Penn State, University Park, Fall 2026

MATH 231 — Calculus of Several Variables

Class Meetings

  • Classes begin on Monday, August 24, 2026, and end on Friday, December 11, 2026.
  • Thanksgiving Break: Sunday, November 22, 2026 – Saturday, November 28, 2026.
  • All electronic devices must be silenced during lectures. Disrupting class in any way will not be tolerated.

Lectures

Section Days Time Classroom Location Instructor
MATH 231.016 Wed, Fri 09:05 AM — 09:55 AM Sparks Building 121 Mathieu Stiénon
MATH 231.017 Wed, Fri 11:15 AM — 12:05 PM Borland Building 112 Ping Xu
MATH 231.018 Wed, Fri 12:20 PM — 01:10 PM Sparks Building 010 Mathieu Stiénon
MATH 231.019 Wed, Fri 01:25 PM — 02:15 PM Wartik Lab 110 Ping Xu

Recitations

Section Days Time Classroom Location TA
MATH 231.001R Mon 08:00 AM — 08:50 AM Elec Eng East 123 Austin Davis
MATH 231.002R Mon 08:00 AM — 08:50 AM Mateer Bldg 011 Kaichuan Qi
MATH 231.003R Mon 09:05 AM — 09:55 AM Nursing Sciences Bldg 316 Austin Davis
MATH 231.004R Mon 09:05 AM — 09:55 AM Huck Life Sciences Bldg 009 Nguyen Nguyen
MATH 231.005R Mon 10:10 AM — 11:00 AM Huck Life Sciences Bldg 009 Austin Davis
MATH 231.006R Mon 10:10 AM — 11:00 AM Nursing Sciences Bldg 316 Nguyen Nguyen
MATH 231.007R Mon 11:15 AM — 12:05 PM Osmond Lab 106 Austin Davis
MATH 231.008R Mon 11:15 AM — 12:05 PM Osmond Lab 103 Kaichuan Qi
MATH 231.009R Mon 11:15 AM — 12:05 PM Wagner Bldg 316 Nguyen Nguyen
MATH 231.010R Mon 12:20 PM — 13:10 PM Willard Bldg 273 Kaichuan Qi
MATH 231.011R Mon 01:25 PM — 02:15 PM Nursing Sciences Bldg 322 Ufuoma Asarhasa
MATH 231.012R Mon 01:25 PM — 02:15 PM Thomas Bldg 216 Kaichuan Qi
MATH 231.013R Mon 02:30 PM — 03:20 PM Osmond Lab 105 Ufuoma Asarhasa
MATH 231.014R Mon 02:30 PM — 03:20 PM Osmond Lab 106 Kaichuan Qi
MATH 231.015R Mon 03:35 PM — 04:25 PM Osmond Lab 105 Ufuoma Asarhasa

Instructors & Office Hours

Name Email Office Office Hours
Mathieu Stiénon mps16@psu.edu McAllister 325 Wed, Fri 10:30 AM — 11:30 AM
Ping Xu pxx2@psu.edu McAllister 329 Wed, Fri 2:30 PM — 3:30 PM
Austin Davis ahd5198@psu.edu    
Kaichuan Qi kkq5040@psu.edu    
Nguyen Nguyen ndn5109@psu.edu    
Ufuoma Asarhasa uva5039@psu.edu    
  • Please always include MATH 231 in the subject line of every email message.
  • Do NOT contact your instructor from within Canvas.
  • It may take up to two business days to receive an answer. Response windows exclude weekends and holidays; emails sent on Friday may not receive a reply until the following week.
  • Please refrain from asking extensive homework questions via email. Reserve such questions for Office Hours.
  • Office hours are designed for clarification and conceptual guidance. They are not a time for instructors to re-lecture missed content. If you miss class, obtain notes from a classmate.

Course Description & Prerequisites

  • Course description: vector geometry, vector-valued functions, functions of several variables, limits, continuity, differentiation, and applications.
  • Students who have passed either MATH 230 or MATH 230H may not schedule MATH 231 for credit.
  • Enforced prerequisite at enrollment: MATH 141 or MATH 141B or MATH 141E or MATH 141G or MATH 141H.

Required Textbook

Calculus: Early Transcendentals by Jon Rogawski, Colin Adams, and Robert Franzosa, 4th edition, (C) 2019 W. H. Freeman and Company.

We will cover chapters 12, 13, and 14. Before making a purchase, please ensure that the book includes these chapters.

Check whether you have an active Achieve account remaining from MATH 140/141, as students are typically instructed to purchase multiple-semester access. Achieve provides access to the electronic version of the textbook.

Here is a list of suggested exercises from the textbook.

Canvas & Gradescope

We will use Canvas and Gradescope to administer assignments, record scores and share course materials.

IT support is available 24/7.

Gradescope is a website designed to streamline the process of submitting, grading, and providing feedback on assignments. It allows students to submit their work online. Gradescope is widely used in higher education to improve the grading process.

To get access to our course on Gradescope, click on the “Gradescope” link in the navigation menu on the left in our Canvas course.

Install the Gradescope mobile app (iOS) (android) on your phone and/or tablet to scan your homework and submit it for credit.

Once an assignment is graded, the scores are available in Gradescope.

Instructions for Homework Submission on Gradescope

  1. Download the PDF of the assignment from Gradescope.
  2. Solve the problems using a black pen either on the printout or on blank sheets of white letter-size printer paper. Show all your work and explain it briefly in full sentences. Final answers without supporting work and explanations will not receive credit. Write cleanly! If your work is not easily readable and intelligible, you will lose points!
  3. Scan your work, and submit it as one single PDF file in Gradescope. If you’d rather work directly on your pen-enabled tablet, make sure to submit all layers of the PDF document.
  4. In Gradescope, once you have uploaded your PDF file, you must match the pages of your document to the questions of the assignment. Otherwise, your submission will be considered incomplete and will receive a zero score.
  5. Check that your submission is complete and that you have submitted all pages. Unreadable work will result in a zero score.
  6. Assignments dropped in the instructor’s mailbox, sent to his email address, or slipped under his office door are not acceptable, will not be acknowledged, will be ignored, and will not be graded. You must submit your work through Gradescope.

Assessment & Grades

Assignments will be weighed as follows:

Assessment Component Weight
Weekly Homework 10%
In-Class Quizzes 15%
Evening Exam 1 20%
Evening Exam 2 20%
Comprehensive Final Exam 35%
Total 100%

Course letter grades will be assigned as follows:

Percentage Range Letter Grade
93.0% – 100.0% A
90.0% – 92.9% A-
87.0% – 89.9% B+
83.0% – 86.9% B
80.0% – 82.9% B-
77.0% – 79.9% C+
70.0% – 76.9% C
60.0% – 69.9% D
0.0% – 59.9% F

Your grade will be based exclusively on the weekly homework, in-class quizzes, the two evening examinations, and the comprehensive final exam. There is no ‘extra credit’ work.

Calculators, AI, etc

Calculators, mobile apps, or electronic problem solvers (e.g., GeoGebra, WolframAlpha) are strictly forbidden on all quizzes and exams. Unauthorized use on tests constitutes an Academic Integrity violation resulting in a formal report. All assessment arithmetic is designed to be completed easily by hand.

Weekly Homework

Homework is due weekly on Mondays at 11:59 PM. Submit your work well ahead of the deadline. Assignments submitted late will automatically be marked as such in Gradescope. Repeated late submission will result in a penalty. Homework assignments will lock 24 hours after their respective due dates and late submission will be disabled at that time. No homework submissions will be accepted after the assignment has locked.

Students who have a valid and documented reason for not submitting homework on time may request to be excused for that assignment. However, there will be no makeup homework assignments.

In-Class Quizzes

Quizzes will be given in class on Monday every week (except during Week 1).

If you must miss a quiz due to a valid, university-approved excuse, you must notify your TA via email no later than 11:59 PM on the day of the quiz. Approved quiz makeups must be completed before the end of the week in which the quiz took place. Makeup scores may not be entered into the Canvas grade book until the end of the term.

Evening Examinations

  Exam 1 Exam 2
Regular Wed, Oct 7 (6:15 PM – 7:30 PM) Mon, Nov 9 (6:15 PM – 7:30 PM)
Early Wed, Oct 7 (4:50 PM – 6:05 PM) Mon, Nov 9 (4:50 PM – 6:05 PM)
Makeup Thu, Oct 8 (6:15 PM – 7:30 PM) Tue, Nov 10 (6:15 PM – 7:30 PM)

Exam room assignments will be announced by your instructor or TA and published on the math department website.

Students must bring their official Penn State ID, several pencils, and an eraser to all exams.

Early Exams & Makeup Exams

  • For each midterm, an early exam will be held on the same night as the regular exam beginning at 4:50 PM. Students attending the early exam are not permitted to leave the room before the end of the exam period.

  • For each midterm, a makeup exam will be held the day after the regular exam. This exam is meant for students unable to take the regular or early exam due to valid, documented reasons.

  • To request an early or makeup exam, visit Canvas and use the registration link provided in the course administration module. Prepare to provide documentation that supports the validity of your request.

  • Notify your instructor immediately regarding last-minute conflicts or sudden illness. If you can attend the early exam, you are not permitted to take the makeup exam.

Validity of Excuses for Missed Assessments

  • Personal business, travel, employment, family vacations, early flights, bus tickets, weddings, graduations, or attending public events (e.g., concerts, sporting events) are not valid excuses.
  • Forgetting the date or time of an exam is not a valid excuse.
  • Showing up late does not qualify you for a makeup exam; you will receive only the remaining time in the exam period.
  • Missing an exam without a valid excuse results in a score of 0. If an instructor grants a makeup exam without a valid, timely excuse, the exam will automatically receive a straight 25% deduction with no exceptions.
  • Students who have taken the original examination are strictly forbidden from taking a makeup examination. If a student receives multiple versions in error, only the first attempt counts; secondary versions will be discarded.

Final Examination

A comprehensive final examination will be given during the final examination period (December 14-18, 2026). The final examination may be scheduled on any day of finals week. Do not plan to leave University Park until after Friday, December 18, 2026. Students may access their final exam schedules on Monday, September 28, 2026, through their LionPATH account.

Conflict Final Exam

Personal final exam schedules will be available through your LionPATH account on Monday September 28, 2026. Notification of conflicts is given on the student’s final exam schedule.

  • Direct Conflict: Two examinations scheduled at the exact same time.
  • Overload Conflict: Three or more examinations scheduled in consecutive time periods or within a single calendar day.

Students must file for conflict exams through LionPATH between Monday, September 28, 2026, and Sunday, October 25, 2026. Conflict final exams cannot be scheduled through the Mathematics Department.

Makeup Final Exam

Students missing the final exam due to a documented emergency/illness may take a makeup final exam at the start of the following semester.

Personal business, such as travel, employment, weddings, graduations, or attendance at public events such as concerts and sporting events is not a valid excuse. Travel or early flight plans are not valid excuses; schedule departures after all final exams are complete. Forgetting the date or time of the examination is not a valid excuse.

To request a makeup exam, students must email their instructor with the documented reason within 24 hours of the final exam.

Students who miss the final exam without a valid reason might be allowed to take a makeup exam but a 25% penalty will be imposed.

Students who have taken the original final examination are not permitted to take a makeup examination.

Assessment Review & Grade Disputes

If you suspect a grading error on your exam or quiz, please submit a regrade request via Gradescope for that specific question. Be sure to provide a clear explanation of why you believe your work warrants a review.

Evening Exams: Direct grading questions or report missing exam grades to your instructor immediately. You have until the next midterm exam occurs to review your exam, report missing grades, or request a regrade.

Final Exam: Final exams are not released. Students have one week from the final exam date to report missing grades or contact the instructor. Work may be reviewed by setting up an appointment during the following academic term.

Students with Disabilities

Penn State welcomes students with disabilities into the University’s educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact Student Disability Resources at 814-863-1807 (V/TTY). For further information, please visit the Student Disability Resources web site. In order to receive consideration for accommodations, you must contact SDR and provide documentation (see the documentation guidelines at the Student Disability Resources web site). If the documentation supports your request for reasonable accommodations, SDR will provide you with an accommodation letter identifying appropriate academic adjustments. Please share this letter with your instructors and discuss the accommodations with them as early in your courses as possible. You must follow this process for every semester that you request accommodations.

Accommodations: Contact your instructor immediately and email your accommodation letter to Exam Coordinator Kyrsten Murphy (kml5346@psu.edu).

Attendance & Absence Policies

Regular class attendance is one of the most important ways that students learn and understand course materials. It is a critical element of student success. Accordingly, it is the policy of the University that class attendance is expected. A student should attend every scheduled class and should be held responsible for all work covered in the courses taken.

Class attendance is expected regardless of the format of the course and this expectation applies equally to students in face-to-face, online, and hybrid courses. It is the student’s responsibility to complete work early, or make alternate arrangements with the course instructor, if due dates or required work will be missed because of a University-approved absence.

Prolonged Absence (>1 Week): Documentation verifying significant prolonged illness is required. If requesting makeups more than twice, instructors may deny requests unless supported by University-approved documentation.

University Health Services (UHS) Guidelines: For routine illness, email faculty before missing quizzes or examinations. UHS provides illness verification forms only for major illnesses lasting at least a week. Request forms during clinical visits or through myUHS at studentaffairs.psu.edu/health/myuhs. Outside medical documentation must be submitted to the UHS Director (502A Student Health Center, 814-865-6555).

Relevant Senate Policies: Senate Policy 42-27, Policy E-11, and the University Excused Absence Form.

Course Learning Objectives

Upon successful completion of MATH 231, students should be able to demonstrate mastery of the following objectives:

Chapter 12: Vectors and 3D Geometry

  • Use vectors to describe various mathematical concepts, such as position and direction.
  • Perform computations involving vectors including addition, subtraction, multiplication, division, dot product, and cross product.
  • Calculate the magnitude/length of a vector.
  • Determine the angle between two vectors using appropriate vector computations.
  • Normalize a given vector and understand the reasons for using normalized vectors.
  • Perform vector projection onto a given vector.
  • Perform vector decomposition into parallel and perpendicular vectors to a given vector.
  • Calculate and interpret the meaning of the dot product.
  • Calculate and, in contextual situations, understand the meaning of the cross product.
  • Use the cross product to calculate areas of parallelograms and triangles and to calculate volumes of parallelepipeds.
  • Find a normal vector to a given pair of vectors, or to a given plane.
  • Find the equation of a plane with sufficient given information.
  • Sketch planes in $\mathbb{R}^3$.
  • Generate graphs of traces of quadric surfaces.
  • Identify the type of quadric surface based on traces.
  • Use symbolic and graphical techniques to solve problems involving points, vectors, lines, planes, and quadric surfaces in both $\mathbb{R}^2$ and $\mathbb{R}^3$.

Chapter 13: Calculus of Vector-Valued Functions

  • Use vector functions to describe concepts of position, velocity, acceleration, among other concepts.
  • Parametrize curves in both $\mathbb{R}^2$ and $\mathbb{R}^3$.
  • Recognize and understand differences between traditional function notation and parametric form of curves.
  • Perform differentiation and integration on vector-valued functions.
  • Determine equations of tangent lines using a system of parametric equations.
  • Solve initial-value problems for vector-valued functions.
  • Use calculus techniques in solving/answering questions concerning position, velocity, and acceleration.
  • Calculate and interpret the meaning of arc length.
  • Determine the arc length parametrization of a curve.

Chapter 14: Calculus of Multivariable Functions

  • Evaluate and use multivariable functions.
  • Visualize two and three variable functions using graphs, contour maps, and scalar fields.
  • Calculate the limit of a multivariable function.
  • Understand when a limit exists and does not exist for multivariable functions.
  • Calculate approximations of rates of change for multivariable functions.
  • Calculate and interpret partial derivatives of multivariable functions.
  • Interpret partial derivatives in applications.
  • Perform linear approximations of multivariable functions.
  • Justify when and how a multivariable function is differentiable both on a given domain and at specified points.
  • Determine the equation of a tangent plane to the graph of a function at a given point.
  • Calculate the gradient of a multivariable function.
  • Understand properties of the gradient and interpret the meaning of the gradient.
  • Determine the directional derivative at a given point and provide interpretation.
  • Use various multivariable chain rules to calculate rates of change for composite functions.
  • Find and classify local extrema of a multivariable function.
  • Find and classify global extrema of a multivariable function restricted to a closed and bounded domain.
  • Find and classify extrema on a boundary curve or path using either parametrization or Lagrange multipliers.

Tutoring

Free mathematics tutoring is available at Penn State Learning. They offer both online and in-person options.

For more help, the Department of Mathematics maintains a list of private tutors.

Late-Drop

Students may add/drop a course without academic penalty within the first six calendar days of the semester. A student may late drop a course within the first twelve weeks of the semester but accrues late drop credits equal to the number of credits in the dropped course. A baccalaureate student is limited to 16 late drop credits. Consult your academic advisor before late-dropping. The late drop deadline is Friday November 13, 2026 at 11:59 PM (Eastern Time).

Deferred Grades

Students who are currently passing a course but are unable to complete the course because of illness or emergency may be granted a deferred grade which will allow the student to complete the course within the first several weeks of the following semester. Note that deferred grades are limited to those students who can verify and document a valid reason for not being able to take the final examination. A deferred grade which is not changed to a letter grade by the instructor by 10 weeks after the course ends will automatically become an F. For more information see Deferred Grades.

Counseling and Psychological Services

Many students at Penn State face personal challenges or have psychological needs that may interfere with their academic progress, social development, or emotional well-being. The university offers a variety of confidential services to help you through difficult times, including individual and group counseling, crisis intervention, consultations, online chats, and mental health screenings. These services are provided by staff who welcome all students and embrace a philosophy respectful of students’ cultural and religious backgrounds, and sensitive to differences in race, ability, gender identity and sexual orientation.

988 Suicide & Crisis Lifeline

The 988 Lifeline is a national network of local crisis centers that provides free and confidential emotional support to people in suicidal crisis or emotional distress 24 hours a day, 7 days a week in the United States.

There is hope. Providing 24/7, free and confidential support to people in suicidal crisis or emotional distress works. The Lifeline helps thousands of people overcome crisis situations every day.

Need Support Now? If you or someone you know is struggling or in crisis, help is available. Call or text 988 or chat 988lifeline.org.

Academic Integrity

According to Penn State policy G-9: Academic Integrity, an academic integrity violation is “an intentional, unintentional, or attempted violation of course or assessment policies to gain an academic advantage or to advantage or disadvantage another student academically.” Unless your instructor tells you otherwise, you must complete all course work entirely on your own, using only sources that have been permitted by your instructor, and you may not assist other students with exams or other assessments.

Using ideas, images, or word phrases created by another person (e.g., from Course Hero or Chegg) or by generative technology, such as ChatGPT, is prohibited in this course. You may not submit false or fabricated information, use the same academic work for credit in multiple courses, or share instructional content. Students with questions about academic integrity should ask their instructor before submitting work.

Students facing allegations of academic misconduct may not drop/withdraw from the affected course unless they are cleared of wrongdoing (see G-9: Academic Integrity). Attempted drops will be prevented or reversed, and students will be expected to complete course work and meet course deadlines. Students who are found responsible for academic integrity violations face academic outcomes, which can be severe, and put themselves at jeopardy for other outcomes which may include ineligibility for Dean’s List, pass/fail elections, and grade forgiveness. Students may also face consequences from their home/major program and/or The Schreyer Honors College.

Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. Academic integrity is a basic guiding principle for all academic activity at The Pennsylvania State University, and all members of the University community are expected to act in accordance with this principle. Consistent with this expectation, the University’s Code of Conduct states that all students should act with personal integrity, respect other students’ dignity, rights and property, and help create and maintain an environment in which all can succeed through the fruits of their efforts. Academic integrity includes a commitment not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others. In order to ensure all students have a fair and equal opportunity to succeed in this course, the Mathematics Department is committed to enforcing the University’s academic integrity policy. Below is a description of academic misconduct and the department’s responsibilities when misconduct is suspected.

Academic Misconduct

In this course, academic misconduct includes, but is not limited to:

  • Copying the work of another student on an exam, quiz, or assignment;
  • Passing off the work of another individual as your own;
  • Using non-approved devices or aids on exams, quizzes, or assignments;
  • Having unauthorized possession of exams or quizzes;
  • Engaging in deception in order to extend or reschedule an exam, quiz, or assignment;
  • Facilitating acts of academic misconduct by others.

When Academic Misconduct is Suspected

If a student is suspected of academic misconduct, the instructor’s duties are to:

  • Confidentially inform the student of the allegation;
  • Enter the charge and recommended sanctions on an Eberly College of Science Academic Integrity form;
  • Ask the student to meet in order to review the form and discuss the charges and sanctions. The student can choose to accept or contest the allegation at this point.

Note that a student’s refusal to meet with the instructor or respond to the charges within a reasonable period of time is construed as acceptance of the allegation and proposed sanctions.

Once the Academic Integrity form has been accepted or contested by the student, it is sent to the College’s Academic Integrity Committee for adjudication. A student cannot drop or withdraw from the course during the adjudication process.

Sanctions

If a student accepts an academic misconduct allegation, or if (s)he is found guilty during adjudication, probable sanctions include:

  • A warning and
  • Reduction of the assignment grade to zero or
  • Reduction of the quiz or exam grade to zero.

Additional sanctions might include:

  • Reduction in the final course grade;
  • An F in the course.

In addition, the student will be unable to drop or withdraw from the course.

Please see the Eberly College of Science Academic Integrity homepage for additional information and procedures. Also see the Code of Ethics for Engineers published by the National Society of Professional Engineers.

Educational Equity

The Office of the Vice Provost for Educational Equity serves as a catalyst and advocate for Penn State’s diversity and inclusion initiatives. Educational Equity’s vision is a Penn State community that is an inclusive and welcoming environment for all. If you wish to learn more or if you wish to report bias, please visit the Educational Equity website.

All course materials students receive or to which students have online access are protected by copyright laws. Students may use course materials and make copies for their own use as needed, but unauthorized distribution and/or uploading of materials without the instructor’s express permission is strictly prohibited. University Policy AD 40: Recording of Classroom Activities and Note-Taking Services addresses this issue. Students who engage in the unauthorized distribution of copyrighted materials may be held in violation of the University’s Code of Conduct and/or liable under Federal and State laws.

A rising trend across the University is the posting and/or retrieval of material from course-share sites. Generally speaking, the uploading of materials to a course-share site is viewed as an Intellectual Property violation, and the downloading and use of materials from a course-share site could be a violation of academic integrity. If you have questions regarding the specific use of such a site, seek clarification directly from your instructor.

Student Class Recordings

Students are not allowed to record class sessions without permission.

According to University Policy, students must get express permission from their instructor to record class sessions. Screenshots showing instructors and students are considered recordings. Even if permission is granted, student-initiated recordings must be used only for educational purposes for the students enrolled in the initiating student’s class. Recordings may be used only during the period in which the student is enrolled in the class. Authorized student-initiated recordings may not be posted or shared in any fashion outside of the class, including online or through other media, without the express written consent of the course instructor or appropriate University administrator. Students who engage in the unauthorized distribution of class recordings may be held in violation of the University’s Code of Conduct, and/or liable under Federal and State laws.

Calendar

Week Mon Wed Fri
1 Aug 24 Aug 26 Aug 28
2 Aug 31 Sep 2 Sep 4
3   Sep 9 Sep 11
4 Sep 14 Sep 16 Sep 18
5 Sep 21 Sep 23 Sep 25
6 Sep 28 Sep 30 Oct 2
7 Oct 5 Oct 7 Oct 9
8 Oct 12 Oct 14 Oct 16
9 Oct 19 Oct 21 Oct 23
10 Oct 26 Oct 28 Oct 30
11 Nov 2 Nov 4 Nov 6
12 Nov 9 Nov 11 Nov 13
13 Nov 16 Nov 18 Nov 20
14 Nov 30 Dec 2 Dec 4
15 Dec 7 Dec 9 Dec 11

Tentative Lecture Schedule

Textbook Section Date
12.1 — Vectors in the Plane Aug 26
12.2 — Three-Dimensional Space Aug 28
12.3 — Dot Product Sep 2
12.4 — Cross Product Sep 4 & Sep 9
12.5 — Planes in 3-Space Sep 11
12.6 — Quadric Surfaces Sep 16 & Sep 18
13.1 — Vector-Valued Functions Sep 23
13.2 — Calculus of Vector-Valued Functions Sep 25
13.3 — Arc Length and Speed Sep 30
13.4 — Curvature Oct 2 & Oct 7
13.5 — Motion in 3-Space Oct 9 & Oct 14
14.1 — Functions of Two or More Variables Oct 16
14.2 — Limits and Continuity in Several Variables Oct 21 & Oct 23
14.3 — Partial Derivatives Oct 28
14.4 — Differentiability, Tangent Planes, and Linear Approximation Oct 30 & Nov 4
14.5 — Directional Derivatives and the Gradient Nov 6 & Nov 11
14.6 — Chain Rule Nov 13
14.7 — Optimization Nov 18 & Nov 20
14.8 — Lagrange Multipliers: Optimizing with a Constraint Dec 2 & Dec 4