Vector Calculus Spring 2025 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.
This course follows the old Lehman College Vector Calculus Syllabus. No textbook is required however we recommend Calculus with Early Transcendentals by Larson, Hostetler, and Edwards Edition 4, which may be bought used for under $20. Be sure to verify your book has Chapters 11-15 if you do decide to purchase it. We will not use blackboard in the course nor the expensive textbook that some sections of Vector Calculus are requiring. Each lesson has notes by the professor so no textbook is needed.
This is course meets: at Lehman College Gillet Hall Room 305 on Mondays and Wednesdays 6:00 pm -7:40 pm.
Office hours. 5:00-5:30 pm and 7:00-8:00 pm Mon and Wed either in Gillet Hall Room 200A (my office) or in our classroom Gillet Hall Room 305.
Attendance, notes, classwork, and homework are required. Be sure to attend the lesson and do classwork, then do the homework listed below the lesson including the review homework, before proceeding to the next lesson. You will upload notes, classwork, and homework for each lesson into a googledoc for each lesson. If you miss class, then you will watch videos for the lesson. Everything should be written neatly and clearly including the assigned questions, the completed solutions to the classwork, and the corrections of the classwork, as well as the assigned homework. If the notes, classwork, or homework is incomplete, then you may be required to complete it. Full credit for a lesson will be awarded if completed on time before the next lesson, and half credit if incomplete or late. Work does not need to be done perfectly but all work should be attempted.
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 attended the class or 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.
Grading: There are twenty-five lessons with classwork and homework (worth 25% of the course), two Midterm Exams (each worth 25% of the course), and a Final Project (worth 25% of the course).
Midterm Exam I: This exam covers topics completed Lessons 1-8.
Midterm Exam II: This exam covers topics completed Lessons 9-18.
Final Project: The Final Project will be due during Finals Week covering topics completed in Lessons 1-28. Each student will be assigned a different project and must work alone. The final project may be related to an application of interest to the student if the student wishes.
Materials, Resources and Accommodating Disabilities
Textbook (not required): Larson, Hostetler and Edwards, Calculus: Early Transcendentals Ed. 4, Houghton Mifflin
Technology: Students should purchase a basic scientific calculator for $9 able to compute trigonometric and exponenetial functions, but unable to complete algebraic manipulations and take derivatives. Phones may not be used in class or for exams.
Supplies: Students should purchase spiral notebooks with graph paper to take notes for this course. Pencils and four colar pens are also recommended.
Tutoring: Departmental tutoring is available in the Math Lab in Gillet Hall.
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)
Schedule:
(with links to notes, videos and homework to appear)
(students who miss class need to watch the videos)
Lesson 1: (Mon 1/27/25) Review of Vectors and Plotting Points in 3D
Lunar New Year: (Wed 1/29/25) No Lehman Classes
Lesson 2: (Mon 2/3/2025) Dot and Cross Products
Lesson 3: (Wed 2/5/25) Parametric Equations and Polar Coordinates
Lesson 4: (Mon 2/10/25) Lines and Planes
Lincoln's Birthday: (Wed 2/12/25) No Lehman Classes
Lesson 5: Video Lesson: Hyperboloids, Paraboloids
Presidents Day: (Mon 2/17/25) No Lehman Classes
Note Lehman has class scheduled on Tu 2/18 but our Lesson 5 is videos online.
Lesson 6: (Wed 2/19/25) Vector valued functions, Limits, and Continuity
Lesson 7: (Mon 2/24/25) Differentiation and Velocity
Lesson 8: (Wed 2/26/25) Tangent Vectors and Arclength
Lesson 9: (Mon 3/3/25) Cylindrical and Spherical Coordinates
Lesson 10: (Wed 3/5/25) Functions of several variables
Lesson 11: (Th 3/6/25) Video Lesson: Level sets (due Saturday after the Midterm)
Lesson 12: (Mon 3/10/25) Review for Midterm Exam I
Lesson 13: (Wed 3/12/25) Midterm Exam I on Lessons 1-8
Lesson 14: (Mon 3/17/25) Partial derivatives
Lesson 15: (Wed 3/19/25) Chain Rule and Gradients
Lesson 16: (Mon 3/24/25) Tangent Planes
Lesson 17: (Wed 3/26/25) Extrema and Saddle Points
Eid al-Fitr: (Mon 3/31/25) No Lehman Classes
Lesson 18: (Wed 4/2/25) Optimization and Review
Lesson 19: (Mon 4/7/25) Midterm Exam II on Lessons 9-18: students who score less than 20 0oints on any part of the exam may retake that part on Monday April 21. Students who need to retake more than one part may need to stay after class to complete their work. It is 25 minutes per part.
Lesson 20: (Wed 4/9/25) Lagrange Multipliers
Passover: (Mon 4/14/25) No Lehman Classes
Passover: (Wed 4/16/25) No Lehman Classes
Lesson 21: (Mon 4/21/25) Lagrange Multipliers Extra Credit in class Quiz and retakes of parts of Midterm Exam II.
Lesson 22: (Wed 4/23/25) Iterated Integrals and Area
Lesson 23: (Mon 4/28/25) Double Integrals and Fubini's Theorem
Lesson 24: (Wed 4/30/25) More Integration
Lesson 25: (Mon 5/5/25) Integration and polar coordinates
Personal Final Projects have been shared with each student and students may begin working on the parts that they are ready to start. See MAT226S26-Final-last, first in your googledocs.
Lesson 26: (Wed 5/7/25) Video Lesson: Vector Fields and Line Integrals Extended deadline: now due Tu May 13
Lesson 27: (Mon 5/12/25) Video Lesson: Path independence and Green’s Theorem Deadline: due Sat May 17
Lesson 28: (Wed 5/14/25) Video Lesson: Surface Integrals for math and physics and chem majors.
Final Review (Wed 5/14/25) we did a Review for the Final instead of Lesson 28.
Finals Week: The final project is due at the end of finals week
(Wed May 21) Be sure to complete lessons 22-24 before trying Part I, complete Lesson 26 before Part II and Lesson 27 before Part 3. Everyone has a personal final project in a googledoc with the name: MAT226S26-Final-last, first
You will add photos of your solutions into this doc.
I will be available in our classroom
Wednesday 5/21/2025 6:15-8:15 pm
to ensure proper submission of work on your final projects is completed. If necessary I will photograph your work.
Lessons 18, 20, 28, and extra credit are due Thursday 5/22.
I must submit grades on Friday.
If you are behind schedule and have passed the two midterms, then you may request an incomplete (with a temporary grade of INC) and complete the final project in June after completing these lessons. When your work is completed including the final project then I will change the INC into the grade that you earn.
Department of Mathematics, Lehman College, City University of New York