Math 2321 (Multivariable Calculus), Summer-II 2023
| Course Information | |||||
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| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
MTWR, 9:50am-11:30am Richards 253 |
T 12:05pm-1:05pm (Zoom) R 3:30pm-5:30pm (Zoom or in person) or by appointment 571 Lake Hall |
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| 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.) | |||||
| Teaching Assistant | Problem Session | Office Hours | |||
| Evan Griggs griggs.e at northeastern dot edu |
F, noon-2:30pm Richards 253 |
By appointment Online, via Zoom |
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| Zach Greenfield greenfield.z at northeastern dot edu |
F, 3:00pm-5:00pm Richards 253 |
By appointment Online, via Zoom |
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| 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. | |||||
| All homework assignments are available on the 2321 WeBWorK page. All problems have unlimited attempts and you may work on the assignments at any time up until the due date. Your username is your Northeastern username, and your password is your 7-digit Northeastern ID number without the two leading zeroes. | |||||
| The final exam (either version) starts at 3:30pm on Tue, Aug 22nd. The short final exam runs from 3:30pm-4:20pm in 253 Richards (the regular course classroom). The comprehensive final exam runs from 3:30pm-5:30pm in 235 Richards. | |||||
| Handouts / Lecture Notes | |||||
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| The instructor will write lecture notes for the course in place of an official textbook as the semester progresses. Essentially all multivariable calculus textbooks (e.g., Stewart, Anton, etc.) cover the same material in the same order, so if you have a multivariable calculus textbook, you can use it as an additional resource. | |||||
| Handout | Topics | ||||
| Chapter 1: Vectors and 3-Dimensional Geometry (20pp, v4.50, posted 6/30) | 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 |
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| Chapter 2: Partial Derivatives (26pp, v4.50, posted 7/5) | 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 |
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| Chapter 3: Multiple Integration (25pp, v4.50, posted 7/17) | 3.1 ~ Double Integrals (Riemann Sums, Iterated Integrals, Changing Integration Order, Integrals in Polar Coordinates, General Changes of Variable) 3.2 ~ Triple Integrals (Riemann Sums, Iterated Integrals, Integrals in Cylindrical Coordinates, Integrals in Spherical Coordinates, Additional Examples) 3.3 ~ Applications of Multiple Integration (Areas, Volumes, Averages, Masses and Moments) |
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| Chapter 4: Vector Calculus (34pp, v4.50, posted 8/1) | 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 4.7 ~ Applications of Vector Calculus |
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| Exam Information | ||||
|---|---|---|---|---|
| Exams will be distributed in person during the course lecture period. Midterm exams are 100 minutes, while the comprehensive final is 2 hours and the short final is 1 hour. | ||||
| Exam | Date, Time, Location | Topics | Review Material | |
| Midterm 1 (exam), (sols) |
Mon, Jul 17th In lecture |
WeBWorKs 1-2 Notes §1.1-1.4 + §2.1-2.5.1 |
Review Problems, (answers) Review session Sat Jul 15th, 3pm via Zoom |
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| Midterm 2 (exam), (sols) |
Mon, Jul 31st In lecture |
WeBWorKs 3-4 Notes §2.5.2-2.6 + §3.1-3.4 |
Review Problems, (answers) Review session Sat Jul 29th, 3pm via Zoom |
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| Midterm 3 (exam), (sols) |
Mon, Aug 14th In lecture |
WeBWorKs 5-6 Notes §4.1-4.4 |
Review Problems, (answers) Review session Sat Aug 12th, 3pm via Zoom |
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| Final | Tue Aug 22nd Short: 3:30pm-4:20pm, Richards 253 Comprehensive: 3:30pm-5:30pm, Richards 235 |
Comprehensive: WeBWorKs 1-7 Notes §1.1-4.7 |
Short: WeBWorK 7 Notes §4.5-4.7 |
Short-Final Review Problems, (answers) Review sessions Sat Aug 19th + Sun Aug 20th, time and location TBA |
| For exams, you are permitted one "cheat sheet", consisting of a double-sided 8.5in-by-11in piece of paper. Calculators are permitted, but cell phones, other electronic devices, books, and additional notes of any kind will NOT be permitted in exams. | ||||
| Tips For Success In This Course | |||
|---|---|---|---|
| Attend Lecture | Missing lecture is a bad idea! If for any reason you cannot make it to a class, 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 almost certainly struggle on the exams. Exam problems are generally similar in style and difficulty to WeBWorK problems, but often feel harder because of the limited time and the fact that you do not have multiple attempts on the exam! | ||
| Attend Problem Sessions | There is a 2.5-hour weekly problem session run by the course TA. This session runs from noon-2:30pm on Fridays, ahead of the time the WeBWorK assignment is due. The goal of the problem session is to provide you a location where you can work collaboratively with other students on assignments, and also get TA assistance. | ||
| Attend Office Hours | Office hours are specifically reserved for you to receive individual, one-on-one help from the instructor or TAs. 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. | ||
| Course Schedule | |||
|---|---|---|---|
| The schedule is subject to change! All sections refer to the course lecture notes. | |||
| Week | Schedule | ||
| Week of July 3 (class starts 7/3, no class 7/4) |
§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 WeBWorK 1 due Saturday 7/8 at 5am Eastern. |
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| Week of July 10 | §2.1.2: Partial Derivatives §2.2: Directional Derivatives and the Gradient §2.3: The Chain Rule §2.4.1: Linearization §2.5.1: Critical Points and Their Classification Review for Exam 1 WeBWorK 2 due Saturday 7/15 at 5am Eastern. |
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| Week of July 17 | MIDTERM 1 in class on Monday, July 17th §2.5.2: Optimization of a Function on a Region §2.6: Lagrange Multipliers §3.1.1: Double Integrals in Rectangular Coordinates §3.1.2: Iterated Double Integrals and Fubini's Theorem §3.1.3: Changing the Order of Integration §3.1.4: Double Integrals in Polar Coordinates WeBWorK 3 due Saturday 7/22 at 5am Eastern. |
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| Week of July 24 |
§3.2.1: Triple Integrals in Rectangular Coordinates §3.2.2: Fubini's Theorem and Methods of Evaluation §3.2.3: Triple Integrals in Cylindrical Coordinates §3.2.4: Triple Integrals in Spherical Coordinates §3.3: Applications of Multiple Integration Review for Midterm 2. WeBWorK 4 due Saturday 7/29 at 5am Eastern. |
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| Week of July 31 | MIDTERM 2 in class on Monday, July 31st §4.1: Line Integrals §4.2.1: Parametric Surfaces §4.2.2: Surface Integrals §4.3.1: Circulation and Work Integrals WeBWorK 5 due Saturday 8/5 at 5am Eastern. |
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| Week of August 7 | §4.3.2: Flux Across Curves §4.3.2: Flux Across Surfaces §4.4: Conservative Fields, Path-Independence, and Potential Functions §4.5: Green's Theorem WeBWorK 6 due Saturday 8/12 at 5am Eastern. |
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| Week of August 14 (class ends 8/17) |
MIDTERM 3 in class on Monday, August 14th §4.6.1: Stokes's Theorem §4.6.2: Gauss's Divergence Theorem §4.7: Applications of Multivariable Calculus Review for Final Exam. WeBWorK 7 due Saturday 8/19 at 5am Eastern. |
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| Week of August 21 |
FINAL EXAM, 3:30pm Tue Aug 22nd, (Short) Richards 253, (Comprehensive) Richards 235 | ||