MATH 427L: ADVANCED CALCULUS FOR APPLICATIONS II

Course Unique Number: 54895

General Information

Instructor: David Clark (clark@math.utexas.edu)

Lectures: Monday, Wednesday, Friday, 3:00pm-3:50pm. Hosted on Zoom: https://utexas.zoom.us/j/91224584618. Notes will be provided after each lecture. Recordings of the lectures will be available on Zoom.

Office hours: Tuesday 11am-noon, Thursday 2pm-3pm, Sunday 3pm-4pm, or by appointment. Hosted on Zoom, https://utexas.zoom.us/j/5689856057.

Teaching Assistant: Zhengshuo Liu (zl5438@utexas.edu).

Discussion Section: Tuesday, Thursday 12:30pm-1:30pm. Hosted on Zoom: https://utexas.zoom.us/j/99759022826.

TA Office hours: Monday, Wednesday, and Friday 4pm-5pm. Hosted on Zoom: https://utexas.zoom.us/j/91947000827.

Text: Vector Calculus, 6th ed., by Marsden and Tromba.

Piazza: There will be a discussion board monitored by the instructor and teaching assistant. This will be the best location to ask questions about the course.

Course webpage: http://www.ma.utexas.edu/users/clark/Courses/2021/Spring/427L/.

Course Description

Matrices, elements of vector analysis and calculus of 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, Green's theorems in the plane and space.

Prerequisites

The prerequisite is a grade of at least C- in Mathematics 408D, 408L, or 408S.

Grading for this Course

Homework: There will be homework after each lecture, done online using the Quest system, located at https://quest.cns.utexas.edu/. The homework must be completed online by the date posted, typically about four days after it becomes available. Note that Quest will subtract points for wrong answers, so think carefully before you answer or you could end up with a negative score. Students may request automatic extensions to homework due dates.

Quizzes: There will be weekly quizzes in the discussion sessions.

Exams: There will be three midterm exams, two held during the usual class period, and the third during the scheduled final exam time. The first two midterms are tentatively scheduled for February 26 and April 5. The third midterm exam is scheduled for Wednesday, May 12, 7:00pm-8:15pm. Please mark on your calendars now the time and date of the exams. Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams. Access to the exams will be provided through Canvas. Completed exams will be uploaded to Gradescope. Any student with difficulties uploading the exam should email the exam to the instructor. Any student, who is unable to take an exam at the scheduled time, should contact the insturctor to make alternative arrangements.

Grading Scheme: The final grade will be determined by thegrading scheme:

Activity Percentage

Homework 30%

Quizzes 10%

Midterm Exams 60%

Letter Grades

The grading convention, 90.00-100% A, 86.67-90.00% A-, 83.33-86.67% B+, 80-83.33% B, 76.67%-80.00% B-, 73.33-76.67% C+, 70.00-73.33% C, 66.67%-70.00% C-, 63.33-66.67% D+, 60.00-63.33% D,56.67%-60.00% D-, less than 56.67% F, will be followed. If for some reason there is a deviation from this scale it will be applied uniformly to the whole class. Changes to the scale will only make the scale more generous.

Class Resources

Quest: This course makes use of the web-based Quest content delivery and homework server system maintained by the College of Natural Sciences. This homework service will require a $30 charge per student per class for its use, with no student being charged more than $60 a semester. This goes toward the maintenance and operation of the resource. Please go to http://quest.cns.utexas.edu to log in to the Quest system for this class. After the 12th day of class, when you log into Quest you will be asked to pay via credit card on a secure payment site. Quest provides mandatory instructional material for this course, just as is your textbook, etc. For payment questions, email quest.billing@cns.utexas.edu.

University Policies

University Code of Conduct: The core values of The University of Texas at Austin are learning, discovery, freedom, leadership, individual opportunity, and responsibility. Each member of the university is expected to uphold these values through integrity, honesty, trust, fairness, and respect toward peers and community.

Student 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."

Academic Integrity: A fundamental principle for any educational institution, academic integrity is highly valued and seriously regarded at The University of Texas at Austin. More specifically, you and other students are expected to maintain absolute integrity and a high standard of individual honor in scholastic work undertaken at the University. This is a very basic expectation that is further reinforced by the University's Honor Code. At a minimum, you should complete any assignments, exams, and other scholastic endeavors with the utmost honesty which requires you to:

acknowledge the contributions of other sources to your scholastic efforts;
complete your assignments independently unless expressly authorized to seek or obtain assistance in preparing them;
follow instructions for assignments and exams, and observe the standards of your academic discipline; and
avoid engaging in any form of academic dishonesty on behalf of yourself or another student.

Students who violate university rules regarding academic integrity are subject to disciplinary penalties, including the possibility of failure in the course and/or dismissal from the university. Policies on scholastic honesty will be strictly enforced. This includes but is not limited to: writing another student’s name on an in-class activity, or otherwise taking or giving credit for work that is not one’s own. This is viewed as a form of cheating by The University of Texas and will be treated as such in this class as well. You are responsible for understanding UT’s Academic Honesty and the University Honor Code which can be found at the following web address: http://deanofstudents.utexas.edu/sjs/acint_student.php

Sharing of Course Materials is Prohibited: No materials used in this class, including, but not limited to, lecture hand-outs, videos, assessments (quizzes, exams, papers, projects, homework assignments), in-class materials, review sheets, and additional problem sets, may be shared online or with anyone outside of the class unless you have my explicit, written permission. Unauthorized sharing of materials promotes cheating. It is a violation of the University’s Student Honor Code and an act of academic dishonesty. I am well aware of the sites used for sharing materials, and any materials found online that are associated with you, or any suspected unauthorized sharing of materials, will be reported to Student Conduct and Academic Integrity in the Office of the Dean of Students. These reports can result in sanctions, including failure in the course.

Class Recordings: Class recordings are reserved only for students in this class for educational purposes and are protected under FERPA. The recordings should not be shared outside the class in any form. Violation of this restriction by a student could lead to Student Misconduct proceedings.

Excused Absences: For an absence to be excused you must provide legitimate documentation prior to or no later than one week after your absence. Excused absences include:

Illness (must have a signed note from your physician on their letterhead; generic “no excuse” form letters from University Health Services will not be accepted)
Critical family events (e.g., weddings or funerals)
Official UT events (e.g., games if you’re an athlete, concerts if you’re a band member)
Religious Holy Days

If you have an excused absence, you will have one week to complete whatever in-class work you missed (quiz, exam, etc.). If your excused absence occurred on a day when a quiz or an exam was given, it is your responsibility to arrange to take a make-up quiz or exam. It is also your responsibility to leave the classroom if the quiz or exam is being discussed before you take the make-up version. Failure to do so will result in forfeiting your opportunity to take the make-up.

Drop dates: January 22 is the last day to drop without approval of the department chair; February 3 is the last day to drop the course for a possible refund; April 5 is the last day an undergraduate student may, with the dean's approval, withdraw from the University or drop a class, referred to as Q drop, except for urgent and substantiated, nonacademic reasons. Under Texas law, you are only allowed six Q drops while you are in college at any public Texas institution. For more information, see: http://www.utexas.edu/ugs/csacc/academic/adddrop/qdrop. For more information about deadlines for adding and dropping the course under different circumstances, please consult the Registrar's web page, http://registrar.utexas.edu/calendars/20-21/.

University Resources for Students

Your success in the class is important to me. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. Together we will develop strategies to meet both your needs and the requirements of the course.

Personal or Family Emergencies: If you you experience a personal or family emergency (death in the family, protracted sickness, serious mental health issues) you should contact Student Emergency Services in the Office of the Dean of Students. Student Emergency Services supports students by providing the most comprehensive outreach, assistance, intervention, and referrals. They will also work with you to communicate with me and your other professors and let them know of your situation. http://deanofstudents.utexas.edu/emergency/index.php

BeVocal:BeVocal is a university-wide initiative to promote the idea that individual Longhorns have the power to prevent high-risk behavior and harm. At UT Austin all Longhorns have the power to intervene and reduce harm. To learn more about BeVocal and how you can help to build a culture of care on campus, go to http://wellnessnetwork.utexas.edu/BeVocal

Title IX Reporting Title IX is a federal law that protects against sex and gender-based discrimination, sexual harassment, sexual assault, sexual misconduct, dating/domestic violence and stalking at federally funded educational institutions. UT Austin is committed to fostering a learning and working environment free from discrimination in all its forms. When sexual misconduct occurs in our community, the university can:

Intervene to prevent harmful behavior from continuing or escalating.
Provide support and remedies to students and employees who have experienced harm or have become involved in a Title IX investigation.
Investigate and discipline violations of the university’s relevant policies(https://titleix.utexas.edu/relevant-policies).

Beginning January 1, 2020, Texas Senate Bill 212 requires all employees of Texas universities, including faculty, report any information to the Title IX Office regarding sexual harassment, sexual assault, dating violence, and stalking that is disclosed to them. Texas law requires that all employees who witness or receive any information of this type (including, but not limited to, writing assignments, class discussions, or one-on-one conversations) must be reported. I am a Responsible Employee and must report any Title IX related incidentsthat are disclosed in writing, discussion, or one-on-one. Before talking with me, or with any faculty or staff member about a Title IX related incident, be sure to ask whether they are a responsible employee. If you would like to speak with someone who can provide support or remedies without making an official report to the university, please email advocate@austin.utexas.edu. For more information about reporting options and resources, visit http://www.titleix.utexas.edu/, contact the Title IX Office via email at titleix@austin.utexas.edu, or call 512-471-0419. Although graduate teaching and research assistants are not subject to Texas Senate Bill 212, they are still mandatory reporters under Federal Title IX laws and are required to report a wide range of behaviors we refer to as sexual misconduct, including the types of sexual misconduct covered under Texas Senate Bill 212. The Title IX office has developed supportive ways to respond to a survivor and compiled campus resources to support survivors.

Services for Students with Disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Division of Diversity and Community Engagement, Services for Students with Disabilities at 471-6259 (voice) or 232-2937 (video phone) or http://ddce.utexas.edu/disability/

Behavior Concerns Advice Line (BCAL): If you are worried about someone who is acting differently, you may use the Behavior Concerns Advice Line to discuss by phone your concerns about another individual’s behavior. This service is provided through a partnership among the Office of the Dean of Students, the Counseling and Mental Health Center (CMHC), the Employee Assistance Program (EAP), and The University of Texas Police Department (UTPD). Call 512-232-5050 or visit http://www.utexas.edu/safety/bcal

Campus Safety and Security: In case of an emergency evacuation, please be aware of the following recommendations the Office of Campus Safety and Security has outlined to keep you and others safe. Additional information may be available at 512-471-5767 or http://www.utexas.edu/safety/.

Occupants of buildings on The University of Texas at Austin campus are required to evacuate buildings when a fire alarm is activated. Alarm activation or announcement requires exiting and assembling outside.
Familiarize yourself with all exit doors of each classroom and building you may occupy. Remember that the nearest exit door may not be the one you used when entering the building.
Students requiring assistance in evacuation shall inform their instructor in writing during the first week of class.
In the event of an evacuation, follow the instruction of faculty or class instructors.
Do not re-enter a building unless given instructions by the following: Austin Fire Department, The University of Texas at Austin Police Department, or Fire Prevention Services office.
Information regarding emergency evacuation routes and emergency procedures can be found at: http://www.utexas.edu/emergency

Counseling and Mental Health Center: Students often encounter non-academic difficulties during the semester, including stresses from family, health issues, and lifestyle choices. The Counseling and Mental Health Center (CMHC) provides counseling, psychiatric consultation, and prevention services that facilitate students' academic and life goals and enhance their personal growth and well-being. Counseling and Mental Health Center, Student Services Bldg (SSB), 5th Floor, open M-F 8am-5pm. Tel. 512-471-3515 (appointments), 512-471-CALL (crisis line), or www.cmhc.utexas.edu

Student Rights and Responsibilities

You have a right to a learning environment that supports mental and physical wellness.
You have a right to respect.
You have a right to be assessed and graded fairly.
You have a right to freedom of opinion and expression.
You have a right to privacy and confidentiality.
You have a right to meaningful and equal participation.
You have a right to learn in an environment that is welcoming to all people.

With these rights come responsibilities:

You are responsible for taking care of yourself, managing your time, and communicating with the teaching team and with others if things start to feel out of control or overwhelming.
You are responsible for acting in a way that is worthy of respect and always respectful of others.
Your experience with this course is directly related to the quality of the energy that you bring to it, and your energy shapes the quality of your peers' experiences.
You are responsible for creating an inclusive environment and for speaking up when someone is excluded.
You are responsible for holding yourself accountable to these standards, holding each other to these standards, and holding the teaching team accountable as well.

Personal Names and Pronouns: Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, culture, religion, politics, sexual orientation, gender, gender variance, and nationalities. Class rosters are provided to the instructor with the student's legal name, unless they have added a "preferred name" with the Gender and Sexuality Center. I will gladly honor your request to address you by a name that is different from what appears on the official roster and by the gender pronoun you use. Please advise me of this early in the semester so that I may make appropriate changes to my records.

Schedule

Date	Section	Learning Objectives
Jan 20	1.1	Compute addition and scalar multiplication of vectors in two and three dimensional space
Jan 22	1.2	Compute the dot product of two vectors, length of a vector, angle between two vectors, projection of one vector in direction of another vector, and distance from a point to a line.
Jan 25	1.3	Compute determinants of 2×2 and 3×3 matrices. Compute the cross product of two vectors. Interpret the area of a parallelogram and the volume of a parallelepiped using determinants. Find the equation of a plane. Compute the distance from a point to a plane.
Jan 27	1.4	Relate rectangular coordinates to polar, cylindrical, and spherical coordinates.
Jan 29	1.5	Compute the scalar multiplication, addition, dot product, and length of vectors in Euclidean n-space. Compute the addition and multiplication of two matrices, transpose of a matrix. Compute the inverse of 2×2 matrices.
Feb 1	2.1	Sketch and describe the level curves or level surfaces of a function.
Feb 3	2.2	Find limits of multivariable functions. Show that limits of multivariable functions do not exist. Identify where multivariable functions are continuous or not continuous.
Feb 5	2.3	Calculate partial derivatives of functions of several variables. Determine if a function of several variables is differentiable. Determine the tangent plane to the graph of a function. Compute the gradient of a function.
Feb 8	2.4	Parameterize curves in Euclidean spaces.
Feb 10	2.5	Find derivatives of functions of several variables using the product rule, quotient rule, and chain rule.
Feb 12	2.6	Relate directional derivatives to the gradient. Interpret the gradient as the direction of greatest increase of a function. Determine the tangent plane to a level surface.
Feb 15	3.1	Compute higher order partial derivatives of functions of several variables, and apply the theorem of equality of mixed partials.
Feb 17	3.2	Apply Taylor's theorem to find quadratic approximations to function values.
Feb 19	3.3	Determine the extrema of functions of several variables.
Feb 22	3.4	Use the Lagrange multiplier method to find extrema of functions with constraints.
Feb 24	Review
Feb 26	Midterm 1
Mar 1	4.1	Find the velocity and acceleration of a particle moving along a space curve.
Mar 3	4.2	Find the arc length, unit tangent vector, curvature, and arc length reparametrization of space curves.
Mar 5	4.3	Define vector fields and gradient vector fields. Find flow lines of vector fields.
Mar 8	4.4	Compute the divergence and curl of a vector field.
Mar 10	5.1	Calculate volumes using the disk method, slice method, and iterated integrals.
Mar 12	5.2	Define double integrals over rectangles as limits of Riemann sums. Calculate double integrals using properties of the Riemann integral. Apply Fubini's Theorem to double integrals.
Mar 15	Spring Break
Mar 17	Spring Break
Mar 19	Spring Break
Mar 22	5.3	Calculate double integrals over more general regions.
Mar 24	5.4	Calculate double integrals by changing the order of integration.
Mar 26	5.5	Define triple integrals as limits of Riemann sums. Calculate triple integrals by extending techniques used for double integrals.
Mar 29	6.1	Determine if maps from ℝ to ℝ are one-to-one or onto. Determine the images of geometric objects (e.g. triangles or rectangles) under maps from ℝ to ℝ.
Mar 31	6.2	Calculate double and triple integrals using the Change of Variables Theorem.
Apr 2	Review
Apr 5	Midterm 2
Apr 7	7.1	Compute path integrals.
Apr 9	7.2	Compute line integrals. Use the Fundamental Theorem of Calculus for Vector Fields to compute line integrals of gradient fields.
Apr 12	7.3	Determine the parametrizations of surfaces such as planes, spheres, cylinders, and spirals.
Apr 14	7.4	Calculate the area of a surface.
Apr 16	7.5	Compute integrals of scalar functions over surfaces.
Apr 19	7.6	Compute surface integrals of vector fields.
Apr 21	7.6(cont.)
Apr 23	8.1	Use Green's theorem to evaluate line integrals along simple closed contours in the plane.
Apr 26	8.2	Apply Stokes' Theorem to compute line integrals along the boundary of a surface.
Apr 28	8.2(cont.)
Apr 30	8.3	Determine when a vector field is a gradient field.
May 3	8.4	Apply the Divergence-Gauss' Theorem to evaluate surface integrals.
May 5	Review
May 7	Review

This list of learning objectives is intended as a minimal list to be mastered in order to be reasonably sure of passing the course. It is not guaranteed that particular learning objectives will occur on examinations.