Math 2321 (Multivariable Calculus), Spring 2021
| Course Information | |||||
|---|---|---|---|---|---|
| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
(Sec 04) MWR, 1:35pm-2:40pm (Sec 12) MWR, 4:35pm-5:40pm Online, via Zoom |
W 3:00pm-4:15pm R 12:15pm-1:15pm Online, via Zoom |
|||
| I am teaching two sections of Math 2321, corresponding to the two lecture times listed. You are requested to attend your assigned lecture, but in the event you are not able, you are allowed to attend the other one (the lectures will cover the same content at the same pace). All lectures will be recorded and made available for on-demand viewing at any time. | |||||
| Math 2321 uses a Piazza page for course discussion. Links to all of the live lectures, office hours, problem sessions, and lecture recordings are hosted there. | |||||
| Teaching Assistant | Recitation Time | Office Hours | |||
| Anupam Kumar kumar.anupa at northeastern dot edu |
M, 2:50pm-4:30pm Online, via Zoom |
TBA Online, via Zoom |
|||
| For detailed information about the course, please consult the 2321 Course Syllabus. (Note: any information given in class or on this webpage supersedes the written syllabus.) | |||||
| All homework assignments are available on the 2321 WeBWorK page. | |||||
| Lecture Slides | |||
|---|---|---|---|
| These are the slides used during the lectures. They will usually be posted ahead of the lecture time. | |||
| Date | Material | ||
| Wed, Jan 20th Thu, Jan 21st |
Lecture 1: Welcome + 3D Graphing (Notes 1.1)
Lecture 2: Vectors + Dot Products (Notes 1.2.1-1.2.2) |
||
| Mon, Jan 25th Wed, Jan 27th Thu, Jan 28th |
Lecture 3: Cross Products, Lines and Planes (Notes 1.2.3-1.2.4)
Lecture 4: Lines and Planes, Vector-Valued Functions (Notes 1.2.4-1.3.1) Lecture 5: Parametric Curves, Motion in 3-Space (Notes 1.3.1-1.3.2) |
||
| Mon, Feb 1st Wed, Feb 3rd Thu, Feb 4th |
Lecture 6: Limits and Partial Derivatives (Notes 2.1)
Lecture 7: Directional Derivatives and Gradients (Notes 2.2.1) Lecture 8: Tangent Lines and Planes, Linearization (Notes 2.2.2 + 2.4.1) |
||
| Mon, Feb 8th Wed, Feb 10th Thu, Feb 11th |
Lecture 9: The Chain Rule + Implicit Differentiation (Notes 2.3)
Lecture 10: Critical Points, Minima + Maxima (Notes 2.5.1) Lecture 11: Optimization on a Region (Notes 2.5.2) |
||
| Mon, Feb 15th Wed, Feb 17th Thu, Feb 18th |
No class; university holiday.
Lecture 12: Midterm 1 Review, part 1 Lecture 13: Midterm 1 Review, part 2 |
||
| Mon, Feb 22nd Wed, Feb 24th Thu, Feb 25th |
Lecture 14: Lagrange Multipliers (Notes 2.6) [Typos fixed]
Lecture 15: Double Integrals (Notes 3.1.1-3.1.2) Lecture 16: Computing Double Integrals (Notes 3.1.2-3.1.3) |
||
| Mon, Mar 1st Wed, Mar 3rd Thu, Mar 4th |
Lecture 17: Double Integrals in Polar Coordinates (Notes 3.3.2)
Lecture 18: Triple Integrals in Rectangular Coordinates (Notes 3.2) Lecture 19: Change of Coordinates, Cylindrical Coordinates (Notes 3.3.1 + 3.3.3) |
||
| Mon, Mar 8th Wed, Mar 10th Thu, Mar 11th |
Lecture 20: Triple Integrals in Cylindrical and Spherical (Notes 3.3.3-3.3.4)
Lecture 21: More Cylindrical and Spherical + Areas, Volumes (Notes 3.3.3-3.4.1) Lecture 22: Areas, Volumes, Masses, and Moments (Notes 3.4.1-3.4.2) |
||
| Mon, Mar 15th Wed, Mar 17th Thu, Mar 18th |
Lecture 23: Line Integrals (Notes 4.1)
Lecture 24: Midterm 2 Review, part 1 Lecture 25: Midterm 2 Review, part 2 |
||
| Mon, Mar 22nd Wed, Mar 24th Thu, Mar 25th |
Lecture 26: Parametric Surfaces (Notes 4.2.1)
Classes cancelled ("CARE Day") Lecture 27: Surface Integrals (Notes 4.2.2) |
||
| Mon, Mar 29th Wed, Mar 31st Thu, Apr 1st |
Lecture 28: Vector Fields, Work, Circulation, and Flux (Notes 4.3.1-4.3.2)
Lecture 29: Flux Across Surfaces (Notes 4.3.3) Lecture 30: Conservative Fields and Potential Functions (Notes 4.4) |
||
| Mon, Apr 5th Wed, Apr 7th Thu, Apr 8th |
Lecture 31: Green's Theorem (Notes 4.5)
Lecture 32: Midterm 3 Review, part 1 Lecture 33: Midterm 3 Review, part 2 |
||
| Mon, Apr 12th Wed, Apr 14th Thu, Apr 15th |
Classes cancelled ("CARE Day")
Lecture 34: Stokes's Theorem and the Divergence Theorem (Notes 4.6) Lecture 35: Applications of Vector Calculus, part 1 (Notes 4.7.1) |
||
| Mon, Apr 19th Wed, Apr 21st |
Lecture 36: Applications of Vector Calculus, part 2 (Notes 4.7.2-4.7.4)
Lecture 37: Final Exam Review, part 1 |
||
| Tue, Apr 27th | Review: Final Exam Review, part 2 | ||
| Handouts / Lecture Notes | |||
|---|---|---|---|
| Handout | Topics | ||
| Chapter 1: Vectors and 3-Dimensional Geometry (20pp, v4.00, posted 1/15) | 1.1 ~ Functions of Several Variables and 3-Space 1.2 ~ Vectors, Dot and Cross Products, Lines and Planes 1.3 ~ Vector-Valued Functions, Curves and Motion in 3-Space |
||
| Chapter 2: Partial Derivatives (26pp, v4.00, posted 1/27) | 2.1 ~ Limits and Partial Derivatives 2.2 ~ Directional Derivatives and the Gradient 2.3 ~ The Chain Rule 2.4 ~ Linearization 2.5 ~ Local Extreme Points and Optimization 2.6 ~ Lagrange Multipliers and Constrained Optimization |
||
| Chapter 3: Multiple Integration (24pp, v4.00, posted 2/21) | 3.1 ~ Double Integrals in Rectangular Coordinates 3.2 ~ Triple Integrals in Rectangular Coordinates 3.3 ~ Alternative Coordinate Systems and Changes of Variable 3.4 ~ Applications of Multiple Integration (Areas, Volumes, Averages) |
||
| Chapter 4: Vector Calculus (34pp, v4.00, posted 3/9) | 4.1 ~ Line Integrals 4.2 ~ Surfaces and Surface Integrals 4.3 ~ Vector Fields, Work, Circulation, Flux 4.4 ~ Conservative Vector Fields, Path-Independence, and Potential Functions 4.5 ~ Green's Theorem 4.6 ~ Stokes's Theorem and Gauss's Divergence Theorem 4.7 ~ Applications of Vector Calculus |
||
| Exam Information | |||
|---|---|---|---|
| Exam | Date, Time, Format | Topics | Review Material |
| Midterm 1 (Form A), (sols) (Form B), (sols) |
Fri, Feb 19th Online, via Canvas |
WeBWorKs 1-4 Notes §1.1-1.3 + §2.1-§2.5 |
Review Problems, (answers) In-class review Wed Feb 17th + Thu Feb 18th |
| Midterm 2 (Form A), (sols) (Form B), (sols) |
Fri, Mar 19th Online, via Canvas |
WeBWorKs 5-8 Notes §2.6 + §3.1-§3.4 |
Review Problems, (answers) In-class review Wed Mar 17th + Thu Mar 18th |
| Midterm 3 (Form A), (sols) (Form B), (sols) |
Tue, Apr 13th Online, via Canvas |
WeBWorKs 9-11 Notes §4.1-4.5 |
Review Problems, (answers) In-class review Wed Apr 7th + Thu Apr 8th |
| Final | Thu, Apr 29th, 10:30am-12:30pm Online, via Canvas |
WeBWorKs 1-12 Notes §1.1-4.6 |
The final is COMPREHENSIVE! Extra Review Problems, (answers) In-class review Wed Apr 21st Review session Tue Apr 27th |
| Bring your University ID to all exams. Calculators may be used, provided they do not have qwerty keyboards and cannot do symbolic algebra. Cell phones, other electronic devices, books, and notes of any kind will NOT be permitted in exams. | |||
| Old Final Exams |
|---|
| Below are some old final exams from past semesters of Math 2321, which should be fairly representative of the final exam this semester. The time limit for each exam is 2 hours, if you wish to use them for practice. |
|
Fall 2013, (solutions)
Fall 2014, (solutions) Spring 2015 Fall 2015, (solutions) Fall 2016 with solutions Fall 2017, (solutions) Fall 2018, (solutions) Spring 2019 (solutions) Fall 2019 Fall 2020 (solutions) |
| Tips For Success In This Course | |||
|---|---|---|---|
| Attend Lecture | Missing lecture is a bad idea! If for any reason you cannot attend the lecture live, you should watch the recording of the lecture. You are responsible for all material covered in lecture. | ||
| Read the Lecture Notes (or Textbook) | The lecture notes and the textbook are comprehensive sources of material for the course. The notes are intended as review material, although many students like to read them as preparation before attending the lecture on the corresponding topics. Please note that the electronic notes are not identical to the material covered in class: this is by design, so as to provide you a slightly different perspective on the material. | ||
| Use WeBWorK Effectively | WeBWorK assignments are intended to help you learn the course material at a basic level. Look over the problems well before the due date, and work on them in concert with the corresponding lectures. You may use technology (calculators, Wolfram Alpha, computer software) and other people to help you (so long as you are submitting your own work), but be mindful: if you do not understand how to do the WeBWorK problems, you will probably struggle on the exams! (Exam problems are often harder than WeBWorK problems.) | ||
| Attend Office Hours | Office hours are specifically reserved for you to receive individual, one-on-one help from the instructor or TA. Office hours will be the most effective when you have already put in effort to learn the material on your own (including trying to solve the homework problems), and when you come in with a list of specific questions or topics you are struggling with. | ||
| Attend Optional Recitation | There is an optional weekly recitation section run by the course's TA, in which the TA will review problems from the course textbook. In addition to seeing additional problems worked out, you may also ask your own questions to the TA. The TA also has weekly office hours, where you may also ask questions. | ||
| Use Tutoring Services | The university offers a wide variety of (free) tutoring services. Please consult the Northeastern Tutoring page for additional information on peer tutoring. The Math Tutoring Center is specifically set up for tutoring in mathematics courses. Tutoring appointments can be made via MyNEU (which will provide lists of available appointments for the tutors for your specific classes); walk-in tutoring is very limited and tends to be unavailable near exam dates. All tutoring sessions are held virtually. | ||
| Course Schedule | |||
|---|---|---|---|
| The schedule is subject to change! All sections refer to the course lecture notes. | |||
| Week | Schedule | ||
| Week of Jan 18 (class starts 1/20) |
§1.1: Functions of Several Variables and 3-Space §1.2.1: Vectors and Scalars §1.2.2: The Dot Product No homework this week. |
||
| Week of Jan 25 | §1.2.3: The Cross Product §1.2.4: Lines and Planes in 3-Space §1.3: Vector-Valued Functions, Curves and Motion in 3-Space WeBWorK 1 due Thursday 1/28 at 5am. |
||
| Week of Feb 1 |
§2.1: Limits and Partial Derivatives §2.2: Directional Derivatives and the Gradient §2.4.1: Linearization WeBWorK 2 due Thursday 2/4 at 5am. |
||
| Week of Feb 8 |
§2.3: The Chain Rule §2.5.1: Critical Points and Their Classification §2.5.2: Optimization of a Function on a Region WeBWorK 3 due Thursday 2/11 at 5am. |
||
| Week of Feb 15 (no class 2/15) |
Review for Midterm 1. WeBWorK 4 due Thursday 2/18 at 5am. MIDTERM 1 Friday, Feb 19th via Canvas |
||
| Week of Feb 22 | §2.6: Lagrange Multipliers §3.1: Double Integrals in Rectangular Coordinates §3.3.2: Double Integrals in Polar Coordinates WeBWorK 5 due Friday 2/26 at 5am. |
||
| Week of Mar 1 |
§3.3.2: Double Integrals in Polar Coordinates §3.2: Triple Integrals in Rectangular Coordinates §3.3.1: Changes of Coordinates in Multiple Integrals WeBWorK 6 due Thursday 3/4 at 5am. |
||
| Week of Mar 8 |
§3.3.3: Triple Integrals in Cylindrical Coordinates §3.3.4: Triple Integrals in Spherical Coordinates §3.4: Applications of Multiple Integration WeBWorK 7 due Thursday 3/11 at 5am. |
||
| Week of Mar 15 |
§4.1: Line Integrals WeBWorK 8 due Thursday 3/18 at 5am. Review for Midterm 2. MIDTERM 2 Friday, Mar 19 via Canvas |
||
| Week of Mar 22 (no class 3/24) |
§4.2.1: Parametric Surfaces §4.2.2: Surface Integrals WeBWorK 9 due |
||
| Week of Mar 29 | §4.3: Vector Fields, Work, Circulation, Flux §4.4: Conservative Fields, Path-Independence, and Potential Functions WeBWorK 10 due |
||
| Week of Apr 5 | §4.5: Green's Theorem Review for Midterm 3. WeBWorK 11 due Friday 4/9 at 5am. |
||
| Week of Apr 12 (no class 3/12) |
Review for Midterm 3. MIDTERM 3 Tuesday, Apr 13 via Canvas §4.6: Stokes's Theorem and Gauss's Divergence Theorem §4.7: Applications of Multivariable Calculus No homework this week. |
||
| Week of Apr 19 (class ends 4/21) |
§4.7: Applications of Multivariable Calculus Review for Final Exam WeBWorK 12 due Thursday 4/22 at 5am. |
||
| FINAL EXAM, 10:30am-12:30pm on Thursday, April 29th, via Canvas | |||