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This is Calculus III with vector fields, an undergraduate course.
It is taught at the United States Naval Academy, Annapolis, MD.
We will be using Calculus Early Transcendentals (8th Edition) by James Stewart.
I look forward to meeting you IN-PERSON!!
Instructor: Professor Mee Seong Im
Office: Chauvenet Hall, Office 342, Department of Mathematics, United States Naval Academy, Annapolis, MD 21402
Office phone number: (410) 293-6776
Email: im [at] usna [dot] edu
Extra Instructions (E.I.): please request for them at least 2 working days in advance (excluding weekends and Federal Holidays) in order to give Professor Im enough time to do the scheduling. I will be available to meet via Zoom and in person (in CH130).
Mathematics Lab: I will be at the math lab (free tutoring room via Google Meet) on Wednesdays 1055-1145.
All course material will be posted here. Your grades will be regularly posted in Blackboard.
Due to some changes to our class this semester, you will have TWO WebAssign assignments due on some days (not many, but some). I will explain further when we meet this week. Thus, please check your homework due dates in advance.
Go to the Google Drive for ALL course material.
Calculus III with vector fields (2 sections, 4 classrooms). During Blue weeks, the Blue Section Leader and the Blue Assistant Section Leader will be in charge of the administrative detail related to the course. During Gold weeks, the Gold Section Leader and the Gold Assistant Section Leader will be in charge. More detail in the Course Policy Statement.
Section 5021B, MTWF5, Room CH155, 1330-1420 (Blue)
Section Leader: Midshipman Brynley Nordgauer
First Assistant Section Leader: Midshipman Emma (Andrea) Granada
Second Assistant Section Leader: Midshipman Peter Shaner
Section 5021G, MTWF5, Room CH157, 1330-1420 (Gold)
Section Leader: Midshipman Jackson Tacka
First Assistant Section Leader: Midshipman Samantha (Sam) Schofield
Second Assistant Section Leader: Midshipman Jennifer (Jenny) Gao
Section 6022B, MTWF6, Room CH155, 1430-1520 (Blue)
Section Leader: Midshipman Phoebe Spackman
First Assistant Section Leader: Midshipman Madison Lin
Second Assistant Section Leader: Midshipman Eric Gegenheimer
Section 6022G, MTWF6, Room CH157, 1430-1520 (Gold)
Section Leader: Midshipman Bradyn Kaiser
First Assistant Section Leader: Midshipman Jordan Detwiler
Second Assistant Section Leader: Midshipman Dylan Poirier
Go to the Google Drive for ALL course material.
Breakdown of the points:
Final Exam: 35%
Exams: 40%
Quizzes: 10%
Homework (WebAssign): 10%
Worksheets: 05%
Bonus: ≤1%
Go to the Google Drive for ALL course material.
Academy-wide tutoring (all are free, see USNA Blackboard for the Google Meet links)
Mathematics Lab (via Google Meet), run by the Department of Mathematics faculty members at the US Naval Academy, Annapolis, MD.
Mondays through Fridays, 1st through 6th period: 0755-1520.
I will be at the math lab on Wednesdays 1055-1145.
Midshipmen Group Study Program (MGSP, via Google Meet and CH103), peer tutoring.
Mondays 2000-2100, with MIDN Amanda Marie Agustin.
Tuesdays 2000-2100, with MIDN Joseph Ozgar.
Wednesdays 2000-2100, with MIDN Kevin Bae.
Academic Center, US Naval Academy, Annapolis, MD. Faculty and Staff (Professional Tutors).
One-on-one professional tutoring during the day (appointments may be necessary).
Evening professional tutoring is available (walk-ins are encouraged).
Study Groups, a great way to learn from your peers and to teach your peers, and to form friendships.
You are ALWAYS welcome to form study groups with your classmates using all the tools that we have (Zoom, Google Meet, Skype, tablets, jamboard, etc.).
Go to the Google Drive for ALL course material.
Course Schedule
Lesson 1 (Tues 19 Jan): Review of operations with vectors (Sections 12.1-12.4) [Blue Day, stay in your rooms]
Lesson 2 (Wed 20 Jan): Circles, cylinders, and spheres; lines and planes (Sections 12.1/12.5) [Blue Day, stay in your rooms]
Lesson 3 (Fri 22 Jan): Lines and planes (Section 12.5) [Blue Day, stay in your rooms]
Lesson 4 (Mon 25 Jan): Cylinders and quadric surfaces (Sections 12.6) [Gold Day, optional: stay in your rooms or classroom]
Memorize names/surfaces/equations for: planes, (parabolic) cylinders, ellipsoids, elliptic paraboloids (bowls), and cones.
Lesson 5 (Tues 26 Jan): Quadric surfaces/rotation about the z-axis (Section 12.6) [Gold Day, optional: stay in your rooms or classroom]
No need to memorize names, surfaces or equations for hyperbolic paraboloid (horse saddle), hyperboloid of one sheet, and hyperboloid of two sheets, but you should be able to match the graphs (surfaces) with equations (for example, the surfaces for z = x^2 - y^2 and x = y^2 - 3z^2 are saddles, etc.).
Lesson 6 (Wed 27 Jan): Curves defined by parametric equations (Section 10.1), quiz [Gold Day, optional: stay in your rooms or classroom]
Lesson 7 (Fri 29 Jan): No class [classes canceled per Associate Provost]
Lesson 8 (Mon 1 Feb): No class [snow day per Associate Provost]
Lesson 9 (Tues 2 Feb): Vector functions and space curves (Section 13.1) [Blue Day, classroom]
Lesson 10 (Wed 3 Feb): Derivatives and integrals of vector functions (Section 13.2), quiz [Blue Day, classroom]
Lesson 11 (Fri 5 Feb): Arc length; motion in space (Sections 13.3-13.4) [Blue Day, classroom]
Lesson 12 (Mon 8 Feb): Motion in space (constant acceleration) (Section 13.4) [Gold Day, classroom]
Lesson 13 (Tues 9 Feb): Midshipmen-driven review [Gold Day, classroom]
Lesson 14 (Wed 10 Feb): Exam 1 [Gold Day, classroom] Exam 1 will cover only Chapters 10.1, 12-13.
USNA Practice Exams (see additional practice exams in the Google Drive).
Lesson 15 (Fri 12 Feb): Functions of several variables (Section 14.1) [Gold Day, classroom]
Lesson 16 (Tues 16 Feb): Partial derivatives (Section 14.3) [Blue Day, classroom, with Prof. Irina Popovici]
Lesson 17 (Wed 17 Feb): Partial derivatives (Section 14.3), quiz [Blue Day, classroom, with Prof. Irina Popovici]
Prof. Im will not be at the Math Lab today, but Prof. Dan Bates will be in there! =o)
Lesson 18 (Fri 19 Feb): Tangent planes and linear approximation (Section 14.4) [Blue Day, classroom]
Lesson 19 (Mon 22 Feb): The chain rule (Section 14.5) [Gold Day, classroom]
Lesson 20 (Tues 23 Feb): Midshipmen-driven review [Gold Day, classroom]
Lesson 21 (Wed 24 Feb): Directional derivatives and the gradient (Section 14.6), quiz [Gold Day, classroom]
Lesson 22 (Fri 26 Feb): Directional derivatives and the gradient (Section 14.6) [Gold Day, classroom]
Lesson 23 (Mon 1 Mar): Maximum and minimum values (Section 14.7) [Blue Day, stay in your rooms]
Lesson 24 (Tues 2 Mar): Double integrals over rectangles (Section 15.1) [Blue Day, stay in your rooms]
Lesson 25 (Wed 3 Mar): Double integrals over general regions (Section 15.2), quiz [Blue Day, stay in your rooms]
Lesson 26 (Fri 5 Mar): Double integrals over general regions (Section 15.2) [Blue Day, stay in your rooms]
Lesson 27 (Mon 8 Mar): Double integrals in polar coordinates (Section 15.3) [Gold Day, stay in your rooms]
Lesson 28 (Tues 9 Mar): Applications of double integrals (Section 15.4) [Gold Day, stay in your rooms]
Lesson 29 (Wed 10 Mar): Midshipmen-driven review, quiz [Gold Day, stay in your rooms]
Lesson 30 (Fri 12 Mar): Triple integrals (Section 15.6) [Gold Day, stay in your rooms]
Lesson 31 (Mon 15 Mar): Triple integrals (Section 15.6) [Blue Day, stay in your rooms]
Lesson 32 (Tues 16 Mar): Triple integrals in cylindrical coordinates (Section 15.7) [Blue Day, stay in your rooms]
Lesson 33 (Wed 17 Mar): Triple integrals in cylindrical and spherical coordinates (Sections 15.7-15.8), quiz [Blue Day, stay in your rooms]
Lesson 34 (Fri 19 Mar): Triple integrals in spherical coordinates (Section 15.8) [Blue Day, stay in your rooms]
Lesson 35 (Mon 22 Mar): Vector fields (Section 16.1) [Gold Day, stay in your rooms]
Lesson 36 (Tues 23 Mar): Gradient (conservative) vector fields (Section 16.1) [Gold Day, stay in your rooms]
Lesson 37 (Wed 24 Mar): Gradient (conservative) vector fields (Section 16.1), quiz [Gold Day, stay in your rooms]
Lesson 38 (Fri 26 Mar): Line integrals of scalar functions (Section 16.2) [Gold Day, stay in your rooms]
Lesson 39 (Mon 29 Mar): Midshipmen-driven review [Blue Day, classroom]
Lesson 40 (Tues 30 Mar): Midshipmen-driven review [Blue Day, classroom]
Lesson 41 (Wed 31 Mar): Exam 2, quiz [Blue Day, classroom] Exam 2 has been postponed to today. It will cover Chapters 14-15. There are a total of 5 problems (some problems have multiple parts).
USNA Practice Exams (see additional practice exams in the Google Drive).
Lesson 42 (Fri 2 Apr): Line integrals of vector fields (Section 16.2) [Blue Day, classroom]
Lesson 43 (Tues 6 Apr): Line integrals of vector fields (Section 16.2) [Gold Day, classroom]
Lesson 44 (Wed 7 Apr): The fundamental theorem for line integrals (Section 16.3), quiz [Gold Day, classroom]
Lesson 45 (Fri 9 Apr): The fundamental theorem for line integrals (Section 16.3) [Gold Day, classroom or meet from your rooms]
Lesson 46 (Mon 12 Apr): Green's theorem (Section 16.4) [Blue Day, classroom]
Professor Geoff Price's visitation (5th period only).
Lesson 47 (Tues 13 Apr): Green's theorem (Section 16.4) [Blue Day, classroom]
Lesson 48 (Wed 14 Apr): Curl and divergence (Section 16.5), quiz [Blue Day, classroom]
Note: If the vector field is increasing in magnitude as you move along the flow of a vector field, then the divergence is positive. If the vector field is decreasing in magnitude as you move along the flow of a vector field, then the divergence is negative.
Lesson 49 (Fri 16 Apr): Parametric surfaces (Section 16.6) [Blue Day, classroom]
A supplementary worksheet on the gradient, curl, and divergence has been passed out today.
Lesson 50 (Mon 19 Apr): Parametric surfaces (Section 16.6) [Gold Day, classroom]
Lesson 51 (Tues 20 Apr): Surface integrals of scalar functions (Section 16.7) [Gold Day, classroom]
Lesson 52 (Wed 21 Apr): Surface integrals of vector fields (Section 16.7), quiz [Gold Day, classroom]
Lesson 53 (Fri 23 Apr): Surface integrals of vector fields (Section 16.7) [Gold Day, classroom]
Practice Test 4 (Chapter 16) Solutions will be posted next week.
Lesson 54 (Mon 26 Apr): The divergence theorem (Section 16.9) [Blue Day, classroom]
Practice Test 4 (Chapter 16) Solutions have been posted (see Google Drive).
Lesson 55 (Tues 27 Apr): Stokes' theorem (Section 16.8) [Blue Day, classroom]
Lesson 56 (Wed 28 Apr): Stokes' theorem (Section 16.8), quiz [Blue Day, classroom]
Lesson 57 (Fri 30 Apr): Midshipmen-driven review [Blue Day, classroom]
An important advice: work on many practice problems before your test, but make sure to get plenty of sleep the night before your exam. Remember that you have accumulated a lot of knowledge. Now, it's a matter of putting the pieces together.
Lesson 58 (Mon 3 May): Exam 3 [Gold Day, classroom] Exam 3 will cover only Chapter 16.
USNA Practice Exams (see additional practice exams in the Google Drive).
Practice Final Exam Solutions have been posted in the Google Drive.
Lesson 59 (Tues 4 May): Midshipmen-driven review [Gold Day, classroom]
Lesson 60 (Wed 5 May): Midshipmen-driven review, quiz [Gold Day, classroom]
Optional (Fri 7 May, 1100-1245): Meet Professor Im in or outside of Chauvenet Hall (Room 130) to pick up your Exam 3 and/or to ask any last minute questions. Professor Im will also bring your Exam 3 to your Final Exam classrooms on Monday.
Congratulations on your success in completing this spring semester! You all have learned so much and have displayed your knowledge to other midshipmen and me in many ways! Now, let's finish this semester with victory!!
Final Exam (Mon 10 May, 1300-1600): The final exam is cumulative.
Final Exam Instructions are now posted!
USNA Practice Exams (see additional practice exams in the Google Drive; there are two practice final exams in the Google Drive).
Please write your name and the 6-digit Alpha number on your multiple choice packet, free-response packet, and scantron. On your scantron, write down the VERSION of your multiple choice packet.
Calculators are not allowed on the multiple choice portion. So if you want to use your calculator on the free response portion, you must turn in your scantron. Remember that you do not need to simplify your final solution to get full credit.
There will be no formula sheet, but we will provide to you conversion formulas from spherical to rectangular coordinates (we will not provide the reverse conversion, from rectangular to spherical coordinates).
Half-angle formulas will not be on the final exam (so you do not need to know them since you will not be applying them while working through a problem).
One of the following proofs will be on the final exam:
Proof of Theorem 15 (page 952, maximizing the directional derivative),
Proof of Theorem 2 (page 1087, the fundamental theorem for (vector) line integrals),
Proof of Theorem 3 (page 1104, gradient vector fields have zero curl).
If you need to leave the classroom, you must LEAVE all technology (cell phone, tablet, laptop, etc.) in your backpacks.
The scantrons are due as we enter the last 30 minutes of the final exam. That is, they are due around 1530.
Since this is a department-wide final exam, your multiple-choice packet, free-response packet, and all scratch work papers are due no later than 1600.
5021B: CH104
5021G: CH101
6022B: CH103
6022G: CH102
Congratulations, you have completed vector calculus! Have a safe and enjoyable summer!!!
Go to the Google Drive for ALL course material.
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Gray colored word with a strike through implies the event is canceled since it is close to one of the four exams.
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