Math 2321 (Multivariable Calculus), Fall 2020
| Course Information | |||||
|---|---|---|---|---|---|
| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
(Sec 09) MWR, 4:35pm-5:40pm (Sec 19) MWR, 1:35pm-2:40pm Online, via Zoom |
MW 3:00pm-4:15pm or by appointment 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 |
W, 2:00pm-5:00pm 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, Sep 9th Thu, Sep 10th |
Lecture 1: Welcome + 3D Graphing (Notes 1.1)
Lecture 2: Vectors + Dot Products (Notes 1.2.1-1.2.2) |
||
| Mon, Sep 14th Wed, Sep 16th Thu, Sep 17th |
Lecture 3: Cross Products, Lines and Planes 1 (Notes 1.2.3-1.2.4) [Typos fixed]
Lecture 4: Lines and Planes 2, Vector-Valued Functions (Notes 1.2.4-1.3.1) [Typos fixed] Lecture 5: Curves and Motion in 3-Space (Notes 1.3.2) [Typos fixed] |
||
| Mon, Sep 21st Wed, Sep 23rd Thu, Sep 24th |
Lecture 6: Limits and Partial Derivatives (Notes 2.1) [Typos fixed]
Lecture 7: Directional Derivatives and Gradients (Notes 2.2.1) [Typos fixed] Lecture 8: Tangent Lines and Planes, Linearization (Notes 2.2.2 + 2.4) [Typos fixed] |
||
| Mon, Sep 28th Wed, Sep 30th Thu, Oct 1st |
Lecture 9: The Chain Rule and Implicit Differentiation (Notes 2.3) [Typos fixed]
Lecture 10: Critical Points, Minima, and Maxima (Notes 2.5.1) Lecture 11: Optimization on a Region (Notes 2.5.2) |
||
| Mon, Oct 5th Wed, Oct 7th Thu, Oct 8th |
Lecture 12: Lagrange Multipliers (Notes 2.6) [Typos fixed]
Lecture 13: Midterm 1 Review, part 1 Lecture 14: Midterm 1 Review, part 2 |
||
| Mon, Oct 12th Wed, Oct 14th Thu, Oct 15th |
University holiday, no class today
Lecture 15: Miscellaneous Optimization, Double Integrals (Notes 3.1.1-3.1.2) Lecture 16: Computing Double Integrals (Notes 3.1.2-3.1.3) |
||
| Mon, Oct 19th Wed, Oct 21st Thu, Oct 22nd |
Lecture 17: Double Integrals in Polar (Notes 3.3.2)
Lecture 18: Triple Integrals (Notes 3.2) [Updated] Lecture 19: More Triple Integrals + Change of Coordinates (Notes 3.2 + 3.3.1) |
||
| Mon, Oct 26th Wed, Oct 28th Thu, Oct 29th |
Lecture 20: Cylindrical and Spherical Integrals (Notes 3.3.3-3.3.4)
Lecture 21: Cylindrical and Spherical, Areas and Volumes (Notes 3.3.5-3.4.1) Lecture 22: Applications of Integration (Notes 3.4.1-3.4.2) |
||
| Mon, Nov 2nd Wed, Nov 4th Thu, Nov 5th |
Lecture 23: Line Integrals (Notes 4.1)
Lecture 24: Midterm 2 Review, part 1 Lecture 25: Midterm 2 Review, part 2 |
||
| Mon, Nov 9th Wed, Nov 11th Thu, Nov 12th |
Lecture 26: Parametric Surfaces (Notes 4.2.1)
University holiday, no class today Lecture 27: Surface Integrals (Notes 4.2.2) |
||
| Mon, Nov 16th Wed, Nov 18th Thu, Nov 19th |
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 Vector Fields and Potential Functions (Notes 4.4) |
||
| Mon, Nov 23rd Thu, Nov 26th |
Lecture 31: Green's Theorem (Notes 4.5) [Updated]
University holiday, no classes -- happy Thanksgiving! |
||
| Mon, Nov 30th Wed, Dec 2nd Thu, Dec 3rd |
Lecture 32: Stokes's Theorem and the Divergence Theorem (Notes 4.6)
Lecture 33: Midterm 3 Review, part 1 Lecture 34: Midterm 3 Review, part 2 |
||
| Mon, Dec 6th Wed, Dec 8th Thu, Dec 9th |
Lecture 35: Applications of Multivariable Calculus
Lecture 36: Final Exam Review, part 1 No more lectures: the course is over! |
||
| Tue, Dec 14th |
"Lecture" 37: Final Exam Review, part 1 |
||
| Handouts / Lecture Notes | |||
|---|---|---|---|
| Handout | Topics | ||
| Chapter 1: Vectors and 3-Dimensional Geometry (20pp, v3.50, posted 9/7) | 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 (25pp, v3.55, updated 9/21) (updates in v3.55: fixed typos, fixed out-of-order material at start of 2.5.1) |
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, v3.51, updated 10/13) (updates in v3.51: fixed typo in first example of 3.1.3) |
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 (26pp, v3.50, posted 11/1) | 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 |
||
| Exam Information | |||
|---|---|---|---|
| Exam | Date, Time, Format | Topics | Review Material |
| Midterm 1 | Fri, Oct 9th Online, via Canvas |
WeBWorKs 1-4 Notes §1.1-1.3 + §2.1-§2.5.1 |
Review Problems, (answers) In-class review Wed Oct 7th + Thu Oct 8th |
| Midterm 2 | Fri, Nov 6th Online, via Canvas |
WeBWorKs 5-8 Notes §2.5.2-2.6 + §3.1-§3.4 |
Review Problems, (answers) In-class review Wed Nov 4th + Thu Nov 5th |
| Midterm 3 | Thu, Dec 3rd Online, via Canvas |
WeBWorKs 9-11 Notes §4.1-4.5 |
Review Problems, (answers) In-class review Wed Dec 2nd + Thu Dec 3rd |
| Final | Thu, Dec 17th 3:30pm-5:30pm Online, via Canvas |
WeBWorKs 1-12 Notes §1.1-4.6 |
The final is COMPREHENSIVE! Extra Review Problems, (answers) In-class review Thu Dec 9th |
| 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 |
| 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 on (date TBA, time TBA) 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 (time TBA), 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 Sep 7 (class starts 9/9) |
§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 Sep 14 | §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 Wednesday 9/16 at 5am. |
||
| Week of Sep 21 |
§2.1: Limits and Partial Derivatives §2.2: Directional Derivatives and the Gradient §2.4.1: Linearization WeBWorK 2 due Wednesday 9/23 at 5am. |
||
| Week of Sep 28 |
§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 Wednesday 9/30 at 5am. |
||
| Week of Oct 5 |
§2.6: Lagrange Multipliers WeBWorK 4 due Wednesday 10/7 at 5am. Review for Midterm 1. MIDTERM 1 Friday 10/9 via Canvas |
||
| Week of Oct 12 (no class 10/12) |
§2.6: Lagrange Multipliers §3.1: Double Integrals in Rectangular Coordinates §3.3.2: Double Integrals in Polar Coordinates WeBWorK 5 due Wednesday 10/14 at 5am. |
||
| Week of Oct 19 |
§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 Wednesday 10/21 at 5am. |
||
| Week of Oct 26 |
§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 Wednesday 10/28 at 5am. |
||
| Week of Nov 2 |
§4.1: Line Integrals WeBWorK 8 due Wednesday 11/4 at 5am. Review for Midterm 2. MIDTERM 2 Friday 11/6 via Canvas |
||
| Week of Nov 9 (no class 11/11) |
§4.2.1: Parametric Surfaces §4.2.2: Surface Integrals No homework this week. |
||
| Week of Nov 16 |
§4.3: Vector Fields, Work, Circulation, Flux §4.4: Conservative Fields, Path-Independence, and Potential Functions WeBWorK 9 due Wednesday 11/18 at 5am. |
||
| Week of Nov 23 (no class 11/25-26) |
§4.5: Green's Theorem WeBWorK 10 due Wednesday 11/25 at 5am. |
||
| Week of Nov 30 |
§4.6: Stokes's Theorem and Gauss's Divergence Theorem WeBWorK 11 due Wednesday 12/2 at 5am. Review for Midterm 3. MIDTERM 3 Thursday 12/3 via Canvas |
||
| Week of Dec 7 (class ends 12/9) |
Applications of Multivariable Calculus Review for Final Exam WeBWorK 12 due Wednesday 12/9 at 5am. |
||
| FINAL EXAM on Thursday December 17th from 3:30pm-5:30pm, via Canvas | |||