Math 2130

Course Sections

Instructors

Assistants to Instructors

Course Logistics

Course Description

Multivariable calculus, including vectors and curves in space; partial derivatives; multiple, line, and surface integrals; and the major theorems of vector calculus.

Lecture

Lectures meet Monday, Wednesday, and Friday. Attendance is expected.

Communication

Course announcements will be posted in Canvas. For questions about course material, attend office hours or post on Piazza through Canvas.
For administrative questions, email both lecture instructors.

Help & Assistant Office Hours

Mathematics Help Room . Attend during any open time. Any available assistant can help with this course.

Texts

Text 1: Workbook and Lecture Notes (Strongly Recommended)

ISBN: 9798319740939

A physical copy is strongly recommended because it contains the problems used in lecture and space for notes and written work. Solutions and answers will be posted in Canvas as the course progresses.

Student feedback: Most previous students found the workbook helpful and recommended purchasing a physical copy.

Required edition: Use Edition 7 with the gray cover. Earlier editions do not align with the current course.

Where to buy: Copies are available through the WashU Bookstore.

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, Multivariable Calculus, 7th ed. (other editions are also suitable)
  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-dimensional geometry, partial derivatives, multiple integrals, and vector calculus

Discussion Sections

You will meet with an Assistant to the Instructor (AI) each Tuesday, beginning the first Tuesday of classes. Discussion sections are low-stakes, AI-facilitated problem-solving sessions for practice, collaboration, and exploration. They are not additional lectures, although brief new ideas or techniques may be introduced when useful. Come prepared by reviewing the relevant material and attempting the assigned work. Graded group work completed in discussion counts toward the course 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)

PLTL is optional but strongly recommended. Apply during the first week of classes. 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 academic 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. Calculus III RPM hours are offered throughout the week. You may attend any available session.

Course Tools and Policies

Calculators

Calculators may be used for homework but are not permitted on exams .

No calculators are permitted on exams.

Canvas

Grades, WeBWorK, course files, and announcements are available in Canvas . All lecture sections use the combined Math 2130 Canvas course.

WeBWorK

• WeBWorK assignments are generally due Thursday evening.
• Access via Canvas → “Assignments”.
• There may be more than one set due in a week.
• Collaboration: Collaboration is permitted, but each student must understand and submit their own work and be able to solve similar problems independently on exams.
• Due-date logistics: A Thursday deadline may include material covered through Wednesday. Deadlines may be adjusted when lecture progress changes.

Exams

• Each midterm includes approximately 15–20 multiple-choice questions and about two written-response questions. The final exam is entirely multiple choice.
• Only writing instruments are permitted on exams unless an approved accommodation states otherwise.
• Find your assigned exam room and seat: Exam Seating
• Past exams: Old Exams (some semesters are more helpful than others)
• Course grades are posted in Canvas . WeBWorK grades may not be fully synchronized with Canvas until the end of the semester.
• 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 Workday.
• Curving :
  • Exams are designed with a target class average of 70–75%.
  • If the average of an exam is below 70%, the same number of percentage points is added to every score so that the class 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%. Twenty percentage points are added to every score, so your recorded Exam 1 score becomes 100%.

Exam Schedule

Study Suggestions – Daily and Weekly

• Skim the upcoming workbook section before class.
• Do all workbook problems (answers in Canvas → Files). Problems marked “overkill” or “difficult” are optional unless an instructor says otherwise.
• Start WeBWorK early.
• Arrive at discussion after attempting the relevant workbook problems and beginning the WeBWorK assignment.
• 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.
• You may also work during office hours or in the Math Help Room. Listening to other students’ questions is often useful.
• Use RPM hours for additional help.

Extra Credit and Grades

Extra Credit

A 0.5 percentage-point classwide bonus will be added if course-evaluation participation exceeds 80% by Thursday, December 10, at 3:00 PM. The bonus depends only on participation, not on evaluation content.

Grade Formula

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

The three midterms and the final determine 75% of the course grade. Normally, each exam contributes one-fourth of that exam component. If the final-exam score exceeds the lowest midterm score, the final replaces that midterm within the exam component. WeBWorK contributes 15%, and discussion group work contributes 10%.

The three lowest discussion scores and the five lowest WeBWorK assignment scores are dropped. These drops are intended to cover ordinary absences, illness, travel, and similar disruptions. Contact an instructor if extended circumstances affect more work than the drop policy covers.

Note on WeBWorK averages: multiple assignments may be due in one week. Assignment scores are scaled so that each assignment has equal weight in the WeBWorK average.

Rounding: Grade intervals are exact. For example, an A− is earned for a final numerical grade in [90, 93). Grades are not rounded across cutoffs.

Final Grades

Final letter grades are determined from the published grading formula and scale and are applied consistently across the class.

Grades are not individually adjusted because a student is close to a cutoff or based on effort, improvement, or personal circumstances. Any classwide adjustment is initiated by the instructors after reviewing the full grade distribution and is applied consistently.

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

Links and Resources

• 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

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.

The course learning objectives appear below 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. The course meets for 150 lecture minutes each week, plus a weekly discussion section. Students should expect approximately 6–9 hours of work outside scheduled class meetings each week.

Mode

In person.

Other WashU Policies & Resources

University policies and resources concerning disability accommodations, academic integrity, religious observances, military service, preferred names and pronouns, emergencies, discrimination, harassment, and student support are available through the 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 the academic integrity policy that applies to your school or program.

Generative AI Policy

Generative AI tools, including ChatGPT and Copilot, may be used for ungraded study and exploration. They may not be used on graded work unless the instructor explicitly authorizes their use for that assignment. When authorized, students must disclose and cite their use as directed. Prohibited or undisclosed use may constitute 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. Disability Resources

Sexual Harassment and Assault

If you have experienced sex discrimination, harassment, or violence, support is available. If you disclose such information to an instructor, the instructor may be required to report it to the appropriate university 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 the instructors in writing by 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.