Spring 2027

Calculus--functions of Several Variables

Calculus of functions of several variables covering parameterized curves, derivatives, multiple integrals, and vector calculus.

offering recorded4 credits
Recorded instructors · Spring 2027 Brandis WhitfieldSoledad Benguria Andrews

Summary

1 / 6

Past student reviews · Alexander Hanhart

A student taking Alexander Hanhart’s class found the homework took a lot of time to complete, though they felt the exams were not notably more difficult than previous semesters.

What you’ll be able to do

  • Analyze the behavior of functions of several variables, including their asymptotic behavior, local behavior, and existence of extrema with the tools of calculus (e.g., limits and continuity of multidimensional functions, derivatives and integrals of vector valued functions, arc length and curvature, partial derivatives, tangent planes, etc.).

  • Describe and analyze motion in space with the tools of calculus (velocity vector and acceleration, directional derivatives and the gradient vector, etc.).

  • Represent and compute areas and volumes by means of multiple integrals (e.g., integration over rectangles and more general spaces, average values, integration with polar, cylindrical, and spherical coordinates, general changes of variables, etc.).

  • Derive relations between different physical phenomena and their integral representations (e.g., using Green's theorem, the Divergence theorem, and Stokes' theorem).

  • Describe physical, biological, and/or economic phenomena using mathematical models (e.g., topographical maps and level curves, Lagrange multipliers, etc.).

  • Offer informal mathematical arguments and formal computations in English using appropriate mathematical terminology, notation, and grammar.

Source: UW Guide

Grade history

↗
average GPA
letter grades
A
AB
B
BC
C
D
F

All recorded terms · compare terms & instructors

Prerequisites

Course map

MATH 222

MATH 234 used by

“Used by” includes alternatives; linked courses may have other requirements. This is a best-effort interpretation; check the catalog requirements above.

Prerequisite text tree

Professors

Spring 2027
Historical instructors & teaching patterns

ALEX WALDRON is recorded teaching in Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

ALEXANDER HANHART is recorded teaching in Spring 2015, Spring 2020, Spring 2022. Recorded history may be incomplete and does not establish a future schedule.

AMIR ASSADI is recorded teaching in Spring 2007, Fall 2007, Spring 2008, Spring 2009, Fall 2009. Recorded history may be incomplete and does not establish a future schedule.

FEDOR NAZAROV is recorded teaching in Spring 2011. Recorded history may be incomplete and does not establish a future schedule.

HANLONG FANG is recorded teaching in Fall 2019, Spring 2020. Recorded history may be incomplete and does not establish a future schedule.

JEFF VIACLOVSKY is recorded teaching in Fall 2014. Recorded history may be incomplete and does not establish a future schedule.

JULIE MITCHELL is recorded teaching in Spring 2014, Spring 2016. Recorded history may be incomplete and does not establish a future schedule.

LEV BORISOV is recorded teaching in Fall 2007. Recorded history may be incomplete and does not establish a future schedule.

MIKHAIL FELDMAN is recorded teaching in Fall 2011, Fall 2012, Spring 2013, Spring 2015, Fall 2015, Fall 2016, Spring 2017, Spring 2019, Fall 2019. Recorded history may be incomplete and does not establish a future schedule.

SIGURD ANGENENT is recorded teaching in Fall 2009, Fall 2013, Fall 2015, Fall 2017. Recorded history may be incomplete and does not establish a future schedule.

Recorded history may be incomplete and does not establish a future schedule.

Calendar & sections

Spring 2027

Schedule loads here as you scroll.

SectionModeEnrolled / capacityWaitlist
LEC 001Classroom Instruction0 / 2960
LEC 002Classroom Instruction0 / 2890
LEC 003Classroom Instruction0 / 3090
DIS 325Classroom Instruction0 / 300
DIS 326Classroom Instruction0 / 300
DIS 323Classroom Instruction0 / 300
DIS 307Classroom Instruction0 / 300
DIS 343Classroom Instruction0 / 300
DIS 345Classroom Instruction0 / 300
DIS 347Classroom Instruction0 / 300
DIS 306Classroom Instruction0 / 300
DIS 346Classroom Instruction0 / 300
DIS 305Classroom Instruction0 / 300
DIS 308Classroom Instruction0 / 300
DIS 324Classroom Instruction0 / 300
DIS 327Classroom Instruction0 / 300
DIS 344Classroom Instruction0 / 300
DIS 348Classroom Instruction0 / 300
DIS 304Classroom Instruction0 / 300
DIS 322Classroom Instruction0 / 300
DIS 302Classroom Instruction0 / 300
DIS 309Classroom Instruction0 / 300
DIS 310Classroom Instruction0 / 300
DIS 329Classroom Instruction0 / 300
DIS 330Classroom Instruction0 / 300
DIS 349Classroom Instruction0 / 300
DIS 303Classroom Instruction0 / 300
DIS 328Classroom Instruction0 / 300
DIS 331Classroom Instruction0 / 300
DIS 311Classroom Instruction0 / 300
DIS 341Classroom Instruction0 / 300
DIS 350Classroom Instruction0 / 300
DIS 351Classroom Instruction0 / 300
DIS 342Classroom Instruction0 / 300
DIS 301Classroom Instruction0 / 00
DIS 321Classroom Instruction0 / 300

Times are Central. Select a meeting for details; export includes recorded dates for the selected sections. Enrollment reflects scan time.

Meeting source records
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Student experience

the class

Past student reviews · Betsy (Lindsay) Stovall

Students described the course as challenging but noted that instructors genuinely care about student learning and guide them through the material.

Recent recorded grades — Spring 2025: 2.96 GPA, 37.5% A/AB (n=762 letter grades); Fall 2025: 2.97 GPA, 41.3% A/AB (n=1263 letter grades); Spring 2026: 2.92 GPA, 35.2% A/AB (n=839 letter grades).

difficulty & workload

Past student reviews · Alexander Hanhart

A student taking Alexander Hanhart’s class found the homework took a lot of time to complete, though they felt the exams were not notably more difficult than previous semesters.

Past student reviews · Sigurd Angenent

One student found Sigurd Angenent enthusiastic and praised his ability to simplify difficult multivariable calculus topics, noting he posted useful study guides before exams.

Topics

  • Calculus on parameterized curves
  • Derivatives of functions of several variables
  • Multiple integrals
  • Vector calculus

Skills

  • Analyzing functions of several variables using limits, continuity, and derivatives.
  • Computing areas and volumes using multiple integrals and coordinate transformations.
  • Describing and analyzing motion in space using velocity vectors and gradients.
  • Applying Green's, Divergence, and Stokes' theorems to derive relations between physical phenomena.

Grades

Historical instructor

Spring 2027 · Projected

Before grades are released

– average GPA

Approximate 80% prediction interval

About this estimate

The course’s semester-average GPA, not an individual student’s grade. The center uses 5 same-season terms, weighted toward recent results.

The range uses the finite-sample 80th-percentile rank of absolute errors from earlier same-season forecasts. Each forecast uses only records from earlier terms. At least four forecasts are required; bounds are rounded outward and limited to 0–4. This is an empirical estimate: changing instructors or grading policies can reduce its coverage.

8 earlier forecasts · 0.21 GPA average error.

Grades over time

Through Spring 2027

More grade details Grade mix, volume & source data

Where this course fits relative to

Latest available grades · Spring 2026 · all course levels

GPA

Higher than % of other courses in this group.

Course GPAs · red marks this course’s range

letter grades

More recorded grades than % of other courses in this group.

Typical course in this group: letter grades.

About this comparison

1280 courses over the same term, each with at least 30 recorded letter grades. Cross-listed courses count once. GPA is not a measure of difficulty or teaching quality. The typical course is the median by recorded grade count; tied values are not counted as lower. Grade counts describe course scale, not unique students or typical section size.

Descriptions compare GPA with this group’s average: at least 0.20 higher or lower; otherwise close to average. Section size uses median recorded enrollment: small up to 30, mid-sized 31–99, large 100+. Lectures and discussion/lab sections are described separately.

Sources & history

UW–Madison

Catalog & offerings

Descriptions, prerequisites, and recorded course offerings.

Catalog observation history

Observations at scan time; dates do not imply when a catalog change took effect.

Download part 1
Selected offering source records
MATH 234 · Spring 2027

Calculus--Functions of Several Variables

Recorded 2026-10-14
Raw records 
[
  {
    "run_id": "20261014T203208-0851c9a1",
    "semester": "1274",
    "observed_at": "2026-10-14 17:50:09.728220+00:00",
    "offering_id": "1274:600:011628",
    "course_id": "MATH 234",
    "course_uid": "course_8634dde81cc95f6c58014087",
    "term_id": "1274",
    "source_course_id": "011628",
    "source_subject_id": "600",
    "title": "Calculus--Functions of Several Variables",
    "credits_min": 4,
    "credits_max": 4,
    "typically_offered": "Fall, Spring, Summer"
  }
]
Rate My Professors

Student reviews

Original comments behind the course and instructor summaries.

Read original reviews
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Madgrades

Grade history

Recorded grade distributions by term, section, and instructor.

Explore recorded grades
Dataset & model

Recorded 2026-10-14

View the dataset on Hugging Face
Model outputs & technical records
Qwen/Qwen3.8-27B
LLM outputs across runs
Download part 1
Full model traces

Recorded model configuration, reasoning, and tool conversations.

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Model & dataset provenance 
{
  "model": "Qwen/Qwen3.8-27B",
  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
  "task_version": "17",
  "output_id": "f04f603dd1e5b32c1d0b7140ecbadde748601d9775476680f269cb040cebbb22",
  "requirements_status": "valid",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}