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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…

General Information

The official course page is at the following link:

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.


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 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.


Multivariable Calculus (8e) by Stewart

The textbook (as an e-book) comes with a subscription to WebAssign, so just get that…



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.


This class uses 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 assign written homework throughout the semester. Here is a record.

Practice Problems

Here are some practice problems (updated 5 September 2019) I like. Check back for updates…


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.

  • 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.
  • 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…
  • Academo is a browser 3D graphing calculator. It provides nice shading, but has a limited rotation.


This section is a record of what I have covered and plan to cover in my sections. See also the 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

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

26 August 2019 M

  • Quiz: Vector operations, definition of the dot product
  • 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

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
  • Returned first quiz at class end
  • Homework

30 August 2019 F

2 September 2019 M

No Classes (Labor Day: Don't wear white after today?)

4 September 2019 W

6 September 2019 F

  • Recap of Vector Functions (textbook section 13.1)
  • Calculus of Vector Functions (textbook section 13.2)
    • Running Example: 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 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

11 September 2019 W

  • Motion in Space (textbook section 13.4)
    • Problem Session on Vector Functions and Space Curves
  • NB: End material for Midterm 1.
  • Homework

Tentative Future Schedule

Everything past this point is tentative and will be updated as time goes by…

13 September 2019 F

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

  • Derivatives of Multivariable Functions (textbook section 14.3)
  • Homework
    • Read: Textbook sections 14.1 and 14.2; get started on 14.3
people/grads/eppolito/math323-05_06-f19.txt · Last modified: 2019/09/13 13:30 by eppolito