~~NOTOC~~
====== Calculus III (Fall 2019, Sections 05 and 06) ======

This is a website built for math323-05-f19 and math323-06-f19.  If you have an idea to improve this space, please email eppolito-at-math-dot-binghamton-dot-edu with your suggestion; I would like this space to be as useful to students as possible...

**THIS PAGE IS NO LONGER UPDATED**
===== General Information =====

The official course page is at the following link:

[[calculus:math_323:start|https://www2.math.binghamton.edu/p/calculus/math_323/start]].

Its contents are our syllabus.


=== Contact Information ===

Your instructor is Chris Eppolito (hey, that's me!).  Email me at eppolito-at-math-dot-binghamton-dot-edu for anything regarding this class.  Be sure to include your name and section number in the email.


=== Meetings ===

Section 5: MWF 14:50 - 16:20 in LH 3

Section 6: MWF 16:40 - 18:10 in CW 323


=== Office Hours ===

Our help room for this class is WH 233.  Please see the {{helprooms:233.pdf|schedule}} for my hours.  I can also meet by appointment (email me to set up an appointment).

You can visit any Calculus III instructor in the help room, and I encourage you to do so!  Different folks think differently; maybe someone else thinks more like you, and you can get help from them too.


=== Textbook ===

//Multivariable Calculus (8e)// by Stewart

The textbook (as an e-book) comes with a subscription to [[https://www.webassign.net|WebAssign]], so just get that...


=== Grading ===

See the [[calculus:math_323:start#evaluation|official grading distribution]].


=== Content ===

Reasoning in three dimensions.  Calculus of functions in several variables.  We will cover most of chapters 12 - 16 in the textbook, together with some small excursions as I see fit.


=== Homework ===

This class uses [[https://www.webassign.net|WebAssign]] for online homework assignments.  You are expected to check WebAssign daily, and to know when assignments are due.  //I will NOT notify you of assignment due dates// (all due dates are already posted).

Email me if you need the key to our class in WebAssign.


== Written Homework ==

I sometimes assign written homework to collect in class.


== Practice Problems ==

Here are some {{exercises-math323-05_06-f19.pdf|practice problems (updated 16 November 2019)}} I like. Check back for updates...


=== Quizzes ===

Quizzes will be given frequently throughout the course.  Quizzes are intended to check that you understand basic concepts from previous classes and from assigned reading.

I typically grade quiz questions on a 5-point scale.  The following is a ROUGH guide to interpreting each score.
  * **5**: Understands concept, with minor errors
  * **4**: Mostly understands concept, with errors in execution or minor misunderstanding
  * **3**: Conceptual misunderstanding present, but not yet serious
  * **2**: Major conceptual misunderstandings, with shallow understanding (if any)
  * **1**: Mostly nonsense, with serious errors
  * **0**: Demonstrates no understanding of the topic


===== Useful Software =====

Here are some useful technological tools for this class, together with some descriptions.

  * [[http://grapher.mathpix.com/|Mathpix]] is a browser 3D graphing calculator.  The interface is self explanatory, produces very nice pictures, and doesn't use a lot of computing power.
  * [[https://www.geogebra.org/3d|GeoGebra]] is a math learning software (that link is to the browser 3D graphing calculator).  You can download a copy (for Linux, Mac, or Windows) and write your own sheets, too!  There is a learning curve...
  * [[https://academo.org/demos/3d-surface-plotter/|Academo]] is a browser 3D graphing calculator.  It provides nice shading, but has a limited rotation.

/*
  * [[https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/|CalcPlot3D]] is a browser 3d graphing calculator.  This one adds nice shading, making the pictures easy to study, but can be a bit slow.
  * [[https://www.desmos.com/calculator/nqom2ih05g|Desmos]] is a browser graphing calculator.  Move the a, b, and c sliders to rotate the axes in this 3D grapher.
*/


===== Schedule =====

This section is a record of what I have covered and plan to cover in my sections.  See also the [[calculus:math_323:start#tentative_schedule|official schedule]].


=== 21 August 2019 W ===
  * First-day stuff
    * Discussed the syllabus
    * Introductions from students
  * Geometry in three dimensions (textbook section 12.1)
    * Proved the Distance Formula.
  * __Homework__
    * __Read__: Textbook sections 12.1 and 12.2
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}

=== 23 August 2019 F ===
  * Vectors and Vector Operations (textbook section 12.2)
    * Algebraic and geometric descriptions of vectors
    * Addition and scalar multiplication operations on vectors
    * Algebraic properties of vector addition and scalar multiplication
  * __Homework__
    * __Read__: Textbook section 12.3
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}

=== 26 August 2019 M ===
  * The Dot Product (textbook section 12.3)
    * Algebraic definition of the dot product
    * Algebraic properties of the dot product
    * Geometric interpretation of the dot product and consequences
  * The Cross Product (textbook section 12.4)
    * Briefly constructed the cross product as a particular vector orthogonal to two given vectors
  * __Homework__
    * __Read__: Textbook sections 12.4 and 12.5
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}

=== 28 August 2019 W ===
  * The Cross Product (textbook section 12.4)
    * Construction as a "determinant"
    * Algebraic Properties
    * Geometric Properties
  * Lines and Planes in 3-Space (textbook section 12.5)
    * Lines
      * Vector parametrizations
      * Coordinate functions
      * Symmetric equations
    * Planes
      * Vector sums of non-parallel vectors
      * Normal vector to a plane
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}

=== 30 August 2019 F ===
  * Brief review of lines and planes in 3-space
  * {{exercises-math323-05_06-f19.pdf|Problem Session on Chapter 12}}
  * __Homework__
    * __Read__: Textbook sections 12.6 and 13.1
    * __Do__: Play with quadric surfaces and curves in 3-space--use a [[http://grapher.mathpix.com/|3D graphing calculator]] as you read!
  * **Written Homework**: {{homework1_math323-05_06-f19.pdf|Complete these exercises--Due 6 September 2019}}

=== 2 September 2019 M ===
No Classes (Labor Day: Don't wear white after today?)

=== 4 September 2019 W ===
  * Quadratic Surfaces (textbook section 12.6)--The links below are to [[https://www.geogebra.org/3d|GeoGebra]] sheets I made for class; play with the parameters to get a feel for quadratic surfaces.
    * [[https://www.geogebra.org/m/rwhkuvmy|Ellipsoid]]
    * [[https://www.geogebra.org/m/jdfmtzkb|Elliptic Paraboloid]]
    * [[https://www.geogebra.org/m/dbnwzd8w|Hyperbolic Paraboloid]]
    * [[https://www.geogebra.org/m/qjvbmxk3|One Sheet Hyperboloid]]
    * [[https://www.geogebra.org/m/jtjfutc5|Cone]]
    * [[https://www.geogebra.org/m/fvcrynby|Two Sheet Hyperboloid]]
    * [[https://www.geogebra.org/m/pbr3bxug|Hyperboloids connected through a cone]]
  * Vector Functions and Curves in 3-Space (textbook section 13.1)
    * Vector function definition
    * Limits of vector functions
    * Examples
      * [[https://www.geogebra.org/m/umqybzqf|Helix]]
      * [[https://www.geogebra.org/m/bua7rtzj|Trefoil Knot]]
  * __Homework__:
    * __Read__: Textbook sections 13.1 and 13.2
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}

=== 6 September 2019 F ===
  * Collected {{homework1_math323-05_06-f19.pdf|Written Homework 1}}
  * Recap of Vector Functions (textbook section 13.1)
  * Calculus of Vector Functions (textbook section 13.2)
    * Running Example: [[https://www.geogebra.org/m/ndrjv7tp|Moment Curve]]
    * Properties of the Limit
    * Definition and Properties of the Derivative
    * Definition and Properties of the Integral
  * __Homework__
    * __Read__: Textbook section 13.3 (with special attention to arc length)
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Study__: Start studying for Midterm 1

=== 9 September 2019 M ===
  * Arc Length of Space Curves (textbook section 13.3)
    * Derivation of Formula
    * Examples to Computing Arc Length
    * Reparametrizing a Curve by Arc Length
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Study__: Study (harder?) for Midterm 1

=== 11 September 2019 W ===
/*
  * __Excursion__: Curvature (textbook section 13.3; will not be tested)
    * Definition
    * Examples
*/
  * Motion in Space (textbook section 13.4)
    * Problem Session on Vector Functions and Space Curves
  * **NB**: End material for Midterm 1.
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Study__: Study for Midterm 1.

=== 13 September 2019 F ===
  * Multivariable Functions (textbook section 14.1)
    * [[https://www.geogebra.org/m/c5uwyxrb|Multivariable Function Plotter]]
    * [[https://www.geogebra.org/m/R4t3ZYrv#material/xzPwsETp|Contour Map Visualization]]
    * [[https://www.geogebra.org/m/R4t3ZYrv#material/ZMb6uJ6K|Another Contour Plot]]
  * Limits and Continuity of Multivaraible Functions(textbook section 14.2)
    * Definition of the Limit (with much motivation!)
  * __Homework__
    * __Study__: Study for Midterm 1.

=== 16 September 2019 M ===
  * Review Session for Midterm 1
    * Student Questions Only
    * __Study__: Study for Midterm 1

=== 18 September 2019 W ===
  * **Midterm 1 in Class**
    * __Content__: Chapters 12 and 13 (omitting curvature and normal/binormal vectors)

=== 20 September 2019 F ===
  * Limits and Continuity of Multivaraible Functions(textbook section 14.2)
    * Review the definition of the limit
    * The Curves Criterion for Limits
    * Lots of examples
    * {{limit-quiz_solution.pdf|Here are two more examples...}}
  * __Homework__
    * __Read__: Textbook sections 14.1 and 14.2; get started on 14.3

=== 23 September 2019 M ===
  * Derivatives of Multivariate Functions
    * Partial Derivatives (textbook section 14.3)
      * Definition and intuition
      * Computational aspects
      * Examples
    * Directional Derivatives (textbook section 14.6)
      * Definition and intuition
      * Examples
    * Differentiability of Multivariate Functions
      * Definition and intuition
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook sections 14.3 and 14.6

=== 25 September 2019 W ===
  * More on Derivatives of Multivariate  Functions
    * Directional Derivatives in terms of Partial Derivatives
    * Clairaut's Theorem on Mixed Partial Derivatives
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook section 14.4

=== 27 September 2019 F ===
  * Tangent Planes and Linear Approximation (textbook section 14.4)
    * Problem session
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook section 14.5

=== 30 September 2019 M ===
  * No class (Rosh Hashanah: Happy New Year!)

=== 2 October 2019 W ===
  * Multivariable Chain Rule (textbook section 14.5)
    * Derivation for the 2-variable case
    * Statement of the chain rule
    * Many examples
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook sections 14.6 (on gradient) and 14.7

=== 4 October 2019 F ===
  * Gradient (textbook section 14.6)
    * The gradient maximizes the directional derivative!
  * Maxima and Minima (textbook section 14.7)
    * Finding critical points
    * Classifying critical points with the Second Derivative Test
    * Many examples
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook section 14.8

=== 7 October 2019 M ===
  * Lagrange Multipliers (textbook section 14.8)
    * Statement of the method
    * Examples applying the method
    * {{lagrange_multipliers_example-math323-05_06-f19.pdf|Here is another example.}}
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook sections 15.1, 15.2, and 15.3
    * __Study__: Start studying (harder?) for Midterm 2

=== 9 October 2019 W ===
  * No Class (Yom Kippur: Sorry, no class today...)

=== 11 October 2019 F ===
  * Another Lagrange Multipliers example
  * Double Integrals
    * Rectangular Domain (textbook section 15.1)
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook sections 15.1, 15.2, and 15.3
    * __Study__: Study for Midterm 2

=== 14 October 2019 M ===
  * Double Integrals
    * General Domain (textbook section 15.2)
    * Polar Coordinates (textbook section 15.3)
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook sections 15.1, 15.2, and 15.3
    * __Study__: Study for Midterm 2
  * **NB**: End content for Midterm 2

=== 16 October 2019 W ===
  * Double Integrals
    * Problem Session
  * __Homework__
    * __Study__: Study for Midterm 2

=== 18 October 2019 F ===
  * Triple Integrals (textbook section 15.6)
    * Too many examples
    * Application to Physics: Center of Mass
  * __Homework__
    * __Study__: Study for Midterm 2

=== 21 October 2019 M ===
  * Review Session for Midterm 2
    * Student Questions Only
  * __Homework__
    * __Study__: Study for Midterm 2

=== 23 October 2019 W ===
  * **Midterm 2 in Class**
    * __Content__: Chapters 14 and 15.1--15.3

=== 25 October 2019 F ===
  * Cylindrical Coordinates (textbook section 15.7)
  * Spherical Coordinates (textbook section 15.8)
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook sections 15.6, 15.7, and 15.8; get started reading textbook section 15.9

=== 28 October 2019 M ===
  * Change of Variables (textbook section 15.9)
    * Unifying the differentials with Jacobians!
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook section 15.9

=== 30 October 2019 W ===
  * Change of Variables (textbook section 15.9)
    * Lots of examples
    * {{change_of_variables_solutions.pdf|Here are solutions...}}
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook sections 16.1

=== 1 November 2019 F ===
  * Vector Fields (textbook section 16.1)
  * Line Integrals (textbook section 16.2)
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook sections 16.2 and 16.3

=== 4 November 2019 M ===
  * More on line integrals
    * Too many examples
  * Fundamental Theorem of Line Integrals (textbook section 16.3)
    * __Do__: Problem assigned in class
    * __Read__: Textbook section 16.4

=== 6 November 2019 W ===
  * Green's Theorem (textbook section 16.4)
    * Statement and Explanation (proof omitted)
    * Many Examples
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook section 16.5

=== 8 November 2019 F ===
  * Curl and Divergence (textbook section 16.5)
    * Definitions
    * Many examples
    * Fundamental properties
  * **NB**: End content for Midterm 3
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Read__: Textbook sections 16.6 and 16.7
    * __Study__: Start studying (harder?) for Midterm 3

=== 11 November 2019 M ===
  * Parametric Surfaces (textbook section 16.6)
    * Examples
    * Tangent planes from parametrizations
    * Surface areas from parametrizations
  * __Homework__
    * __Do__: Attempt {{exercises-math323-05_06-f19.pdf|practice problems}}
    * __Study__: Study for Midterm 3

=== 13 November 2019 W ===
  * Surface Integrals (textbook section 16.7)
    * Examples
  * __Homework__
    * __Study__: Study for Midterm 3

=== 15 November 2019 F ===
  * Review Session for Midterm 3
    * Student Questions Only
  * __Homework__
    * __Study__: Study for Midterm 3

=== 18 November 2019 M ===
  * **Midterm 3 in Class**
    * __Content__: Chapters 15.6--15.9 and 16.1--16.5

=== 20 November 2019 W ===
  * Stokes's Theorem (textbook section 16.8)
  * __Homework__
    * __Do__: Attempt practice problems from the textbook
    * __Read__: Textbook section 16.8
    * __Study__: Study for the CUMULATIVE Final

=== 22 November 2019 F ===
  * More on Stokes's Theorem
    * Problem session
  * __Homework__
    * __Do__: Attempt practice problems from the textbook
    * __Read__: Textbook sections 16.9
    * __Study__: Study for the CUMULATIVE Final

=== 25 November 2019 M ===
  * Divergence Theorem (textbook section 16.9)
  * __Homework__
    * __Do__: Attempt practice problems from the textbook
    * __Study__: Study for the CUMULATIVE Final

=== 27 November 2019 W ===
No Class (Find-a-T(of)urkey Day: Safe travels!)

=== 29 November 2019 F ===
No Class (Recover-from-Turkey Day: Heat up those leftovers...)

=== 2 December 2019 M ===
Classes Cancelled by the University for SNOW reason

=== 4 December 2019 W ===
  * Review Session for Final
    * Student Questions Only
    * __Study__: Study for CUMULATIVE Final

=== 6 December 2019 F ===
No Class (Reading Day: Read your favorite calculus textbook/notebook!)

=== 12 December 2019 R ===
  * FINAL EXAM!
    * **Exam Room**: LH 001
    * **Exam Time**: 15:15 - 17:15