 -->
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* [[Distance Formula| Length of a Line]] <!-- DNE (recommend pairing with discussion of absolute value function) -->
* [[The Definite Integral|Solving Basic Integrals]] <!-- 1214-5.2 -->
+
* [[Curves in Space and Vector Functions|Vector Functions]] <!-- 1224-7.1 -->
 +
* [[Integrals of Vector Functions]] <!-- 2214-13.2 -->
  
 
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* Find the moments and center of mass of a thin plate of uniform density.
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* Length of a curve in R<sup>3</sup>
 +
* General arc length formula
 +
* Arc length for parameterized curves
 +
* The Unit tangent vector
  
 
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<div style="text-align: center;">3.1</div>
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<div style="text-align: center;">13.4</div>
  
 
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[[Integration by Parts]]
+
[[Curvature and Normal Vectors]]
  
 
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* [[Antiderivatives]] <!-- 1214-4.10 -->  
 
* [[Antiderivatives]] <!-- 1214-4.10 -->  
* [[Linear Approximations and Differentials| Knowledge of Differentials ]] <!-- 1214-4.2 -->
+
* [[Vectors]] <!-- 1214-12.2 -->  
* [[Differentiation Rules|Rules for finding Derivatives]] <!-- 1214-3.3 -->
+
* [[Parametric Equations]] <!-- 1224-7.1 -->
 +
* [[Arc Length|The Unit Tangent Vector]] <!-- 1224-13.3 -->
 +
* ['''[Conics''']] <!-- DNE (recommend 1093) -->
  
 
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* Integrate products of certain functions.
+
* Curvature in R<sup>2</sup>
* Integrate logarithmic and inverse trigonometric functions.
+
* Formula for curvature
 +
* Definition of Principal unit normal
 +
* Curvature and normal vectors for higher dimensions.
  
 
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Revision as of 12:32, 30 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

  • 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
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