Difference between revisions of "MAT2214"

From Department of Mathematics at UTSA
Jump to navigation Jump to search
(Edited weeks column)
(minor edits to table prerequisites)
Line 21: Line 21:
 
* [[Solving Equations| Algebraic Expressions]] <!-- 1073-Mod R -->
 
* [[Solving Equations| Algebraic Expressions]] <!-- 1073-Mod R -->
 
* [[Solving Inequalities]] <!-- 1073-Mod R -->
 
* [[Solving Inequalities]] <!-- 1073-Mod R -->
* '''[[Distance Formula for R<sup>2</sup> ]]''' <!-- DNE (recommend pairing with discussion of absolute value function) -->
+
* '''[[Distance Formula in the Plane]]''' <!-- DNE (recommend pairing with discussion of absolute value function) -->
  
  
Line 80: Line 80:
 
* [[Inverse Trigonometric Functions|Customary domain restrictions for Trigonometric Functions]] <!-- 1093-3.1 -->
 
* [[Inverse Trigonometric Functions|Customary domain restrictions for Trigonometric Functions]] <!-- 1093-3.1 -->
 
* [[Vectors]]  <!-- 2214-12.2 -->  <!-- 2233-1.1 -->
 
* [[Vectors]]  <!-- 2214-12.2 -->  <!-- 2233-1.1 -->
* '''[[Midpoint formula]]''' <!-- Grades 6-12 -->
+
* '''[[Midpoint Formula]]''' <!-- Grades 6-12 -->
  
 
||
 
||
Line 133: Line 133:
 
* [[Quadratic Functions]] <!-- 1073-Mod R -->
 
* [[Quadratic Functions]] <!-- 1073-Mod R -->
 
* [[Parametric Equations]] <!-- 1224-7.1 -->
 
* [[Parametric Equations]] <!-- 1224-7.1 -->
* [['''Conics''']] <!-- DNE (recommend 1093) -->
+
* '''[[Conics]]''' <!-- DNE (recommend 1093) -->
  
 
||
 
||
Line 260: Line 260:
 
* [[Parametric Equations]] <!-- 1224-7.1 -->
 
* [[Parametric Equations]] <!-- 1224-7.1 -->
 
* [[Arc Length|The Unit Tangent Vector]] <!-- 1224-13.3 -->
 
* [[Arc Length|The Unit Tangent Vector]] <!-- 1224-13.3 -->
* ['''[Conics''']] <!-- DNE (recommend 1093) -->
+
* '''[[Conics]]''' <!-- DNE (recommend 1093) -->
  
 
||
 
||
Line 322: Line 322:
 
* [[Solving Inequalities| Interval Notation]] <!-- 1073-Mod R -->
 
* [[Solving Inequalities| Interval Notation]] <!-- 1073-Mod R -->
 
* [[Graphs| Graphing a Function]] <!-- 1073-Mod R -->
 
* [[Graphs| Graphing a Function]] <!-- 1073-Mod R -->
* [[Conics|Equation of a Circle]] <!-- DNE (recommend 1093) -->
+
* '''[[Conics|Equation of a Circle]]''' <!-- DNE (recommend 1093) -->
  
  
Line 636: Line 636:
 
* [[Double Integrals over General Regions]] <!-- 2214-15.2 -->
 
* [[Double Integrals over General Regions]] <!-- 2214-15.2 -->
 
* [[The Definite Integral| Average value of a fucntion]] <!-- 1214-5.2 -->
 
* [[The Definite Integral| Average value of a fucntion]] <!-- 1214-5.2 -->
* [[Conics]] <!-- DNE (recommend 1093) -->
+
* '''[[Conics]]''' <!-- DNE (recommend 1093) -->
  
 
||
 
||
Line 660: Line 660:
  
 
* [[Double Integrals over General Regions]] <!-- 2214-15.2 -->
 
* [[Double Integrals over General Regions]] <!-- 2214-15.2 -->
* '''[[Parametric Equations| Polar Form]]''' <!-- 1224-7.1 -->
+
* [[Parametric Equations| Polar Coordinates]] <!-- 1093-5.1 -->
  
 
||
 
||
Line 713: Line 713:
 
* [[Moments and Center of Mass]] <!-- 1224-2.6 -->
 
* [[Moments and Center of Mass]] <!-- 1224-2.6 -->
 
* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
 
* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
* [[Partial Derivatives]] <!-- 1214-14.3 -->
+
* [[Partial Derivatives]] <!-- 1214-14.3 -->
  
 
||
 
||
Line 739: Line 739:
  
 
* [[Double Integrals in Polar Form]]  <!-- 2214-15.4 -->
 
* [[Double Integrals in Polar Form]]  <!-- 2214-15.4 -->
* '''[[Parametric Equations| Polar Form]]''' <!-- 1224-7.1 -->
+
* [[Parametric Equations| Polar Form]] <!-- 1093-5.1 -->
 
* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
 
* [[Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
  

Revision as of 07:16, 7 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 1/2
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 2
12.3

The Dot Product


  • Find the area of plane regions bounded by the graphs of functions.
Week 2/3
12.4

The Cross Product

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


Week 3
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 3/4
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 4
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 4/5
13.3


Arc Length

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


Week 5
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 5/6
13.5


Tangential and Normal Components of Acceleration

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


Week 7
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 7/8
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 8
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 the derivative for functions of two variables


Week 8/9
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 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 9/10
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
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 10/11
14.8

Lagrange Multipliers

  • Define the convergence or divergence of an infinite series.
  • Find the sum of a geometric or telescoping series.
Week 12
14.9

Taylors formula for Two Variables

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


Week 12/13
15.1

Double and Iterated Integrals over Rectangles

  • Double Integrals
  • Fubini's Theorem (part 1)
Week 14
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 14/15
15.3

Area by Double Intgration

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


Week 15
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 15/16
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 16
15.6

Applications of Double and Triple Integrals

  • Masses and First moments
  • Moments of Inertia



Week 16/17
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
16.1

Line Integrals of Scalar Functions

  • Evaluating a Line Integral
  • Additivity of Line Integrals
  • Mass and Moments
  • Line Integrals in the plane


Week 18
16.2

Vector Fields and Line Integrals

  • Vector Fields
  • Gradient Fields
  • Line Integrals of vector fields
  • Line integrals with respect to each components direction
  • Work done by a force over a curve in space
  • Flow integrals and circulation for velocity fields
  • Flux across a simple closed plane curve


Week 18/19
16.3

Path Independence and Conservation Fields

  • Path Independence
  • Piecewise smooth curves and connected domains in open regions
  • Line integrals in Conservation fields
  • Finding potentials for conservative fields
  • Exact Differential forms


Week 20
16.4

Green's Theorem

  • Circulation Density
  • Divergence (flux density) of a vector field
  • The two forms of Green's theorem (Tangential and Normal forms)
  • Green's theorem for evaluating line integrals