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You are here: Homepage » People » Graduate Students » Chris Eppolito » Calculus III (Fall 2019, Sections 05 and 06)

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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**THIS PAGE IS NO LONGER UPDATED**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
*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.
- Vector Functions and Curves in 3-Space (textbook section 13.1)
- Vector function definition
- Limits of vector functions
- Examples

*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)
- 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

*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

*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

*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

people/grads/eppolito/math323-05_06-f19.txt · Last modified: 2022/08/21 14:47 by eppolito

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