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people:grads:eppolito:math323-05_06-f19

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:

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 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 WebAssign, so just get that…

Grading

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 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 practice problems (updated 11 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.

  • 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.

Schedule

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

  • 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
  • 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

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

  • Limits and Continuity of Multivaraible Functions(textbook section 14.2)
  • 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

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

27 September 2019 F

  • Tangent Planes and Linear Approximation (textbook section 14.4)
    • Problem session
  • Homework

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

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

7 October 2019 M

  • Lagrange Multipliers (textbook section 14.8)
  • Homework
    • Do: Attempt 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 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 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 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

30 October 2019 W

1 November 2019 F

  • Vector Fields (textbook section 16.1)
  • Line Integrals (textbook section 16.2)
  • Homework

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

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 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

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

Tentative Future Schedule

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

20 November 2019 W

  • Stokes's Theorem (textbook section 16.8)
  • Homework
    • Do: Attempt practice problems
    • Read: Textbook section 16.8
    • Study: Study for the CUMULATIVE Final

22 November 2019 F

  • More on Stokes's Theorem
  • Homework
    • Do: Attempt practice problems
    • Read: Textbook sections 16.9
    • Study: Study for the CUMULATIVE Final

25 November 2019 M

  • Divergence Theorem (textbook section 16.9)
  • Homework

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

  • More on Divergence Theorem
  • Homework
    • Study: Study for the CUMULATIVE Final

4 December 2019 W

  • Review Session for Final
    • Student Questions Only
    • Study: Study for 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
people/grads/eppolito/math323-05_06-f19.txt · Last modified: 2019/11/13 12:26 by eppolito