Fall 2021 SM221P

This is Calculus III with vector fields, an undergraduate course for plebes (freshmen).

It is taught at the United States Naval Academy, Annapolis, MD.

We will be using Calculus Early Transcendentals (8th Edition) by James Stewart.

Instructor: Professor Mee Seong Im

Office: Chauvenet Hall, Office 342, Department of Mathematics, USNA, 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 (this excludes weekends and Federal Holidays) in order to give Professor Im enough time to do the scheduling. My preference is to meet in-person in my office, rather than over Zoom. Also, each EI will be scheduled for 30 minutes.

Note: for ALL EIs, please come prepared, with homework attempted in advance and with specific questions in mind.

Mathematics Lab: I will be at the math lab (free tutoring room in Chauvenet Hall, room 130) on Fridays during the 6th period (1430-1520).

Go to the Google Drive for ALL course material.

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Math Night (Tues 16 Nov, 1900-2000, CH100, Optional): Math/OR Info Session with smores and homemade desserts. Do you like riddles and problem solving? Do you enjoy logical thinking or always find yourself asking how and why is it true or how and why is it false? Check your email from me and please RSVP so that the Mathematics Department will bring enough smores and homemade desserts. Attend to ask questions about:

• the majors offered by D/MATH, doing a double major (like yours truly!), doing a triple major,

• Reading Course (on more advanced topics), Research Course, Honors Project, Trident Project,

• summer internships, study abroad, careers as a Mathematician, Applied Mathematician, Operation Research Analyst, Consultant, etc.

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If you miss a graded event (quizzes or exams), it is your responsibility to come and find me and set-up a time to do the make-up work.

If you need an extension on your homework, please request for an extension via WebAssign or via an email.

All course material will be posted here. Your grades will be regularly posted in Blackboard.

Go to the Google Drive for ALL course material.

Calculus III with vector fields (2 sections).

• Section 3041, MWRF3, CH175, 0955-1045

  • • • Section Leader: MIDN Jenevieva (Viva) Mulhall

      • First Assistant Section Leader: MIDN Santiago Grisales Arboleda

      • Second Assistant Section Leader: MIDN Corinna (Cora) Skidmore

• Section 4041, MWRF4, CH175, 1055-1145

  • • • Section Leader: MIDN Akshat Maheshwari

      • First Assistant Section Leader: MIDN LeeAnn Beckman

      • Second Assistant Section Leader: MIDN Jacob Price

Go to the Google Drive for ALL course material.

Fall 2021 Calendar

Class Periods

Breakdown of the points:

Final Exam: 35%

Exams: 45%

Individual and Group Pop Quizzes (partner list): 07%

Homework (WebAssign): 13%

Bonus: ≤1%

WebAssign special symbol short-cuts so that you don't have to look for the correct buttons when typing in your solutions (for example, standard unit vectors i, j, k).

Viewing the WebAssign Answer Key before you submit your homework is cheating. If you help someone else to cheat, then you are also guilty of cheating. Please do not look at it before completing your homework, and please discourage others from cheating.

I should emphasize that it is perfectly fine to view the WebAssign Answer Key after you submit your homework in case the book used a different technique to solve a problem; the WebAssign Answer Key may be used as a supplementary course guidance to further help you in this course, rather than as a hindrance to prevent you from learning to the best of your ability.

Everyone, please keep the Midshipmen Honor Code in mind every day: midshipmen will not lie, cheat, or steal. And I want to emphasize that cheating and plagiarism in any form will not be tolerated. You may have gotten the few points if you cheat or plagiarize but in the long run, you are getting NOTHING out if it. Lying, cheating, or stealing will make you a weak, indecisive, unreliable, and untrustworthy leader with a lack of knowledge and preparedness to speedily lead other men and women.

The entire academy offers MANY avenues of assistance. Please come and talk to any of us if you are struggling with anything. It's far better for us to recognize what your needs are earlier in the semester so that we could make appropriate modifications to better assist you.

Grade Quality Points Point Values

A 4.00 92.5 - 100

A- 3.70 90 - 92.49

B+ 3.30 86.5 - 89.99

B 3.00 83.5 - 86.49

B- 2.70 80 - 83.49

C+ 2.30 76.5 - 79.99

C 2.00 73.5 - 76.49

C- 1.70 70 - 73.49

D+ 1.30 66.5 - 69.99

D 1.00 60 - 66.49

F 0.00 0 - 59.99

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 CH130), run by the Department of Mathematics faculty members at the US Naval Academy, Annapolis, MD.

        1. 1. • Mondays through Fridays, 1st through 6th period: 0755-1520.

              • I will be at the math lab on Fridays during the 6th period (1430-1520).

              • You are allowed to go there as many times as you'd like and talk to the professor in the room about the course material. You are also allowed to go to that room to do your homework or study for your tests.

      • Midshipmen Group Study Program (MGSP, via Google Meet and CH110), peer tutoring. MGSP will start on Sunday night on August 29, 2021. Note that SM223 is Calculus III with optimization. You are still allowed to go to that room to discuss Calculus III material with the SM223 midshipmen.

        1. 1. • Sundays 2100-2200 (SM221/SM223), with MIDN Samraat Singh.

              • Mondays 2000-2100 (SM223), with MIDN Alex Turner.

              • Tuesdays 2000-2100 (SM221/SM223), with MIDN Sebastian Martin.

              • Wednesdays 2100-2200 (SM223), with MIDN Andrew Mazza.

              • Thursdays 2000-2100 (SM221/SM223), with MIDN Paul Zimmer.

              • You are allowed to go there as many times as you'd like and talk to the midshipmen in the room about the course material. You are also allowed to go to that room to do your homework or study for your tests.

      • Academic Center, US Naval Academy, Annapolis, MD. Faculty and Staff (Professional Tutors).

        1. 1. • One-on-one professional tutoring during the day (appointments may be necessary).

              • Evening professional tutoring is available (walk-ins are encouraged).

              • The Academic Center also offers help via online platforms, like Google Meet, Zoom, etc. in case you cannot leave your room.

      • Study Groups, a great way to learn from your peers and to teach your peers, and to form friendships.

        1. 1. • 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 (Mon 23 Aug): Three-dimensional coordinate systems (Section 12.1)

Lesson 2 (Wed 25 Aug): Vectors; operations with vectors (Section 12.2)

Lesson 3 (Thurs 26 Aug): The dot product (Section 12.3)

Lesson 4 (Fri 27 Aug): The dot product/the cross product (Sections 12.3-12.4)

Lesson 5 (Mon 30 Aug): The cross-product/(lines and) planes (Sections 12.4-12.5)

Lesson 6 (Wed 1 Sept): Lines and planes (Section 12.5)

Lesson 7 (Thurs 2 Sept): Lines and planes (Section 12.5)

• I will review (vector) equations of lines and planes, and then we will work in small groups starting today!

Lesson 8 (Fri 3 Sept): Cylinders and quadric surfaces/rotation about the z-axis (Section 12.6), Pop Quiz 1

• Memorize names/surfaces/equations for: planes, (parabolic) cylinders, ellipsoids, elliptic paraboloids (bowls), and cones.

• You do not 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 9 (Tues 7 Sept): Curves defined by parametric equations (Section 10.1)

Lesson 10 (Wed 8 Sept): Vector functions and space curves (Section 13.1)

Lesson 11 (Thurs 9 Sept): Derivatives and integrals of vector functions; arc length (Sections 13.2-13.3)

Lesson 12 (Fri 10 Sept): Motion in space (Section 13.4), Pop Quiz 2

Lesson 13 (Mon 13 Sept): Motion in space (constant acceleration) (Section 13.4)

Lesson 14 (Wed 15 Sept): Midshipmen-driven review

Lesson 15 (Thurs 16 Sept): Exam 1 Exam 1 will cover Chapters 10.1, 12-13.

• USNA Practice Exams

• There are more practice exams in the Google Drive.

• There are 7 problems and some problems have multiple parts, spanning over 6 pages.

• There are 4 versions of Exam 1. Pace yourselves, cover your work and keep your eyes on your own paper. Show work for full/partial credit.

Lesson 16 (Fri 17 Sept): Functions of several variables (Section 14.1)

• The graph of a function f(x,y) contains all the points satisfying (x, y, f(x,y)). You would plot these points on R^3 coordinates.

Lesson 17 (Mon 20 Sept): Partial derivatives (Section 14.3), Pop Quiz 3

Lesson 18 (Wed 22 Sept): Partial derivatives (Section 14.3)

• Plebes may pre-register today, beginning at 0700 (make sure to meet with your adviser before registering for your classes).

Lesson 19 (Thurs 23 Sept): Tangent planes and linear approximation (Section 14.4)

• The method of computing a derivative is called differentiation. In simple terms,

  • • • the derivative of a function is the rate of change of the output value with respect to its input value, whereas

      • differential is the actual change of function.

• Plebes may pre-register today.

Lesson 20 (Fri 24 Sept): The chain rule (Section 14.5), Pop Quiz 4

• Plebes may pre-register today. The deadline to get it done is today at 1800.

Lesson 21 (Mon 27 Sept): Directional derivatives and the gradient (Section 14.6)

Lesson 22 (Wed 29 Sept): Directional derivatives and the gradient (Section 14.6)

Lesson 23 (Thurs 30 Sept): Maximum and minimum values (Section 14.7)

Lesson 24 (Fri 1 Oct): Midshipmen-driven review: go through class notes, past worksheets, WebAssign homework assignments, and practice exams with your classmates, Pop Quiz 5

• You will have a substitute today.

  • • • Professor Sommer Gentry will be your instructor during the 3rd period. [Update (Thursday 30 Sept 2021, 2145): Professor Gentry is feeling ill; someone else will be in the room. Please be on your best behavior.]

      • Professor Irina Popovici will be your instructor during the 4th period.

      • Professor Linda Shivok will be in the Math Lab today during the 6th period (1430 -1520) in CH130.

Lesson 25 (Mon 4 Oct): Exam 2 Exam 2 will cover Chapter 14.

• USNA Practice Exams

• There are more practice exams in the Google Drive.

• There are 7 problems and some problems have multiple parts, spanning over 6 pages.

Lesson 26 (Wed 6 Oct): Double integrals over rectangles (Section 15.1)

Lesson 27 (Thurs 7 Oct): Double integrals over general regions (Section 15.2)

Lesson 28 (Fri 8 Oct): Double integrals over general regions (Section 15.2), Pop Quiz 6

Lesson 29 (Wed 13 Oct): Double integrals in polar coordinates (Section 15.3)

Lesson 30 (Thurs 14 Oct): Applications of double integrals (Section 15.4), Pop Quiz 7

Lesson 31 (Fri 15 Oct): Midshipmen-driven review

• Professor Daphne Skipper will be in the Math Lab today during the 6th period (1430 -1520) in CH130.

Lesson 32 (Mon 18 Oct): Triple integrals (Section 15.6)

Lesson 33 (Wed 20 Oct): Triple integrals (Section 15.6)

• Install Mathematica before today's class (install it from the Software Center from your laptop-- you need to be on the yard when installing it or VPN in). I will teach you how to use Mathematica to check your work.

• We may have Trident Days visitors today.

Lesson 34 (Thurs 21 Oct): Triple integrals in cylindrical coordinates (Section 15.7), Pop Quiz 8

• Starting today, we will use a random name generator on Mathematica to choose who will go to a chalkboard and solve a problem.

Lesson 35 (Fri 22 Oct): Triple integrals in cylindrical and spherical coordinates (Sections 15.7-15.8)

Lesson 36 (Mon 25 Oct): Triple integrals in spherical coordinates (Section 15.8)

Lesson 37 (Wed 27 Oct): Midshipmen-driven review

Lesson 38 (Thurs 28 Oct): Exam 3 Exam 3 will cover Chapter 15.

• USNA Practice Exams

• There are more practice exams in the Google Drive.

• There are 8 problems and some problems have multiple parts, spanning over 8 pages.

Lesson 39 (Fri 29 Oct): Vector fields (Section 16.1)

Lesson 40 (Mon 1 Nov): Gradient (conservative) vector fields (Section 16.1)

Lesson 41 (Wed 3 Nov): Line integrals of scalar functions (Section 16.2)

Lesson 42 (Thurs 4 Nov): Line integrals of vector fields (Section 16.2), Pop Quiz 9

Lesson 43 (Fri 5 Nov): Line integrals of vector fields (Section 16.2)

• LCDR Jeff Lineberry will be in the Math Lab today during the 6th period (1430 -1520) in CH130.

Lesson 44 (Mon 8 Nov): The fundamental theorem for line integrals (Section 16.3)

Lesson 45 (Wed 10 Nov): The fundamental theorem for line integrals (Section 16.3), Pop Quiz 10

Lesson 46 (Fri 12 Nov): Green's theorem (Section 16.4)

• Intuition of Green's Theorem: given a continuously differentiable two-dimensional vector field F, the integral of the "microscopic circulation" of F over the region D inside a simple closed curve C is equal to the total circulation of F around C.

Lesson 47 (Mon 15 Nov): Curl and divergence (Section 16.5)

Math Night (Tues 16 Nov, 1900-2000, CH100, Optional): Math/OR Info Session with smores and homemade desserts. Do you like riddles and problem solving? Do you enjoy logical thinking or always find yourself asking how and why is it true or how and why is it false? Check your email from me and please RSVP so that the Mathematics Department will bring enough smores and homemade desserts. Attend to ask questions about:

• the majors offered by D/MATH, doing a double major (like yours truly!), doing a triple major,

• Reading Course (on more advanced topics), Research Course, Honors Project, Trident Project,

• summer internships, study abroad, careers as a Mathematician, Applied Mathematician, Operation Research Analyst, Consultant, etc.

Lesson 48 (Wed 17 Nov): Parametric surfaces (Section 16.6), Pop Quiz 11

Lesson 49 (Thurs 18 Nov): Parametric surfaces (Section 16.6)

Lesson 50 (Fri 19 Nov): Surface integrals of vector fields (Section 16.7)

• LCDR Jeff Lineberry will be in the Math Lab today during the 6th period (1430 -1520) in CH130. If you end up going to the Math Lab for some help, please be sure to thank LCDR Lineberry for his time.

Lesson 51 (Mon 22 Nov): Midshipmen-driven review

• Professor Im is on leave today.

• LCDR Chris Smith will be your instructor during the 3rd period. Everyone, please be nice!

• Professor Alexis Alevras will be your instructor during the 4th period. Everyone, please be nice!

• For today, please work on your past worksheets, WebAssign assignments, or go through a Practice Exam 4 (circle the problems that we haven't discussed yet and return to them later). Extra copies of Worksheet 50 and Worksheet 52 are outside my office door, and on the Google Drive; please stop by to pick up a paper copy if you'd like. Group work is encouraged.

• Your Test 4 has 10 problems and some problems have multiple parts, spanning over 10 pages.

Lesson 52 (Wed 24 Nov): Surface integrals of vector fields (Section 16.7), Pop Quiz 12

• Have a safe Thanksgiving Break, everyone!

Lesson 53 (Mon 29 Nov): The divergence theorem (Section 16.9)

• Intuition of the Divergence Theorem: divergence measures the outward flow of a fluid at individual points, while the flux measures outward fluid flow from an entire region, so adding up the bits of divergence gives the same value as flux.

Lesson 54 (Wed 1 Dec): Stokes' theorem (Section 16.8)

• Intuition of Stokes' Theorem: given a continuously differentiable three-dimensional vector field F, the integral of the "microscopic circulation" of F over the region S bounded by a simple closed curve C is equal to the total circulation of F around C.

Lesson 55 (Thurs 2 Dec): Stokes' theorem (Section 16.8), Pop Quiz 13

• If you are comfortable with Stokes' theorem problems, you may go ahead and begin studying for your exam during class today.

• Professor Im will open SOF.

Lesson 56 (Fri 3 Dec): Midshipmen-driven review

Lesson 57 (Mon 6 Dec): Exam 4 Exam 4 will cover Chapter 16.

• USNA Practice Exams

• There are more practice exams in the Google Drive.

• There are 10 problems and some problems have multiple parts, spanning over 10 pages.

Lesson 58 (Wed 8 Dec): Midshipmen-driven review

• Fall 2018 Practice Final Exam

• Fall 2018 Practice Final Exam Solutions

Lesson 59 (Thurs 9 Dec): Midshipmen-driven review

• Spring 2012 Practice Final Exam

• Spring 2012 Practice Final Exam Solutions

Lesson 60 (Fri 10 Dec): Midshipmen-driven review. Last Day with Professor Im. Woo hoo!! =o)

• Fall 2015 Practice Final Exam

• Fall 2015 Practice Final Exam Solutions

• Fall 2010 Practice Final Exam

• Fall 2010 Practice Final Exam Solutions

• Fill out and submit an SOF.

Optional (Sun 12 Dec): MGSP Review Session

• 2000-2100, CH110 MIDN Paul Zimmer

• 2100-2200, CH110 NONE

Optional (Mon 13 Dec): MGSP Review Session

• 1000-1100, CH110 NONE

• 1100-1200, CH110 NONE

Optional (Mon 13 Dec): Walk-in Extra Instruction (EI)

• Although classes officially end on Friday 10 December, I will be available for EIs after 10 December. You must bring at least 2 other midshipmen in my SM221P classes to the EI, for a combined total of at least 3 midshipmen. So please check with them for their schedule. Once we schedule an EI, I will post the date, time, and room number here so that other midshipmen could attend and participate if they want to. So please refresh this page regularly.

• With MIDN Jack Jabbour, MIDN AJ Merrill, MIDN Jillian Oncay, MIDN Ben Miller, MIDN Trevor Burgess, MIDN Luke Gasper, MIDN Colby Grosse, MIDN Ivette Ayala, and others. Join us if you want!

• Time: 1430 - 1545. I will be at a meeting before this but if that meeting ends early, I will go ahead and go to CH180.

• Room: CH180 has been reserved for us. Meet outside my office. I will reserve a room on Monday morning.

Optional (Tues 14 Dec): Walk-in Extra Instruction (EI)

• Although classes officially end on Friday 10 December, I will be available for EIs after 10 December. You must bring at least 2 other midshipmen in my SM221P classes to the EI, for a combined total of at least 3 midshipmen. So please check with them for their schedule. Once we schedule an EI, I will post the date, time, and room number here so that other midshipmen could attend and participate if they want to. So please refresh this page regularly.

• With MIDN Jack Jabbour, MIDN Noelle De Vente, MIDN Trevor Burgess, MIDN Jillian Oncay, MIDN Ben Miller, MIDN AJ Merrill, MIDN Colby Grosse, MIDN Luke Gasper, MIDN Ivette Ayala, and others. Join us if you want!

• Time: 1600 - 1800.

• Room: CH101 has been reserved for us. Meet outside my office. I will reserve a room on Tuesday morning.

Optional (Tues 14 Dec): MGSP Review Session

• 2000-2100, Sampson G01 G14 MIDN Sebastian Martin

• 2100-2200, Sampson G01 G14 MIDN Samraat Singh

Final Exam (Wed 15 Dec, 0755-1055): The final exam is cumulative.

• Class Photographs.

• USNA Practice Exams

• There are more practice exams in the Google Drive.

• Bring a #2 pencil for the scantron portion of the exam.

• You do not need to buy a blue book, and you may write on the test booklets.

• Bring a calculator. Calculators may be used during the entire exam.

• All cell phones must be secured during the exam. Once the exam has started, you may not leave the exam room in possession of your cell phone until you have finished the exam.

• The exam will consist of two parts: multiple choice and free response. No formulas will be provided. In particular, cheat sheets will not be provided. Therefore, you must know cylindrical coordinates, spherical coordinates, Green's, Stokes, Divergence Theorems, etc.

• Problems will be drawn from the entire syllabus. You are responsible for knowing proofs of the following facts:

  • • • At any point p, the largest value of a directional derivative of f at p is the magnitude of the gradient vector of f at p (Stewart, page 952).

      • The Fundamental Theorem of Calculus for Line Integrals (Stewart, pages 1097-1088).

      • The curl of any gradient vector field is the zero vector (Stewart, page 1106).

• At the end of your exam, I will collect all test booklets, scantrons, notes, scratch work, etc.

• Exam Room for Section 3041 (19 midshipmen): MI107

• Exam Room for Section 4041 (20 midshipmen): MI104

• I am bringing homemade triple chocolate fudge brownie (with chocolate chips, chocolate chunks, and dark Dutch chocolate) with cream cheese frosting to keep you super awake tomorrow morning. So please get plenty of sleep tonight!

• Have a wonderful Winter Break!!

Go to the Google Drive for ALL course material.

Go to the Google Drive for ALL course material.

Why study mathematics?

Is there a secret meaning of numbers?

Go to the Google Drive for ALL course material.