Vector Calculus Fall 2021 at Lehman College
with Professor Sormani (sormanic@gmail.com)
MAT226 Vector Calculus: 4 hours, 4 credits. Vectors in two and three dimensions, equations of lines and planes, functions of several variables, partial differentiation, directional derivatives, gradients, optimization with Lagrange multipliers, multiple integration, line integrals and vector fields
Prerequisite: A grade of C (or better) in MAT 176 Calculus II.
Welcome Video Playlist of Four Videos
This course will follow the Lehman College Vector Calculus Syllabus which includes the textbook information as well as a pacing of topics and the homework problems. Solutions to the homework can be found in the back of the textbook and students are expected to check their own work. The textbook, Calculus with Early Transcendentals by Larson, Hostetler, and Edwards Edition 4, may be bought used for under $20 here. Be sure to verify your book has Chapters 11-15. We will not use blackboard in the course.
Lehman College has loaner tablets that can be used for this course if you need one.
This is an asynchronous online course. Professor Sormani will create playlists of videos for each lesson and post the videos to youtube. The links to those playlists and the corresponding class notes will be found under each lesson in the schedule of lessons below. Students will watch all the videos, take notes on pencil and paper, and pause the videos to complete classwork assigned in the videos before watching the solutions. Everything should be written neatly and clearly including the assigned questions, the completed solutions to the classwork, and the corrections of the classwork. If there is a problem viewing or hearing any video, please email the professor (sormanic@gmail.com) with the subject header MAT226 Video Trouble.
Lehman College requires proof of attendance. To prove that each lesson is completed the student will submit their classwork and homework to the professor by sharing a googledoc full of photos of their work as explained at the top of each lesson and write down the time when they watched the videos. Students will include a photo of themselves holding up the first page of their classwork for each lesson. Students who do not complete at least the first lesson within 2 weeks will be removed from the course by Lehman College Policy.
Homework: Students should complete the homework for each lesson and submit it with that lesson's classwork before starting the next lesson. As in all math courses, write out the question and include any diagrams before solving the problem. The homework is exactly as assigned in the official Lehman College Vector Calculus Syllabus and solutions to the homework are in the back of the textbook. Students must check their own homework, and may ask questions if they are incorrect as explained below. Be sure to watch the lesson and do classwork, then do the homework listed below the lesson including the review homework, before proceeding to the next lesson.
Office hours. Since this course meets asynchronously, there are no fixed office hours. Instead Professor Sormani will answer questions by email within 48 hours. Questions should be emailed to the professor (sormanic@gmail.com) with the subject MAT226 QUESTION with a link to the student's googledoc and a photo of the question in the googledoc next to the typed word QUESTION. Professor Sormani will then post a photo of the answer into the googledoc next to the question and email the student that the answer is ready. Sometimes Professor Sormani will make an extra video with the answer.
Schedule: Students are allowed to complete each lesson at their own pace. To complete the course on time, students must complete two lessons per week. That is about four hours of classwork while watching videos and four-six hours of homework each week because this is a 4 credit course. Students who fall behind schedule may be allowed to request an incomplete in the course. Students may only request an incomplete if they have passed both Exam I and Exam 2 by December 5. Students who fail one of these exams should withdraw from the course because an F would hurt their GPA.
Grading: There are two Midterm Exams (each worth 30% each) and a Final Exam (worth 40%). Homework and classwork is not part of the grade but must be completed before scheduling the exams. Every student will be given a unique exam similar to a sample exam. Students may consult notes and textbooks and online calculators during exams but may not seek help from people. There will have only 25 minutes to complete each of four parts of each exam so there will not be much time to consult notes or textbooks. It is best to create a page of notes to consult quickly during each exam.
Midterm Exam I: Each student will schedule their personal 2 hour Midterm Exam I after they have completed Lessons 1-10. No students may take Midterm Exam I before submitting all their classwork and homework for these lessons. Students should complete two lessons per week and take Midterm Exam I in October.
Midterm Exam II: Each student will schedule their personal 2 hour Midterm Exam II after they have completed Lessons 12-18. No students may take Midterm Exam II before submitting all their classwork and homework for these lessons. Students should complete two lessons per week and take Midterm Exam II in November to complete the course on time.
Final Exam: The Final Exam will be given during Finals Week. Students must complete Lessons 20-28 before taking the Final Exam. Students who have passed both midterm exams by December 5 but need more time to complete Lessons 20-28 may request an Incomplete in the course. Students with incompletes must submit Lessons 20-28 before scheduling their personal Final Exam in January.
Materials, Resources and Accommodating Disabilities
Textbook: Larson, Hostetler and Edwards, Calculus: Early Transcendentals Ed. 4, Houghton Mifflin OR Larson, Hostetler and Edwards, Calculus: Early Transcendentals Special Edition of Lehman College 175-176 Ed. 5, Houghton Mifflin
Technology: Students should purchase a basic scientific calculator able to compute trigonometric and exponenetial functions, but unable to complete algebraic manipulations and take derivatives.
Tutoring: Departmental tutoring is available in the Math Lab on the 2nd floor of Gillet. Reliable Web Resources: See http://comet.lehman.cuny.edu/calculus
Reserve: Selected books have been placed on reserve in the library.
Accommodating Disabilities: Lehman College is committed to providing access to all programs and curricula to all students. Students with disabilities who may need classroom accommodations are encouraged to register with the Office of Student Disability Services. For more info, please contact the Office of Student Disability Services, Shuster Hall, Room 238, phone number, 718-960-8441.
Course Objectives:
At the end of the course students should be able to:
1. Graph and determine the equations for lines and planes (as part of dept objectives a & b) 2. Compute sums, differences, dot products and cross products of vectors (a)
3. Determine velocities and accelerations of vector-valued position functions (a, b & c)
4. Find level sets, gradients and tangent planes to functions of several variables (a, b & e) 5. Apply the method of Lagrange Multipliers (a,b & c)
6. Apply Fubini's Theorem and Green's Theorem to integrate functions and fields (a, b & e)
Official Schedule and official homework (with suggested dates):
(with links to each lesson added as the course progresses)
Lesson I: Review of Vectors and Plotting Points in 3D, 11.1-11.2 (Aug 26-7)
HW (do before next lesson): All odd problems in 11.1-11.2
Lesson II: Dot and Cross Products 11.3-11.4 (Aug 28-9)
HW (do before next lesson): All odd problems in 11.3-11.4
Review Differentiation 3.1-3.2
Lesson III: Parametric Equations and Polar Coordinates 10.2, 10.4 (Sept 1-2)
HW (do before next lesson): 10.2/ 1-50 odd, 10.4/ 1-50 odd
Lesson IV: Lines and Planes 11.5 (Sept 3-4)
HW (do before next lesson): 11.5/ do five problems on parametric equations for lines, do five on equations of planes
Review Differentiation 3.3
Lesson V: Hyperboloids, Paraboloids 11.6 (Sept 8-12)
HW (do before next lesson): 11.6/ 1-6, 9,11,13,15
Review Differentiation 3.4
Lesson VI: Cylindrical and Spherical Coordinates 11.7 (Sept 13-16)
HW (do before next lesson): 11.7/ 1-71 odd, sketch these
Review Limits and Continuity 2.32.4
Lesson VII: Vector valued functions, Limits, and Continuity12.1 (Sept 17-21)
HW (do before next lesson): 12.1/ 1-13 odd, sketch 3 curves using the function, evaluate 3 limits, find 2 intervals of continuity,
Review Integration 5.1, 5.5
Lesson VIII: Differentiation and Velocity 12.2 -12.3 (Sept 22-26)
HW (do before next lesson): 12.2/ 1-17 odd, find 3 indefinite integrals, find two definite integrals; 12.3/ 1-16 odd, do 4 projectile motion, 1 cycloidal motion, and 2 circular motion problems
Lesson IX: Tangent Vectors and Arclength, 12.4-12.5 (Oct 2-3)
HW (do before next lesson): 12.4/ 1-16 odd, 19, 31, 33, 35, 45; 12.5/ 1, 3, 5
Lesson X: Review for Midterm Exam I (Oct 5-6)
Lesson XI: Midterm Exam I (Aim to take Oct 11-12 but must complete Lessons 1-10 first)
Recommended Lecture: Freya Holmér's The Beauty of Bezier Curves
Lesson XII: Functions of several variables 13.1 (Oct 13-14)
HW (do before next lesson): 13.1/ 3 find and simplify function values, 3 describe domain and range,
Lesson XIII: Level sets, 13.1, (Oct 16-18)
HW (do before next lesson): 13.1/ 2 contour maps, 3 descriptions of level sets, 3 sketch graph of levels, 3 applications
Review HW: Dot products and planes 11.3-11.5
Lesson XIV: Partial derivatives 13.2-13.3 (Oct 20-1)
HW (do before next lesson): 13.3/ 9-25 odd, 37, 53, 65, show mixed derivatives are equal, Laplace’s equation, wave equation, heat equation, marginal productivity, ideal gas
Lesson XV: Chain Rule 13.5 and Gradients 13.6 (Oct 23-25)
HW (do before next lesson): 13.5/ 1-11 odd, 23, 27, 31; 13.6/ 1, 3, 13, 15, 21, Review HW: Extrema in 4.1
Lesson XVI: Tangent Planes 13.7 (Oct 26-28)
HW (do before next lesson): 13.6/23, 25, 27, 31, normal to level, topography, heat seeking, meteorology 13.7/ 5, 7, 9, 17, 19, 21
Lesson XVII: Extrema and Saddle Points 13.8 (Nov 1-2)
HW (do before next lesson): 13.8/ 1, 3, 25, 27, (ed4: 41, 45, 53, 57) or (ed5: 55, 37. 43, 45, 47)
Lesson XVIII: Optimization 13.9 and Review (Nov 3-4)
HW (do before next lesson): 13.9/ Max volume package, max volume ellipsoid, max revenue, max profit, min cost
Lesson XIX: Midterm Exam II (Aim to take Nov 8-9 but must complete Lessons 12-18 first)
Review HW: Definition of Integration 5.2-5.3
Lesson XX: Lagrange Multipliers 13.10 (Nov 9-10)
HW (do before next lesson): 13.10/ 1, 3, 5, 7, Review HW: Techniques of Integration 5.5
Lesson XXI: More Lagrange Multipliers 13.10 (Nov 15-6)
HW (do before next lesson): 13.10/ max vol, min cost, refraction of light, production level, putnam challenge
Lesson XXII: Iterated Integrals and Area 14.1 (Nov 17-18)
HW (do before next lesson): 14.1/ 1-9, 2 areas of region problems
Lesson XXIII: Double Integrals 14.2 (Nov 22-3)
HW (do before next lesson): 14.2/ 1, 3, 7, 9, 13, 15,
Lesson XXIV: More Integration 14.2 (Dec 2-3)
HW (do before next lesson): 14.2/ 4 volumes of sketched regions, 3 set up and evaluate double integral, Putnam challenge,
Review HW: Polar Coordinates 10.4
Lesson XXV: Integration and polar coordinates 14.3 (Dec 4-5)
HW (do before next lesson): 14.3/ 1, 3, 5, 7, 9, 11, 3 use double integral to find shaded region problems
Students who have taken linear algebra already should read 14.8
Review HW: Vector valued functions 12.2-12.3
Lesson XXVI: Vector Fields and Line Integrals 15.1-15.2 (Dec 6-7)
HW (do before next lesson): 15.1/ 1, 3, 5, 7, 9, 11, find gradient vector field, verify conservative and find potential, find curl, find divergence, 15.2/ 1, 3, 5, 7, 9, 27, 35, 39,
Lesson XXVII: Path independence and Green’s Theorem 15.3-15.4 (Dec 9-10)
HW (do before next lesson): 15.3/ 1, 3, 5, 7, 11, 15b, 19a, 25, 27, 35, 53, 15.4/ 1, 3, 5, 7, 11, 21,
Lesson XXVIII: Surface Integrals 15.6-15.8 (Dec 14-15)
Topics on the Final
Part 1: Contour maps, level sets, partial derivatives, relative extrema, saddle points, and optimization (finding a max or min over a domain) as taught in Lessons 13-18 (many short questions)
Part 2: Method of Lagrange Multipliers (one long problem to solve with hints)
Part 3: Double Integration, Iterated Integration, Fubini’s Theorem, Antidifferentiation, Setting up Bounds of a Domain, Using Polar Coordinates as taught in Lessons 22-25 (one problem setting up bounds for a given domain that is drawn with stripes, extra credit for completing the integration, extra credits for converting to polar coordinates)
Part 4: Vector Fields, divergence, curl, line integrals, conservative vector fields, and potential functions.
As you can see there are more topics in the textbook, enough for a fourth semester of calculus, and you may wish to learn these topics using existing youtube videos as needed in the future.
The final exam will be given during finals week (must complete lessons 22-28 first) If you are behind schedule and have passed the two midterms, then you may request an incomplete and take the final in January after completing these lessons.
Department of Mathematics, Lehman College, City University of New York