Difference between revisions of "MAT2213"

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! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 
|-   
 
|-   
 
+
|Week 1 || 1.2 || [[Three-Dimensional Coordinate Systems]] || ||
 
 
|Week 1
 
 
 
||
 
 
 
1.1
 
 
 
||
 
       
 
[[Polar Coordinates]]  
 
 
 
||
 
* [[Trigonometric Functions: Unit Circle Approach]]
 
* [[Inverse Trigonometric Functions]]
 
||
 
* 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
 
 
|-
 
|-
 
+
|Weeks 1 ||  2.1 || [[Vectors in The Plane, Space]] || ||
 
 
 
 
|Week 1
 
 
 
||
 
 
 
  1.2
 
 
 
||
 
       
 
[[Three-Dimensional Coordinate Systems]]  
 
 
 
||
 
 
 
* [[Two-dimensional coordinate systems]]
 
* [[Solving Equations and Inequalities| Algebraic Expressions]]
 
 
 
 
 
 
 
||
 
 
 
* Three-dimensional coordinate systems.
 
* Distance Formula in Space.
 
* Standard Equation for a Sphere.
 
 
|-
 
|-
 
+
|Week 1 ||  2.|| [[The Dot Product]] || ||
 
 
|Weeks 1/2 
 
 
 
||
 
 
 
  2.1
 
 
 
||
 
 
 
 
 
[[Vectors in The Plane, Space]]  
 
 
 
||
 
 
 
* [[Linear Equations|Line Segments]]
 
* [[Distance Formula| Distance Formula]]
 
 
 
||
 
 
 
* Vector Algebra Operations
 
* The Magnitude of a vector
 
* Unit Vectors
 
* The Midpoint of a Line Segment
 
* The Vector projection
 
 
|-
 
|-
 
+
|Week 2 ||  2.|| [[The Cross Product]] Scalar triple product  || ||
 
 
 
 
|Week 2
 
 
 
||
 
 
 
  2.3
 
 
 
||
 
 
 
[[The Dot Product]]  
 
 
 
 
 
||
 
 
 
* [[Trigonometric Functions|Basic Trig Functions]] 
 
* [[Vectors]] 
 
 
 
||
 
* Definition of  Dot Product
 
* Properties of Dot Product
 
* Angle between vectors
 
* Orthogonal vectors
 
 
 
 
|-
 
|-
 
+
|Week 2 ||  2.|| [[Equations of Lines, Planes and Surfaces in Space]] || ||
 
 
|Week 2
 
 
 
||
 
 
 
  2.4
 
 
 
||
 
 
 
[[The Cross Product]]  
 
 
 
||
 
 
 
* [[Trigonometric Functions|Basic Trig Functions]] 
 
* [[Determinants]]
 
* [[Vectors]]
 
 
 
||
 
 
 
* Definition of Cross Product
 
* Properties of the cross product
 
* Area of a parallelogram
 
* Cross product as a determinant
 
 
 
 
 
 
|-
 
|-
 
+
|Week 3 ||  2.|| [[Equations of Lines, Planes and Surfaces in Space|Equaitons of Curves. Equations of Surfaces]] || ||
 
 
 
 
|Week 3
 
 
 
||
 
 
 
  2.5
 
 
 
||
 
 
 
 
 
[[Equations of Lines, Planes and Surfaces in Space]]  
 
 
 
||
 
 
 
* [[The Dot Product]]
 
* [[The Cross Product]]
 
* [[Quadratic Functions]]
 
* [[Parametric Equations]]
 
 
 
||
 
 
 
* 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.
 
 
 
 
 
 
|-
 
|-
 
+
|Weeks 3 ||  3.1, 3.2 || [[Curves in Space and Vector-Valued Functions]] Derivatives and integrals of vector functions || ||
 
 
|Week 3
 
 
 
||
 
 
 
  2.6
 
 
 
||
 
 
 
 
 
[[Equations of Lines, Planes and Surfaces in Space|Cylinders and Quadratic Surfaces]]  
 
 
 
||
 
 
 
* [[Quadratic Functions]]
 
* [[Parametric Equations]]
 
* '''[[Conics]]'''
 
 
 
||
 
 
 
* 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 ||  3.3 || [[Arc Length]] || ||
 
 
|Weeks 3/4
 
 
 
||
 
 
 
  3.1, 3.2
 
 
 
||  
 
 
 
[[Curves in Space and Vector-Valued Functions]]  
 
 
 
||
 
 
 
* [[Parametric Equations]]
 
* [[Vectors]] 
 
* [[The Derivative as a Function]]
 
* [[The Limit of a Function]]
 
* [[Continuity]]
 
* [[The Dot Product]]
 
* [[The Cross Product]]
 
 
 
||
 
 
 
* Vector functions
 
* Limits of vector functions
 
* Continuity of vector functions
 
* Differentiation rules for vector functions
 
* Curves and paths in space
 
 
 
 
 
 
|-
 
|-
 
+
|Weeks 4/5 ||  3.|| [[Motion in Space]] || ||
 
 
 
 
|Week 4
 
 
 
||
 
 
 
  3.3
 
 
 
||
 
 
 
[[Arc Length]]
 
 
 
||
 
 
 
* '''[[Distance Formula| The Length of a Line Segment]]'''
 
* [[Curves in Space and Vector-Valued Functions|Vector Functions]]  
 
* [[Line Integrals|Integrals of Vector Functions]], [[Derivatives of Vector Functions]]
 
 
 
||
 
 
 
* The arc Length of a vector function
 
* Arc length parameterization
 
 
 
 
|-
 
|-
 
+
|Week 5/||  4.1 || [[Functions of Several Variables]] || ||
 
 
 
 
|Weeks 4/5
 
 
 
||
 
 
 
  3.4
 
 
 
||
 
 
 
[[Motion in Space]]
 
 
 
||
 
* [[Vectors]] 
 
* [[Parametric Equations]]
 
* [[The Cross Product]]
 
* [[Derivatives of Vector Functions]]
 
||
 
* The Unit tangent vector
 
* The curvature
 
* The Principal Unit Normal Vector
 
* The Binormal Vector
 
* The tangential and normal components of acceleration
 
* The Torsion
 
 
 
 
|-
 
|-
 
+
|Week 6 ||  4.|| [[Limit and Continuity of Function of Several Variables]] || ||
 
 
 
 
|Week 5/6
 
 
 
||
 
 
 
  4.1
 
 
 
||
 
 
 
 
 
[[Functions of Several Variables]]
 
 
 
||
 
 
 
* [[Domain of a Function]]
 
* [[Range of a Function]]
 
* [[Solving Equations and Inequalities]]
 
* [[Graphs| Graphing a Function]]
 
 
 
||
 
* 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 6 ||  4.3 || [[Partial Derivatives]] || ||
 
 
|Week 6
 
 
 
||
 
 
 
  4.2
 
 
 
||
 
 
 
 
 
[[Limit and Continuity of Function of Several Variables]]
 
 
 
||
 
 
 
* [[Continuity]]
 
* [[The Limit Laws]]
 
* [[Composition of Functions]]
 
* [[The Dot Product]]
 
 
 
||
 
 
 
* 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 ||  4.||  [[Directional Derivatives and Gradient Vectors]] || ||
 
 
|Week 6
 
 
 
||
 
 
 
  4.3
 
 
 
||   
 
 
 
[[Partial Derivatives]]
 
 
 
||
 
 
 
* [[The Derivative as a Function|The first]] and [[The Second Derivative|second derivative]] of a function
 
* [[Limit and Continuity of Function of Several Variables]]
 
 
 
 
 
||
 
* 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 7 ||  4.5 ||  [[Tangent Plane]], [[Differentiability]] || ||
 
 
|Week 7
 
 
 
||
 
 
 
  4.4
 
 
 
||   
 
 
 
[[Directional Derivatives and Gradient Vectors]]
 
 
 
||
 
* [[Trigonometric Functions]]  
 
* [[Vectors, Unit Vectors]] 
 
* [[Partial Derivatives]]
 
* [[Gradients]]
 
* [[The Dot Product]]
 
||
 
* Directional derivatives for functions of two variables
 
* Gradients
 
* Properties of directional derivatives
 
* Tangents to level curves
 
* Directional derivatives for functions of three variables
 
 
|-
 
|-
 
+
|Week 7 ||  4.6 ||  [[The Chain Rule for Functions of more than One Variable]] || ||  
 
 
|Week 7  
 
 
 
||
 
 
 
  4.5
 
 
 
||   
 
[[Tangent Plane]],
 
[[Differentiability]]
 
 
 
 
 
||
 
* [[Partial Derivatives]] 
 
* [[Parametric Equations]] of Lines
 
* [[Equations of Lines, Planes and Surfaces in Space]]
 
 
 
||
 
* 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 8 || 4.7 ||  [[Maxima and Minima Problems]] || ||
 
 
 
 
|Week 7
 
 
 
||
 
 
 
4.6
 
 
 
||   
 
 
 
[[The Chain Rule for Functions of more than One Variable]]
 
 
 
||
 
* [[Differentiation Rules]]
 
* [[The Chain Rule]]
 
* [[Partial Derivatives]] 
 
 
 
||
 
* 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 8  
+
|Week 8/9 || 4.8 ||  [[Lagrange Multipliers]] || ||
 
 
||
 
 
 
4.7
 
 
 
||   
 
 
 
[[Maxima and Minima Problems]]
 
 
 
||
 
* [[Extreme values on closed and bounded domains]]
 
* [[Partial Derivatives]] 
 
* [[Maxima and Minima|Maxima, Minima and Critical Points of a Function]]
 
* [[Limit and Continuity of Function of Several Variables]]
 
 
 
||
 
* 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 8/9
+
|Week 9/10 || 5.1 ||  [[Multiple Integrals|Double Integrals over Rectangular Regions]] || ||
 
 
||
 
 
 
4.8
 
 
 
||   
 
 
 
[[Lagrange Multipliers]]
 
 
 
||
 
 
 
* [[Partial Derivatives]] 
 
* [[Critical Points of a Function]]
 
 
 
||
 
* Lagrange Multipliers with One Constraint
 
* Lagrange Multipliers with Two Constraints
 
 
|-
 
|-
 
+
|Week 10 || 5.2 ||  [[Multiple Integrals|Double Integrals over General Regions]] || ||
 
 
 
 
|Week 9/10
 
 
 
||
 
 
 
5.1
 
 
 
||   
 
 
 
[[Multiple Integrals|Double Integrals over Rectangular Regions]]
 
 
 
||
 
 
 
* [[Approximating Areas]]
 
* [[The Definite Integral|Limits of Riemann Sums]]
 
 
 
||
 
* Double Integral is the limit of Double Sums.
 
* Double Integrals over Rectangular Regions.
 
* Interated Integrals.
 
* Fubini's Theorem (part 1).
 
 
|-
 
|-
 
+
|Week 11    || 5.3 ||  [[Multiple Integrals|Double Integrals in Polar Coordinates]] || ||
 
 
|Week 10
 
 
 
||
 
 
 
5.2
 
 
 
||   
 
 
 
[[Multiple Integrals|Double Integrals over General Regions]]
 
 
 
||
 
 
 
* [[Continuity]]
 
* [[Determining Volumes by Slicing]]
 
* [[Multiple Integrals|Double and Iterated Integrals over Rectangular regions]]
 
 
 
||
 
* 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 11 ||  5.4 || [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] || ||
 
 
 
 
|Week 11  
 
 
 
||
 
 
 
  5.3
 
 
 
||
 
 
 
[[Multiple Integrals|Double Integrals in Polar Coordinates]]
 
 
 
||
 
 
 
* [[Multiple Integrals|Double Integrals over General Regions]]
 
* [[Polar Coordinates]]
 
 
 
||
 
* 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 12 || 5.5 || [[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]] || ||
 
 
|Week 11
 
 
 
||
 
 
 
  5.4
 
 
 
||  
 
 
 
[[Multiple Integrals|Triple Integrals in Rectangular Coordinates]]
 
 
 
||
 
 
 
* [[Multiple Integrals|Double Integrals]]
 
* [[Multiple Integrals|Area by Double Integration]]
 
* '''[[Change of Variables]]'''
 
 
 
||
 
 
 
* 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 13  || 5.6 || [[Multiple Integrals|Applications of Multiple Integrals]] || ||
 
 
 
 
|Week 12
 
 
 
||
 
 
 
5.5
 
 
 
||  
 
 
 
[[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]]
 
 
 
||
 
 
 
* [[Multiple Integrals|Double Integrals in Polar Form]] 
 
* [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]]
 
 
 
||
 
 
 
* 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 13/14 || 5.7 || [[Multiple Integrals|Change of Variables in Multiple Integrals]] || ||
 
 
|Week 13   
 
 
 
||
 
 
 
5.6
 
 
 
||
 
 
 
[[Multiple Integrals|Applications of Multiple Integrals]]
 
 
 
||
 
 
 
* [[Multiple Integrals|Double Integral]]
 
* [[Multiple Integrals|Triple Integrals]]
 
 
 
||
 
 
 
* 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 13/14
+
|Week 14 || 6.1 || [[Vector Fields]] || ||  
 
 
||
 
 
 
5.7
 
 
 
||
 
 
 
[[Multiple Integrals|Change of Variables in Multiple Integrals]]
 
 
 
||
 
 
 
* [[Multiple Integrals|Double Integral]]
 
* [[Multiple Integrals|Triple Integrals]]
 
 
 
||
 
 
 
* 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 14  
+
|Week 14 ||  6.|| [[Line Integrals]] || ||
 
 
||
 
 
 
  6.1
 
 
 
||
 
 
 
[[Vector Fields]]
 
 
 
||
 
 
 
* [[The Dot Product]] <!-- 2214-12.3 -->
 
* [[Directional Derivatives and Gradient Vectors]]
 
||
 
* 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 14/15  || 6.3 || [[Conservative Vector Fields]] || ||
 
 
|Week 14  
 
 
 
||
 
 
 
6.2
 
 
 
||
 
 
 
[[Line Integrals]]
 
 
 
||
 
 
 
* [[Parametric Equations]]
 
* [[Curves in Space and Vector-Valued Functions]]
 
* [[Arc Length]]
 
 
 
||
 
* 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.
 
 
|-
 
|-
 
+
|Weeks 14/15  || 6.4 || [[Green's Theorem]] [[Stokes' Theorem]] || ||
 
 
 
 
 
 
 
 
|Week 14/15 
 
 
 
||
 
 
 
6.3
 
 
 
||
 
 
 
[[Conservative Vector Fields]]
 
 
 
||
 
 
 
* [[Vector Fields and Line Integrals]]
 
* [[Partial Derivatives]] 
 
 
 
||
 
* 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 14/15   
 
 
 
||
 
 
 
6.4  
 
 
 
||
 
 
 
[[Green's Theorem]]
 
 
 
[[Stokes' Theorem]]
 
 
 
||
 
 
 
* [[Vector Fields]]
 
* [[Line Integrals]]
 
* [[Partial Derivatives]] 
 
* [[The Dot Product]]
 
* [[Line Integrals|Path Independence]]
 
* [[Conservative Vector Fields]]
 
 
 
||
 
 
 
* Circulation form of Green's Theorem.
 
* Flux Form of Green’s Theorem.
 
* Applying Green's Theorem to find Work, Flux.
 
 
 
 
|}
 
|}

Latest revision as of 15:43, 31 March 2023