fall 2020: M427L advanced calculus for application II

Gradient Descent
Gif from Wikipedia
Instructor:  Dr. Jacky Chong  

Course Syllabus: M427L-Fall 2020

Contact: office hours: T 12:00 pm-2:00 pm
                                    Th 1:00 pm-2:00 pm
               email: jwchong 🍎 math 🐶 utexas 🐶 edu
               office: PMA 12.140

Teaching Assistants: Daniel Restrepo
                                     Hunter Vallejos

Lecture: MWF 3:00 pm- 4:00 pm and 4:00 pm-5:00 pm Zoom Lecture   August 26 - December 7

Textbook: There are two required textbooks listed for the course. I have also included additional reference textbooks for interested students. Note that the PDF file of the second required textbook is "freely" available through the UT Library website.
Prerequisites: Student must have earned at least a C- in M408D, M308L, M408L, M308S, M408S or any equivalent courses.

Course  Description: Topics include matrices, elements of vector analysis and calculus functions of several variables, including gradient, divergence, and curl of a vector field, multiple integrals and chain rules, length and area, line and surface integrals, Greens theorem in the plane and space. If time permits, topics in complex analysis may be included. This course has three lectures and two problem sessions each week. It is anticipated that most students will be engineering majors. Five sessions a week for one semester.

Suggested Exercises: Suggested exercises will be assigned regularly from the course textbook. These problems will not be collected. Students are encouraged to work in groups to help each other on the problems.

Group Worksheets: At the beginning of each week a worksheet will be provided to the class through Canvas. The discussion sessions are devoted to solving these worksheet problems. Students will be randomly divided into groups of 4 (or 5) students; the group's task is not only to produce solutions to the worksheet problems but also to make certain that each group member participates and in the end understands how to solve the problems. The worksheets will only be graded for completeness.
Submission: Each group will submit one PDF of the solutions to the worksheet by every Friday (before Midnight) to Gradescope (choose a group representative).

Gradescope: All your assignments needs to be submitted through Gradescope. View the LINK for more information on how to submit your work electronically.

Course Readings: Reading the sections of the textbook corresponding to the lectured material is essential to succeeding in the course. You are responsible for the topics covered in the assigned reading, whether or not we discussed them in lectures.

Online Quizzes: There will be four timed canvas quizzes throughout the semester. Each quiz is given 40 minutes to complete. The quizzes are open book. You may start each quiz at any time you like throughout the day. The dates of the quizzes are Sept. 8, Oct. 6, Nov. 3, and Dec. 1.

Take-home Exams: There will be three take-home exams. Each take-home exam is given approximately two days (weekend) to complete. The exams are open book. The dates of the exams are
  • Exam 1: Release on Friday, Sept. 18 (before 9:00 PM) and Due on Monday, Sept. 21 (before Noon)
  • Exam 2: Release on Friday, Oct. 16 (before 9:00 PM) and Due on Monday, Oct. 19 (before Noon)
  • Exam 3: Release on Friday, Nov. 13 (before 9:00 PM) and Due on Monday, Nov. 16 (before Noon)
Final Exam: The final exam is cumulative. The exam is given approximately four days to complete. The final exam is open book.
  • Final Exam: Release on Monday, Dec. 7 (before 9:00 PM) and Due on Friday, Dec. 11 (before Midnight)
Make-up Policy: Make-ups for in-class exams will only be given in the case of a documented absence due to illness, religious observance, participation in a University activity at the request of University authorities, or other compelling circumstances. No make-up exam.

Grading: Course grades will be computed based on your worksheets, MATLAB projects, take-home exams, quizzes, and the final exam grades. Your course grade will be determined by the best of the following two weighted averages:
  • 15% Worksheets, 24% Matlab, 16% Quizzes, 30% Exams (10% per Exam), 15% Final,
  • 15% Worksheets, 24% Matlab, 16% Quizzes, 20% Exams (10% per Exam), 25% Final.
After your weighted average is calculated, letter grades will be assigned based on the standard grading scale:

A A- B+ B B- C+ C C-
>92 92-90 89-87 86-83 82-80 79-77 76-73 72-70

It is possible that the cutoffs may be lower at the discretion of the instructor.

Extra Credit: Each (Worksheet) group may earn up to an additional 2% towards their course grade by taking notes for one of the lectures. The notes will be posted below and make available to the public. Requirements:
  • The notes must be in PDF format. (Also, make sure the document is not too large.)
  • The notes must be handwritten (not typed). Make sure your handwriting is legible.
  • The notes must be in print, not cursive.
  • The notes must include comments and insights from the group (8-10 comments or more).
  • Limit your page count. (I don't want to see a textbook. Based on my experiences, I believe each lecture should take approximately 5 pages.)
  • Try to draw pictures with colors. (Optional)
Again, you are taking notes for the class not transcripts of the lectures. The purpose of these notes are suppose to highlight the important ideas presented in the lectures. They should be "useful".

Students with Disabilities:  Students with disabilities may request appropriate accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities (SSD), 512-471-6259, https://diversity.utexas.edu/disability/ . Notify your instructor early in the semester if accommodation is required.

Academic Integrity: Each student in the course is expected to abide by the University of Texas Honor Code: “As a student of The University of Texas at Austin, I shall abide by the core values of the University and uphold academic integrity.” You are expected to read carefully and adhere to the following instruction provided by the Office of the Dean of Students: http://deanofstudents.utexas.edu/conduct/academicintegrity.php

 Counseling and Mental Health Services: Available at the Counseling and Mental Health Center, Student Services Building (SSB), 5th floor, M-F 8:00 a.m. to 5:00 p.m., (Phone) 512-471-3515, website www.cmhc.utexas.edu. Your mental health should be your top priority, so please take good care of yourself.

Tentative Schedule and Suggested Problems: Below is a tentative schedule of the course with the material that I hope to cover and when. This will undoubtedly change as we progresses through the semester, so check here often for updates. However, I will try my best to follow the schedule religiously. The reading and homework are from Marsden and Tromba. The lectures are based on the course textbook and lecture notes by James McKernan.

Date Reading Suggested Problems
W 8/26 Lecture 1: Vectors in Two- and Three-Dimensional Space (McKernan Lect. 1) § 1.1 § 1.1: #3,5,7,11,13,15,22,23,31,36
F 8/28 Lecture 2: The Inner Product, Length, and Distance § 1.2 § 1.2: #3,11,13,19,21,27,29,37,38
M 8/31 Lecture 3: Matrices, Determinants, and Cross Product (McKernan Lect. 3) § 1.3 § 1.3: #1,5,7,11,15,17,19,21,44,45
W 9/2 Lecture 4: Planes in 3D Space § 1.3 § 1.3: #27,29,31,35,39,41,43
F 9/4 Lecture 5: Cylindrical and Spherical Coordinates § 1.4 § 1.4: #3,4,5,7,11,13,17,19,21
M 9/7 Labor Day
T 9/8 Quiz 1
W 9/9 Lecture 6: n-Dimensional Euclidean Space § 1.5 § 1.5: #7,11,15,16,17,19,20,21,22,23
F 9/11 Lecture 7: The Geometry of Real-Valued Functions § 2.1 § 2.1: #3,5,9,13,19,25,29,33,37,39
M 9/14 Lecture 8: Limits and Continuity
(M1 Due)		 § 2.2 § 2.2: #7,9,11,13,17,23,25,27,29,35
W 9/16 Lecture 9: Differentiation
(M1 Due)		 § 2.3 § 2.3: #3,5,9,11,13,15,17,19,21,23
F 9/18 Lecture 10: Introduction to Paths and Curves § 2.4 § 2.4: #1,5,9,13,15,17,19,23,25
9/18-21 Exam 1: § 1.1-1.5 and 2.1-2.3 Exam 1 Study Guide
M 9/21 Lecture 11: Properties of the Derivative § 2.5 § 2.5: #3,5,7,11,13,15,19,21,23,29,31,33,35
W 9/23 Lecture 12: Gradients and Directional Derivatives § 2.6 § 2.6: #3,5,7,15,17,19,21,23,25,29,31
F 9/25 Lecture 13: Iterated Partial Derivatives § 3.1 § 3.1: #5,7,9,11,15,17,23,25,27,29,31
M 9/28 Lecture 14: Taylor's Theorem § 3.2 § 3.2 #1,3,5,7,9,11
W 9/30 Lecture 15: Extrema of Real-Valued Functions Part I § 3.3 § 3.3: #5,7,9,13,15,19,23,25,27,29,33,35
F 10/2 Lecture 16: Extrema of Real-Valued Functions Part II § 3.3 § 3.3: #39,41,43
M 10/5 Lecture 17: Constrained Optimization and Lagrange Multiplers Part I § 3.4 § 3.4: #27,33,35,37,39
T 10/6 Quiz 2
W 10/7 Lecture 18: Constrained Optimization and Lagrange Multiplers Part II § 3.4 § 3.4: #3,5,7,9,11,13,15,17,19,21,23,25
F 10/9 Lecture 19: Arc Length § 13.3 (S)
M 10/12 Lecture 20: Curves in Space
(M2 Due)		 § 13.4 (S)
W 10/14 Lecture 21: Motion in Space § 13.4, § 4.1 (S)
F 10/16 Lecture 22: Vector Fields § 4.3 § 4.3: #7,11,13,15,19,21,23,27
10/16-19 Exam 2: § 2.4-2.5, 3.1-3.2, and 4.1-4.2 Exam 2 Study Guide
M 10/19 Lecture 23: Divergence and Curl § 4.4 § 4.4: #5,7,11,15,17,21,25,29,33,35,37,39
W 10/21 Lecture 24: Double Integrals § 5.1 (O)
F 10/23 Lecture 25: Double Integral over General Regions § 5.2 (O)
M 10/26 Lecture 26: Double Integrals in Polar Coordinates § 5.3 (O)
W 10/28 Lecture 27: The Triple Integral § 5.4 (O)
F 10/30 Lecture 28: Triple Integrals in Cylindrical and Spherical Coordinates § 5.5 (O)
M 11/2 Lecture 29: The Change of Variables Theorem § 5.7 (O) § 5.7: #361,365,367,371,381,391,393,395,
397,399,405,413
T 11/3 Quiz 3
W 11/4 Lecture 30: The Path Integral § 7.1 § 7.1: #5,7,11,13,17,19,25,27
F 11/6 Lecture 31: Line Integrals § 7.2 § 7.2: #1,3,5,9,11,13,17,19
M 11/9 Lecture 32: Parametrized Surfaces
(M3 Due)		 § 7.3 § 7.3: #3,5,7,9,15,17,19,23
W 11/11 Lecture 33: Area of a Surface § 7.4 § 7.4: #1,3,5,7,9,11,13,15,17,19,21,23,27
F 11/13 Lecture 34: Integrals of Scalar Functions Over Surfaces § 7.5 § 7.5: #1,3,5,7,9,11,13,15,17,19,23,27
11/13-16 Exam 3: § 5.1-5.5, 6.1-6.2, 7.1-7.4 Exam 3 Study Guide
M 11/16 Lecture 35: Surface Integrals of Vector Fields § 7.6 § 7.6: #1,3,5,7,9,11,15,19,21
W 11/18 Lecture 36: Green's Theorem § 8.1 § 8.1: #5,7,9,11,13,15,17
F 11/20 Lecture 37: Green's and Stokes' Theorem § 8.1-8.2 § 8.1: #19,21,23,27
§ 8.2: #1,3,5,7,9,11,13,15,17
M 11/23 Lecture 38: Stokes' Theorem § 8.2 § 8.2 # 19,23,29,31,33
W 11/25 Thanksgiving Break
F 11/27 Thanksgiving Break
M 11/30 Lecture 39: Conservative Fields § 8.3 § 8.3 #1,3,7,11,13,15,17,19,21,23,25,27,29
T 12/1 Quiz 4
W 12/2 Lecture 40: Gauss's Theorem § 8.4 § 8.4 #1,3,5,7,9,11
F 12/4 Lecture 41: Gauss's Theorem § 8.4 § 8.4 #13,15,19,21,29
M 12/7 Lecture 42: Final Review
(M4 Due)
F 12/11 Final Exam

Online Resources: I will updated this as the semester progresses.
  • MIT OpenCourseWare This is an invaluable source. The video lectures are superb. The level of the material is comparable to our course material.
  • Khan Academy Multivariable Calculus Khan Academy has been producing high quality math contents in these recent years. Their videos are relative short and probably easier to disgest. The content might not go into as much depth as what we will be doing in class but it will serve as a great supplement to our lectures.
  • Multivariate Calculus for Machine Learning This is a sequence of short videos on how multivariable calculus is used in machine learning. The content is very elementary but it provides novice with a stepping stone into learning the fundamental of machine learning. These videos are not directly relevant for our course, but, nevertheless, students might find them interesting.
Why MATLAB?: MATLAB stands for MATrix LABoratory. Originally written by Cleve Moler for college linear algebra courses, MATLAB has evolved into a high-level language and interactive environment for linear algebra computations in science and industry all over the world. Using MATLAB will help you visualize problems in vector calculus, and give you a glimpse of how calculus is applied in practical work. Another purpose of introducing MATLAB in this course is to help you obtain a working knowledge with the software for future courses. (Programming experiences is not required.)

MATLAB Projects: There will be four MATLAB group projects. These will be posted below as they become available. Students will be randomly assigned groups of three to discuss and work on the projects. Each group will submit one copy of the project. Downloading MATLAB: To install MATLAB onto your personal devices (laptops and desktops), please follow the instructions on this page to submit a request to download the program. Once you submit a request, you should receive an email (within a few minutes) on your university email account. Follow the instructions on the email to complete the installation.

MATLAB Problems Formatting: Your MATLAB project should be formated as in this example. You should suppress any unnecessary output to keep your page count to the bare minimum. Moreover, please use double-sided printing to minimize paper waste. The m-file template for the above example can be download here.

I have included links to relevant MATLAB tutorials:
Computer Lab: >If you do not already have MATLAB installed on your personal computer, you could go to the Undergraduate Computer Lab (RLM 7.122) and sign-up for an account to access the computers in the lab, which all have MATLAB installed. The lab is accessible whenever the RLM building is accessible. Current RLM operating hours are:
  • M-Th: 6:00am -- 11:00pm
  • F: 6:00am -- 10:00pm
  • Sat: 6:00am -- 5:00pm
  • Sun: 2:00pm -- 11:00pm