Vector Analysis

MATH - 21D

General Information

Instructor: Indrajit Jana
Meeting: WELLMAN 212; MTWR 12:10-1:50 pm
Textbook: I will follow the textbook “Thomas' Calculus Early Transcendentals, 13th Edition by George B. Thomas, Maurice Weir, and Joel Hass; Addison Wesley Publishers”
Syllabus: The syllabus can be found here.
Important Dates: See the summer session calendar here.
Office Hours: MWR 5:00-6:00pm or by appointment, in MSB 3125 or 3240

Homework

Homework will be assigned after each lecture. Homework solutions will not be collected but you are expected to do it by yourself before coming to the next lecture.

Exams

There will be total six/seven pop quizzes in the whole quarter. The lowest score will be dropped. You will be tested on the material which is covered in previous lectures/discussions from any day prior (not the material covered on the same day) to the pop quiz. Quiz problems will be same or very similar to the homework problems. I will pick up two or three problems randomly from the problem set and ask you to solve the problem in class (15-20 mins). The midterm is scheduled on August 25, 2016. The final exam is scheduled on the last day, September 8, 2016, of the course. Note, there are NO MAKEUP EXAMS!

Grading Policy

The grading policy is the following
Quiz: 30%
Midterm: 30%
Final: 40%
The grading curve will be decided later.

SDC

If you need any special arrangement please contact me as early as possible. More precisely, SDC requires me to post the following message.
Any student with a documented disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable accommodations must contact the Student Disability Center (SDC). Faculty are authorized to provide only the accommodations requested by the SDC. If you have any questions, please contact the SDC at (530)752-3184 or sdc@ucdavis.edu.

Online Resources

There are many software and online resources for viewing/plotting three dimensional surfaces.
  1. For drawing 3d surfaces.
  2. For drawing 3d surfaces, vector fields and more.
  3. For drawing 3d parametric curves
  4. For drawing 3d parametric surfaces

Tentative Lecture schedule and Homework

August 1 Double integral over rectangles Ch 15.1: 5, 9, 12, 15, 19, 25, 27 Ch 15.2: 1-18
August 2 Double integral over general region Ch 15.2: 20, 24, 38, 42, 46, 50, 51, 54, 62, 65, 76, 79
Ch 15.3: 3, 4, 7, 12, 13, 15, 18, 20, 22, 24
August 3 Double integrals in polar form / Quiz 1 Ch 15.4: 2, 3, 6, 12, 18, 22, 25, 26, 33, 35, 37, 40, 42.
August 4 Triple integral in Rectangular Coordinates Ch 15.5: 5, 6, 8, 13, 18, 19, 22, 23, 28, 29, 32, 38, 39
August 8 Triple integrals in Cylindrical Coordinates Ch 15.7: 3, 4, 6, 8, 12, 13, 15, 18, 41(b,c), 44, 54, 59, 64
August 9 Triple integrals in Spherical Coordinates / Quiz 2 Ch 15.7: 22, 25, 34, 37, 40, 41, 49, 55, 56, 61, 66
August 10 Substitutions in multiple integrals Ch 15.8: 1, 3, 6, 7, 10, 12, 18, 19, 22, 23
August 11 Moments and centers of Mass Ch 15.6: 2, 5, 8, 14, 21, 22, 27, 29, 33, Ch 15.7: 68, 76, 78 Ch 15.8: 11, 25
August 15 Review of vectors, Arc length in space / Quiz 3 Ch 13.3: 1, 2, 5, 8, 10, 12, 13, 15, 17(a-d), 18, 19
(Optional Ch 12(practice exercises): 13, 14, 17, 18, 29, 30, 31, 32, 35, 36, 43, 44, 55, 58, 67, 72, 76)
August 16 Curvature and Normal Vectors of a Curve Ch 13.4: 1, 4, 5, 6, 9, 14, 16, 18,
August 17 Tangential and Normal Components of Acceleration, Line Integrals Ch 13.5: 1, 4, 6, 10, 14, 17, 20, 23, 26 Ch 16.1: 1-8, 9, 14, 15, 16, 21, 25
August 18 Line Integrals, Vector Fields and Line Integrals: Work / Quiz 4 Ch 16.1: 33, 35, 40 Ch 16.2: 1, 2, 5, 7, 11, 16, 20, 21, 25, 26
August 22 Vector Fields and Line Integrals: Circulation, and Flux Ch 16.2: 29, 30, 34, 38, 39, 43, 49, 50, 53 Ch 16.3: 1- 6
August 23 Path independence Ch 16.3: 9, 10, 16, 17, 18, 19, 22, 25, 28, 29, 31, 33, 35, 36
August 24 Review / Practice Midterm 1 / Practice Midterm 2 Quiz 5 / Practice Midterm 1 Solutions / Practice Midterm 2 Solutions
August 25 Midterm
August 29 Green’s Theorem in the Plane Ch 16.4: 4, 9, 11, 12, 15, 20, 21, 22, 23, 25, 27, 28, 38
August 30 Surfaces and Area Ch 16.5: 3, 4, 6, 7, 10, 11, 19, 22, 24, 27, 29, 30, 33, 36, 41, 44, 47, 51, 56
August 31 Surface Integrals Ch 16.6: 1, 2, 5, 8, 11, 15, 18, 19, 21, 22, 26, 32, 35, 36, 39, 40
Sept 1 Stokes’ Theorem / Quiz 6 Ch 16.7: 1, 5, 6, 7, 8, 11, 13, 15, 17, 19, 20, 21, 26
Sept 5 Holiday, no lecture
Sept 6 The Divergence Theorem and a Unified Theory Ch 16.8: 5, 6, 10, 12, 14, 17, 20, 22, 24, 27, 28, 29
Sept 7 Review / Practice Final 1 / Practice Final 2 Quiz 7 / Practice Final 1 Solutions / Practice Final 2 Solutions
Sept 8 Final Exam