fall 2021: m427L advanced calculus for application II
Course Syllabus: M427L-Fall 2021
Contact: Tentative office hours: T 3:00 pm — 4:00 pm
Th 3:00 pm — 4:00 pm
email: jwchong 🍎 math 🐶 utexas 🐶 edu
office: PMA 12.140
Teaching Assistants: Abhijjith Venkkateshraj
Lecture: MWF 3:00 pm — 4:00 in RLP 0.126 August 25 — December 6
Textbook: There is only one required textbook listed for the course. I have also included additional reference textbooks for the interested student.
- Vector Calculus, 6th edition by J. E. Marsden and A. Tromba (Required)
- Calculus: Early Transcendentals, 8th (or less) edition by J. Stewart (Reference)
- Calculus on Manifolds by M. Spivak (Reference)
- Vector Calculus, Linear Algebra, and Differential Forms A Unified Approach by J. H. Hubbard and B. B. Hubbard (Reference)
- Adanced Calculus by L. H. Loomis and S. Z. Sternberg (Reference)
- Mathematics for Machine Learning by M. P. Deisenroth, A. A. Faisal, and C. S. Ong (Reference) The pdf of this book is actually freely available online.
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.
Homework: Homework problems will be assigned regularly from the course textbook along with problems from the instructor. There will be a total of 10 assignments throughout the semester. Each problem set is assigned 8 points, 6 points for completeness and 2 points for accuracy of one or two randomly selected problems. We drop the lowest score. It is acceptable for groups of students to discuss the problems with each other; however, each student must write up his or her own solutions. See the tentative schedule for the due dates. Every assignment is due at 11:59 PM (CST) on the indicated date. Late assignments will not be accepted.
Submission: All homework should be submitted through Gradescope.
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.
Quizzes: There will be four quizzes throughout the semester (during discussions). Each quiz is about 20 — 25 minutes in length. The quizzes are closed book and notes. The dates of the quizzes are Sept. 9, Oct. 7, Nov. 4, and Dec. 2.
Exams: There will be three 50-minute in-class exams. The dates of the exams are
- Exam 1: Wed, Sept. 22
- Exam 2: Wed, Oct. 20
- Exam 3: Wed, Nov. 17
Final Exam: There will be a 3-hour in-class final exam. The final exam is cumulative.
- Final Exam: Dec. 15, 7:00pm — 10:00pm
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.
Grading: Course grades will be computed based on your homeworks, MATLAB projects, in-class exams, quizzes, and the final exam grades. Your course grade will be determined by the best of the following two weighted averages:
- 18% Homework, 12% Matlab, 16% Quizzes, 30% Exams (10% per Exam), 24% Final,
- 18% Homework, 12% Matlab, 16% Quizzes, 20% Exams (10% per Exam), 34% Final.
| 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.
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 Additional Practice 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 progress 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.
| Date | Reading | Additional Practice Problems | |
|---|---|---|---|
| W 8/25 | Lecture 1: Vectors in Two- and Three-Dimensional Space | § 1.1 | § 1.1: #23, 27, 32, 36 |
| F 8/27 | Lecture 2: The Inner Product, Length, and Distance | § 1.2 | § 1.2: #3, 12, 13, 14b, 26, 31, 35, 37 |
| M 8/30 | Lecture 3: Matrices, Determinants, and Cross Product | § 1.3 | § 1.3: #15ad, 26, 27, 30, 31, 33, 41 |
| W 9/1 | Lecture 4: Planes in 3D Space | § 1.3 | |
| F 9/3 | Lecture 5: Cylindrical and Spherical Coordinates (HW1 Due) | § 1.4 | § 1.4: # 11, 12, 13, 15, 19 |
| M 9/6 | Labor Day | ||
| W 9/8 | Lecture 6: n-Dimensional Euclidean Space | § 1.5 | § 1.5: # 19, 21, 22, 23 § RevEx of Ch 1: # 14, 24, 25, 39, 40 |
| Th 9/9 | Quiz 1 | ||
| F 9/10 | Lecture 7: The Geometry of Real-Valued Functions (HW2 Due) | § 2.1 | § 2.1: # 3, 5, 9, 17, 35, 39 |
| M 9/13 | Lecture 8: Differentiation | § 2.2, 2.3 | § 2.3: # 2, 15, 17, 19, 23, 28 |
| W 9/15 | Lecture 9: Introduction to Paths and Curves | § 2.4 | § 2.4: # 23, 25 |
| F 9/17 | Lecture 10: Properties of the Derivative (HW3 Due) | § 2.5 | § 2.5: # |
| M 9/20 | Lecture 11: Gradients and Directional Derivatives | § 2.6 | § 2.6: # |
| W 9/22 | Exam 1 | ||
| F 9/24 | Lecture 12: Iterated Partial Derivatives and Hessian Matrix (ML1 Due) | § 3.1, 3.2 | § 3.1: # |
| M 9/27 | Lecture 13: Extrema of Real-Valued Functions | § 3.3 | § 3.3: # |
| W 9/29 | Lecture 14: Constrained Optimization and Lagrange Multiplers Part I | § 3.4 | § 3.4 # |
| F 10/1 | Lecture 15: Constrained Optimization and Lagrange Multiplers Part II (HW4 Due) | § 3.4 | § 3.4: # |
| M 10/4 | Lecture 16: Acceleration and Newton's Second Law | § 4.1 | § 4.1: # |
| W 10/6 | Lecture 17: Motion in Space | § 4.1 | |
| Th 10/7 | Quiz 2 | ||
| F 10/8 | Lecture 18: Curvature (HW5 Due) |
§ 4.2 | § 4.2: # |
| M 10/11 | Lecture 19: Vector Fields | § 4.3 | § 4.3: # |
| W 10/13 | Lecture 20: Divergence and Curl | § 4.4 | § 4.4: # |
| F 10/15 | Lecture 21: Double Integrals (HW6 Due) |
§ 5.1-5.3 | § 5.1: # |
| M 10/18 | Lecture 22: Changing Order of Integration | § 5.4 | § 5.4: # |
| W 10/20 | Exam 2 | ||
| F 10/22 | Lecture 23: Triple Integrals (ML2 Due) |
§ 5.5 | § 5.5: # |
| M 10/25 | Lecture 24: Change of Variables Theorem Part I | § 6.2 | § 6.2: # |
| W 10/27 | Lecture 25: Change of Variables Theorem Part II | § 6.2 | § 6.2: # |
| F 10/29 | Lecture 26: Multivariable Integration in Applications (HW7 Due) | § 6.3 | § 6.3: # |
| M 11/1 | Lecture 27: Path Integrals | § 7.1 | § 7.1: # |
| W 11/3 | Lecture 28: Line Integrals | § 7.2 | § 7.2: # |
| Th 11/4 | Quiz 3 | ||
| F 11/5 | Lecture 29: Parametrized Surfaces (HW8 Due) |
§ 7.3 | § 7.3: # |
| M 11/8 | Lecture 30: Area of Surfaces | § 7.4 | § 7.4: # |
| W 11/10 | Lecture 31: Integrals of Scalar Functions Over Surfaces | § 7.5 | § 7.5: # |
| F 11/12 | Lecture 32: Surface Integrals of Vector Fields (HW9 Due) | § 7.6 | § 7.6: # |
| M 11/15 | Lecture 33: Green's Theorem | § 8.1 | § 8.1: # |
| W 11/17 | Exam 3 | ||
| F 11/19 | Lecture 34: Stokes' Theorem | § 8.2 | § 8.2: # |
| M 11/22 | Lecture 35: Stokes' Theorem Cont'd | § 8.2 | § 8.2: # |
| W 11/24 | Thanksgiving Break | ||
| F 11/26 | Thanksgiving Break | ||
| M 11/29 | Lecture 36: Conservative Fields | § 8.3 | § 8.3 # |
| W 12/1 | Lecture 37: Gauss's Theorem | § 8.4 | § 8.4 # |
| Th 12/2 | Quiz 4 | ||
| F 12/4 | Lecture 38: Gauss's Theorem Cont'd (HW10 Due) |
§ 8.4 | § 8.4 # |
| M 12/6 | Lecture 39: Summary (ML3 Due) |
||
| W 12/15 | Final Exam |
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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.
MATLAB Assignment: There will be three MATLAB assignments. These will be posted in Canvas and in Gradescope as they become available.
- MATLAB Assignment 1 Due Sept. 24
- MATLAB Assignment 2 Due Oct. 22
- MATLAB Assignment 3 Due Dec. 6
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. The m-file template for the above example can be download here. All MATLAB assignments will be submitted Gradescope.
I have included links to relevant MATLAB tutorials:
- Publish your m-file as an html file: https://www.mathworks.com/videos/publishing-matlab-code-from-the-editor-101570.html
- Important linear algebra Matlab programs: https://www.mathworks.com/help/matlab/linear-algebra.html
- M-Th: 6:00am -- 11:00pm
- F: 6:00am -- 10:00pm
- Sat: 6:00am -- 5:00pm
- Sun: 2:00pm -- 11:00pm
