MAT2213 - Revision history

Juan.gutierrez3: /* Topics List */

2023-03-31T21:43:51Z

Topics List

Juan.gutierrez3: /* Topics List */

2023-03-31T21:36:50Z

Topics List

Show changes

Juan.gutierrez3: /* Topics List */ Removed HTML formatting

2023-03-31T21:17:57Z

Topics List: Removed HTML formatting

Show changes

Juan.gutierrez3: /* Topics List */ Fixed formnatting

2023-03-29T20:26:50Z

Topics List: Fixed formnatting

Juan.gutierrez3: Created page with "==Topics List== {| class="wikitable sortable" ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes |- |Week 1 ||

2023-03-08T20:49:14Z

Created page with "==Topics List== {| class="wikitable sortable" ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes |- |Week 1 || <div style="text-align:..."

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

|Week 1

||

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

||

[[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
|-

|Week 1

||

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

||

[[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.
|-

|Weeks 1/2

||

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

||

[[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

||

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

||

[[The Dot Product]]

||

* [[Trigonometric Functions|Basic Trig Functions]] 
* [[Vectors]]  

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

|-

|Week 2

||

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

||

[[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

||

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

||

[[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.

||

|-

|Week 3

||

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

||

[[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

||

|-

|Weeks 3/4

||

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

||

[[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

||

|-

|Week 4

||

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

||

[[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
||

|-

|Weeks 4/5

||

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

||

[[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 5/6

||

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

||

[[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

||

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

||

[[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 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 
* [[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

||

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

||

[[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

||

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

||
[[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 7

||

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

||

[[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

||

<div style="text-align: center;">4.7</div>

||

[[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

||

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

||

[[Lagrange Multipliers]]

||

* [[Partial Derivatives]] 
* [[Critical Points of a Function]] 

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

|Week 9/10

||

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

||

[[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 10

||

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

||

[[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

||

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

||

[[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 11

||

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

||

[[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 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]] 
* [[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

||

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

||

[[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

||

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

||

[[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

||

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

||

[[Vector Fields]]

||

* [[The Dot Product]] 
* [[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

||

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

||

[[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.
|-

|Week 14/15

||

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

||

[[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

||

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

||

[[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.
|-

@@ Line 3: / Line 3: @@
 ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 |-
 |Week 1 || 1.2 || [[Three-Dimensional Coordinate Systems]]  || ||
 |-
-|Weeks 1/2  ||  2.1  || [[Vectors in The Plane, Space]]  || ||
+|Weeks 1  ||  2.1  || [[Vectors in The Plane, Space]]  || ||
 |-
-|Week 2 ||  2.3  || [[The Dot Product]]  || ||
+|Week 1 ||  2.3  || [[The Dot Product]]  || ||
 |-
-|Week 2 ||  2.4  || [[The Cross Product]]  || ||
+|Week 2 ||  2.4  || [[The Cross Product]]  Scalar triple product  || ||
 |-
-|Week 3 ||  2.5  || [[Equations of Lines, Planes and Surfaces in Space]]  || ||
+|Week 2 ||  2.5  || [[Equations of Lines, Planes and Surfaces in Space]]  || ||
 |-
-|Week 3 ||  2.6  || [[Equations of Lines, Planes and Surfaces in Space|Cylinders and Quadratic Surfaces]]  || ||
+|Week 3 ||  2.6  || [[Equations of Lines, Planes and Surfaces in Space|Equaitons of Curves. Equations of Surfaces]]  || ||
 |-
-|Weeks 3/4 ||  3.1, 3.2  || [[Curves in Space and Vector-Valued Functions]]  || ||
+|Weeks 3 ||  3.1, 3.2  || [[Curves in Space and Vector-Valued Functions]]  Derivatives and integrals of vector functions || ||
 |-
 |Week 4 ||  3.3  || [[Arc Length]] || ||

@@ Line 125: / Line 125: @@
 * Area of a parallelogram
 * Cross product as a determinant
 |-
@@ Line 158: / Line 154: @@
 * 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.
 |-
@@ Line 186: / Line 180: @@
 * Understand basic quadratic surfaces
 * Understand general quadratic surfaces
 |-
@@ Line 222: / Line 211: @@
 * Differentiation rules for vector functions
 * Curves and paths in space
 |-
@@ Line 250: / Line 236: @@
 * The arc Length of a vector function
 * Arc length parameterization
 |-
@@ Line 280: / Line 262: @@
 * The tangential and normal components of acceleration
 * The Torsion
@@ Line 445: / Line 425: @@
 * Method for implicit differentiation.
 * The general chain rule for functions of several independent variables
 |-
 |Week&nbsp;8
@@ Line 468: / Line 450: @@
 * Second derivative test for local extreme values
 * Absolute maxima and minima on closed and bounded regions
 |-
 |Week&nbsp;8/9
@@ Line 487: / Line 471: @@
 * Lagrange Multipliers with One Constraint
 * Lagrange Multipliers with Two Constraints
 |-
@@ Line 511: / Line 495: @@
 * Interated Integrals.
 * Fubini's Theorem (part 1).
 |-
@@ Line 536: / Line 521: @@
 * Changing the order of Integration.
 * Calculating Volumes, Areas and Average Values
 |-
 |Week&nbsp;11
@@ Line 560: / Line 544: @@
 * Changing Cartesian Integrals into Polar Integrals.
 * Using Double Integrals in Polar Coordinates to find Volumes, Areas.
 |-
@@ Line 585: / Line 570: @@
 * Average value of a function in space.
 * Changing Integration Order and Coordinate systems.
 |-
@@ Line 612: / Line 598: @@
 * Equations relating spherical coordinates to Cartesian and cylindrical coordinates.
 * Changing Cartesian integrations into Cylindrical integrations.
 |-
@@ Line 634: / Line 621: @@
 * 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
@@ Line 656: / Line 645: @@
 * Evaluate a double integral using a change of variables.
 * Evaluate a triple integral using a change of variables.
 |-
 |Week&nbsp;14
@@ Line 678: / Line 669: @@
 * The Cross-Partial Test for Conservative Vector Fields.
 * Determining Whether a Vector Field is conservative.
 |-
@@ Line 703: / Line 695: @@
 * 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.
 |-
@@ Line 730: / Line 720: @@
 * 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
@@ Line 759: / Line 749: @@
 * Flux Form of Green’s Theorem.
 * Applying Green's Theorem to find Work, Flux.
-|-
+|}