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THIS PAGE IS NO LONGER UPDATED

The official course page is at the following link:

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

Its contents are our syllabus.

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

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…

See the official grading distribution.

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.

I sometimes assign written homework to collect in class.

Here are some practice problems (updated 16 November 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

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.

• 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 practice problems

• 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 practice problems

• 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 practice problems

• 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 practice problems

• Brief review of lines and planes in 3-space
• 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 3D graphing calculator as you read!
• Written Homework: Complete these exercises--Due 6 September 2019

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

• Quadratic Surfaces (textbook section 12.6)–The links below are to GeoGebra sheets I made for class; play with the parameters to get a feel for quadratic surfaces.
  • Ellipsoid
  • Elliptic Paraboloid
  • Hyperbolic Paraboloid
  • One Sheet Hyperboloid
  • Cone
  • Two Sheet Hyperboloid
  • Hyperboloids connected through a cone
• Vector Functions and Curves in 3-Space (textbook section 13.1)
  • Vector function definition
  • Limits of vector functions
  • Examples
    • Helix
    • Trefoil Knot
• Homework:
  • Read: Textbook sections 13.1 and 13.2
  • Do: Attempt practice problems

• Collected Written Homework 1
• 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

• 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 practice problems
  • Study: Study (harder?) for Midterm 1

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

• Multivariable Functions (textbook section 14.1)
  • Multivariable Function Plotter
  • Contour Map Visualization
  • 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.

• Review Session for Midterm 1
  • Student Questions Only
  • Study: Study for Midterm 1

• Midterm 1 in Class
  • Content: Chapters 12 and 13 (omitting curvature and normal/binormal vectors)

• Limits and Continuity of Multivaraible Functions(textbook section 14.2)
  • Review the definition of the limit
  • The Curves Criterion for Limits
  • Lots of examples
  • Here are two more examples...
• Homework
  • Read: Textbook sections 14.1 and 14.2; get started on 14.3

• 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 practice problems
  • Read: Textbook sections 14.3 and 14.6

• More on Derivatives of Multivariate Functions
  • Directional Derivatives in terms of Partial Derivatives
  • Clairaut's Theorem on Mixed Partial Derivatives
• Homework
  • Do: Attempt practice problems
  • Read: Textbook section 14.4

• Tangent Planes and Linear Approximation (textbook section 14.4)
  • Problem session
• Homework
  • Do: Attempt practice problems
  • Read: Textbook section 14.5

• No class (Rosh Hashanah: Happy New Year!)

• Multivariable Chain Rule (textbook section 14.5)
  • Derivation for the 2-variable case
  • Statement of the chain rule
  • Many examples
• Homework
  • Do: Attempt practice problems
  • Read: Textbook sections 14.6 (on gradient) and 14.7

• 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 practice problems
  • Read: Textbook section 14.8

• Lagrange Multipliers (textbook section 14.8)
  • Statement of the method
  • Examples applying the method
  • Here is another example.
• Homework
  • Do: Attempt practice problems
  • Read: Textbook sections 15.1, 15.2, and 15.3
  • Study: Start studying (harder?) for Midterm 2

• No Class (Yom Kippur: Sorry, no class today…)

• 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

• 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

• Double Integrals
  • Problem Session
• Homework
  • Study: Study for Midterm 2

• Triple Integrals (textbook section 15.6)
  • Too many examples
  • Application to Physics: Center of Mass
• Homework
  • Study: Study for Midterm 2

• Review Session for Midterm 2
  • Student Questions Only
• Homework
  • Study: Study for Midterm 2

• Midterm 2 in Class
  • Content: Chapters 14 and 15.1–15.3

• 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

• Change of Variables (textbook section 15.9)
  • Unifying the differentials with Jacobians!
• Homework
  • Do: Attempt practice problems
  • Read: Textbook section 15.9

• Change of Variables (textbook section 15.9)
  • Lots of examples
  • Here are solutions...
• Homework
  • Do: Attempt practice problems
  • Read: Textbook sections 16.1

• Vector Fields (textbook section 16.1)
• Line Integrals (textbook section 16.2)
• Homework
  • Do: Attempt practice problems
  • Read: Textbook sections 16.2 and 16.3

• 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

• Green's Theorem (textbook section 16.4)
  • Statement and Explanation (proof omitted)
  • Many Examples
• Homework
  • Do: Attempt practice problems
  • Read: Textbook section 16.5

• 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

• Parametric Surfaces (textbook section 16.6)
  • Examples
  • Tangent planes from parametrizations
  • Surface areas from parametrizations
• Homework
  • Do: Attempt practice problems
  • Study: Study for Midterm 3

• Surface Integrals (textbook section 16.7)
  • Examples
• Homework
  • Study: Study for Midterm 3

• Review Session for Midterm 3
  • Student Questions Only
• Homework
  • Study: Study for Midterm 3

• Midterm 3 in Class
  • Content: Chapters 15.6–15.9 and 16.1–16.5

• 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

• 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

• Divergence Theorem (textbook section 16.9)
• Homework
  • Do: Attempt practice problems from the textbook
  • Study: Study for the CUMULATIVE Final

No Class (Find-a-T(of)urkey Day: Safe travels!)

No Class (Recover-from-Turkey Day: Heat up those leftovers…)

Classes Cancelled by the University for SNOW reason

• Review Session for Final
  • Student Questions Only
  • Study: Study for CUMULATIVE Final

No Class (Reading Day: Read your favorite calculus textbook/notebook!)

• FINAL EXAM!
  • Exam Room: LH 001
  • Exam Time: 15:15 - 17:15