Math 2130

Sections

Instructors

Assistants to Instructors

Course Logistics

Course Description

Multivariable calculus. Topics include differential and integral calculus of functions of two or three variables: vectors and curves in space, partial derivatives, multiple integrals, line integrals, vector calculus at least through Green's Theorem.

Lecture

Lecture meets MWF every week. Attendance is expected.

Communication

Announcements will be posted in Canvas Announcements. Questions on course material: visit office hours or post on Piazza (linked in Canvas).
Administrative questions: email and copy all lecture instructors (Prof Thornton, Prof Moncada, Prof Evans).

Help & Assistant Office Hours

Mathematics Help Room. You are encouraged to attend during any open time—any available assistant can help with this course.

Texts

Text 1: Workbook and Lecture Notes (Strongly Recommended)

Calculus 3 Lecture Workbook
ISBN: 9798385180998

You will almost certainly want a physical copy; it contains the problems we work in lecture. You will do work and take notes in this book. Solutions/answers will be posted in Canvas as we progress.

Student feedback: Most previous students found this text helpful. Many recommended that everyone have a physical copy.

Old editions will not work: Use the current edition, Blue Cover, Edition 6. Earlier editions are not aligned.

Where to buy: Copies are sent to the WashU Bookstore; purchase it there.

Text 2: Calculus Textbooks (Optional)

Traditional textbooks can be helpful for reference and extra exercises; many students do not find them essential. Two options:

• Stewart, Calculus, 7th ed. (any edition is fine)
  Good examples and exercises; used copies are easy to find.
• Lang, Calculus of Several Variables
  Excellent writing and theory; lighter on exercises; typically more expensive.

Are You in the Right Class?

Math 1510 Calculus I

Limits, derivatives, maxima/minima, L’Hôpital’s Rule

Math 1520 Calculus II

Integration, area/volume, surface area, infinite series, Taylor series

Math 2130 Calculus III

Three-space, partial derivatives, multiple integration, Green’s theorem & vector calculus

Discussion Sections

You will meet with your Assistant to Instructor (AI) every Tuesday (starting the first Tuesday of classes). These meetings include new material and problem-solving. Come prepared by doing your homework. Group work in discussion will be graded and counts toward your grade.

Where to Go for Help

• Instructor Office Hours
• Assistant Office Hours: Mathematics Help Room (M–F, 10 AM–4 PM)
• The Learning Center
• Engineering Tutoring Services (EN students only)
• CTL Mentoring
• CTL RPM Schedule

Peer Led Team Learning (PLTL)

The PLTL program is voluntary but highly recommended. Sign up the first week by completing an application. Learning Center PLTL page: PLTL

Residential Peer Mentors (RPMs)

RPMs offer drop-in help hours on the South 40 for Calculus support. Unlike PLTL, RPM hours are unstructured and can be used for quick WebWork questions, concept review, or a regular time and place to work on Calc. RPMs can also help with study strategies and general WashU advice. Schedules and links are posted on the Learning Center’s mentoring calendar. Sessions are typically in the residential colleges; some may be on Zoom. There are four Calc III RPMs with hours spread through the week—attend any RPM’s hours.

Course Tools & Policies

Calculators

While calculators are fine for homework, they are not allowed on exams.

NO CALCULATOR ALLOWED AT EXAMS

Canvas

Grades, WeBWorK access, and more at Canvas. All sections are merged into section 1; log into Math 2130, section 1.

WeBWorK

• WeBWorK is due every Thursday evening.
• Access via Canvas → “Assignments”.
• There may be more than one set due in a week.
• Collaboration: Work together if you like, but you must be able to perform solo on exams.
• Due-date logistics: Material covered by Wednesday’s lecture is fair game for WeBWorK due Thursday of the same week; we may postpone sets depending on lecture progress.

Exams

• Exams include multiple-choice (≈15–20) and hand-graded questions (≈2). The final exam is entirely multiple choice.
• Only writing tools are permitted on exams.
• Find your room/seat: Exam Seating
• Past exams: Old Exams (some semesters are more helpful than others)
• Find all grades on Canvas. WeBWorK grades are uploaded to Canvas at semester’s end.
• Do not miss an exam. Make-ups on different days are not given.
  If you are ill or have a family emergency, contact Prof. Blake Thornton ASAP. You may be eligible for an excused absence for one exam. (No make-up; the exam average will be reweighted across other exams—see instructor for details.)
• The final exam is cumulative.
• Exam schedule appears below and in WebSTAC.
• Curving:
  • If the average of an exam is below 70%, a constant is added to all scores so the average becomes 70%.
  • If the average is at or above 70%, no adjustment is made.
  • Example: You score 80% on Exam 1; the class average is 50.0%. Everyone receives +20.0 curve points; your recorded Exam 1 score becomes 100%. (Don’t expect this—exams are written to average ~70–75.)

Exam Schedule

Study Suggestions – Daily & Weekly

• Skim the upcoming workbook section before class.
• Do all workbook problems (answers in Canvas → Files). It’s okay to skip those marked “overkill” or “difficult”.
• Start WeBWorK early.
• Arrive at discussion prepared—having worked relevant workbook problems and started WeBWorK.
• Attend PLTL if enrolled (or practice with released PLTL problems).
• If you’re stuck, visit instructor and assistant office hours. See the Math Help Room for assistant hours and more help options.
• Drop by office hours / Math Help Room and study—listening to others’ questions often helps.
• Use RPM hours for additional help.

Extra Credit & Grades

Extra Credit

Extra credit is awarded by participation in course evaluations. Participation will be checked Thu, Dec 11 at 3:00 PM and points added to the entire class according to:

Grade Formula

Grade = 0.75*( E1 + E2 + E3 + 2*E4 - min(E1, E2, E3, E4) )/4
	  + 0.15*(WeBWorK) + 0.10*(GroupWork) + (Extra Credit)

All exams are weighted equally within the 75%. The final exam (E4) can replace your lowest semester exam. WeBWorK is 15%; discussion sections are 10%.

In discussion grades, the lowest three discussion scores are dropped (illness, athletic events, etc.). If you are sick more than three times, contact an instructor. For WeBWorK, the lowest five assignments are dropped.

Note on WeBWorK averages: there may be multiple assignments due per week; scores are scaled to equal weight before averaging.

Rounding: Grade intervals are exact (e.g., A- is [90, 93)). Use extra credit to push into the next band.

Pass/Fail Policy: At least a C- is required to earn “Pass”.

Links & Resources

• PLOTIFY
• Calc Plot 3D
• MathWhiteBoard
• Wolfram Alpha
• Desmos 3D
• GeoGebra 3D
• GeoGebra 2D
• Parametric Surface Plotter
• Paul Seeburger’s CalcPlot3D
• CalcPlot3D
• Sage
• Gnuplot
• Maxima
• Octave
• Calculus Page Problems by D. Kouba
• eCalculus.org
• Slader Stewart Textbook Solutions

Tentative Schedule

The schedule will be updated regularly. We will do our best to follow it, but topics may shift week-to-week as the semester progresses.

Course Description

This course introduces the concepts and techniques of calculus in multiple dimensions. Students will learn to visualize and analyze functions of several variables, compute derivatives, gradients, and integrals in two and three dimensions, and apply these tools to optimization and modeling problems. The course also develops proficiency with multiple and surface integrals in various coordinate systems and explores key results of vector calculus, including Green’s, Stokes’, and the Divergence theorems, with applications to physical and geometric problems.

A complete list of learning objectives is available in the appendix and on the course website.

Course Learning Objectives

Spatial Reasoning and Graphing

• Visualize and analyze points, lines, planes, and simple quadratic surfaces in three dimensions.
• Identify and interpret parametrized curves and surfaces from their equations or plots.

Vectors and Geometry

• Perform vector operations, including dot product, cross product, and projections.
• Parametrize lines and planes; compute intersections, angles, and distances between geometric objects.

Multivariable Functions and Limits

• Identify the domain, codomain/target space, and image of multivariable functions.
• Evaluate limits and assess continuity in multiple variables using appropriate definitions or theorems.

Differentiation

• Compute partial derivatives, directional derivatives, and gradients.
• Use the multivariable chain rule and apply implicit differentiation.
• Analyze level curves and level surfaces.
• Determine local and absolute extrema using second-derivative tests, boundary analysis, and Lagrange multipliers.

Integration

• Set up and evaluate double and triple integrals over rectangular, polar, cylindrical, and spherical regions.
• Use change of variables to simplify multivariable integrals.
• Evaluate scalar and vector line integrals and apply the Fundamental Theorem for Line Integrals.
• Identify and analyze vector fields; compute divergence and curl.
• Evaluate scalar and vector (flux) surface integrals.
• Apply Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem to compute integrals.

Credits, Modality, and University Policies

Credits

3 credits. Meets 150 minutes/week. Expect ~6–9 hours/week outside class (≈45 hours/credit).

Mode

In person.

Other WashU Policies & Resources

Covid, Sexual Assault/Harassment, Disability Resources, Military Service, Preferred Name and Pronouns, Emergencies, Academic Integrity, Student Resources, Religious Holidays, and more: Provost Student Resources

Academic Integrity

In all academic work, the ideas and contributions of others (including generative AI) must be appropriately acknowledged. Work presented as original must be, in fact, original. Review your program’s academic integrity policies.

Generative AI Policy

Generative AI tools (e.g., ChatGPT, Copilot) may be used for study and exploration. Unless explicitly allowed by the instructor for an assignment, their use on graded work is prohibited. When use is permitted, students must cite the tool. Undisclosed or prohibited use may be considered an academic integrity violation.

Disability Resources

WashU supports equitable educational opportunity. If any environment or activity creates barriers due to a disability, contact Disability Resources (DR) to determine approved accommodations. Send your Accommodation Letter as soon as possible—accommodations are not applied retroactively. https://disability.wustl.edu/

Sexual Harassment and Assault

If you have experienced sex discrimination, harassment, or violence, please speak with someone. If you share this with me, I am required to report to my department chair/dean or the Gender Equity and Title IX Compliance Office. You may also reach out to the Relationship & Sexual Violence Prevention (RSVP) Center for confidential support: resources & support.

Religious Holidays

To receive accommodations for class/assignments/exams that conflict with religious observances, inform me in writing before the end of the third week of class (or as soon as possible if within the first three weeks). See the University’s Religious Holiday Class Absence Policy for details.

Emergency Preparedness

Prepare by downloading the WashU SAFE App. Each classroom contains a “Quick Guide for Emergencies” near the door.