Math 234: Calculus - Functions of Several Variables

Final: is on Thursday, 5/10 , 12:25 – 2:25 pm in these locations:


Lecture 1 (1 pm lecture)

Biochem 1125

Lecture 2 (11 am lecture)

Agriculture Hall 125, if you are in Ewan’s section, please, go to the balcony.



Topics: This exam is mildly cumulative with at least 70% of the topics from Chapter VII in the Notes.

Review: on Wednesday, 5/9, 4 – 6 pm in 1351 Chemistry. Ivan and Vladimir will go over the practice problems.


Practice problems

You can find the solutions to the practice problems in Learn@UW in the Content Browser under Exam Review, in the file finalRevSolS18.


You are permitted to bring a 5.5 x 8.5 notecard with formulas to the exam.


Names and Sections



Office hours:

Gabriele Meyer

720 Van Vleck

F 10 – noon

David Wagner

820 Van Vleck

We 10 - noon

Polly Yu

518 Van Vleck

Th 4 – 6 pm

Yun Li

816 Van Vleck

MW 3:30 – 4:30 pm

Dima Kuzmenko

716 Van Vleck

MW 11 - noon

Ivan Ongay-Valverde

718 Van Vleck

TTh 2:30 – 3:30 pm

Jenny Hyejin Yeon

822 Van Vleck

W,Th 2:30 - 3:30 pm

Chun Gan

101-13 Van Vleck

MF 2:15 – 3:15 pm

Ewan Dalby

818 Van Vleck

F 11 - 1 pm

Benjamin Branman

818 Van Vleck

WF 12 – 1 pm

Kurt Ehlert

818 Van Vleck

M 11 - noon, Th 12:30 - 1:30 pm

Vladimir Sotirov

722 Van Vleck

TTh 10 – 11 am

Kyriakos Sergiou

716 Van Vleck

W 9:40 - 11:40 am.

Frank Rooney for Math Tutorial Program

320 Van Vleck

Eve Williams for the Engineering Undergraduate Learning Center

3rd floor Wendt Commons


SuMTWTh 6 – 9 pm



Lecture 1

Tu Th 1 – 2:15 pm

B102 Van Vleck

Lecture 2

Tu Th 11 – 12:15 pm

B102 Van Vleck

Text:      Prof Angenent's lecture notes which will be available through the Math Department. I will email you when exactly and where.


Catalog Statement:
This course is the last course in the standard Calculus series at the UW, Math 221-222-234. This series is designed for students with majors in the Sciences or Engineering. Honors student interested in a theoretical approach should consider our sequence 275-276-375-376 instead of 221-222-234. Full credit is not allowed for both 234 and 223.

Alternatives:  Some majors in the school of business require Math 211-213 instead of Math 221-222-234. Math 213 has some content overlap with Math 234 and full credit cannot be received for both Math 234 and Math 213.

Math 222. Closed to students with credit for Math 223.

Credit Hours: 4
This means that you should expect to put in an extra 8 hours per week (aside from class time) on average working on this course. This includes:
- reading the text
- doing homework problems
- preparing for exams
- getting help, when necessary

 Course Content:

·        Vector functions and space curves, velocity and acceleration

·        Arc length and curvature, normal and binormal

·        Motion in space, planetary motion

·        Partial derivatives

·        Tangent planes and normals

·        Linear approximation

·        gradient and total differential

·        Local and absolute extrema

·        Lagrange multipliers

·        Higher derivatives, exact differentials

·        Double and iterated integrals, including polar coordinates

·        Applications of double integrals

·        Triple and iterated integrals, including cylindrical and spherical coordinates

·        Applications of triple integrals, volume and surface areas.

·        Vector fields, surface integrals and line integrals

·        Flux, Green's theorem

·        Divergence Theorem, Stokes' theorem


You will be able to achieve a total of 200 points in this class:

Exam 1


Exam 2


Discussion (Quizzes and Homeworks)






There will be two in-class midterms and one cumulative final. The scores will be curved. The precise curve will NOT be determined until after the final exam. You will need to participate in the final to pass the class. The time and location of the final are set by the university and cannot be changed.  Do NOT make arrangements to leave town until after the final time.

The discussion grade is the sum of the quiz grades (3 points each) and the homework grades (1 point for each submitted homework). Homeworks are due on Mondays in discussion. Quizzes are on Wednesdays in discussion. There will be no make ups for quizzes, but we will drop the lowest quiz score.

Bring your student ID to each exam. Calculators are very useful in practical problems, but they can compensate for a lack of basic understanding. Therefore, calculator and other computing devices will not be allowed on exams in this course. There will be no make ups for exams. Please, contact your lecturer, if you have to miss an exam.

Homework problems will be on the syllabus
page. Solutions must be submitted electronically in Learn@UW.

Making the most of your Math class:

attend the lectures and the discussion sections. In many years of teaching I found that nonattendance almost always goes along with poor grades.

start working on the homework assignments EARLY. If you cannot do a problem, ask for help. Hand in your attempts. Consider the homework as practice for the exams.

if you need help, don't delay. Go to see your TA or Lecturer. If you wait until almost the end of the semester, it is too late to make a significant impact on the grade.

Getting Help:

If you are having difficulty, first talk to your TA or Lecturer. If you cannot come to the scheduled office hours, make an appointment to see either at a different time. Here are some other places you can get help:

                Math Tutorial Program

Please, contact, Dr Frank Rooney (320 Van Vleck) for that in the first 3 weeks of classes.

Math Lab:

The math Lab is is an especially good place to go if you have a quick homework question; more detailed questions are probably better directed to one of the TAs.

Location: B277 Van Vleck Hall (across from the Mathematics Library)
Hours: Monday through Thursday, 3:30 - 8:30 pm, and Sunday 3:30 - 6:50 pm.
Dates: starting the second week of classes (usually), through the end of the semester.
Cost: Free.

Private Tutoring:

The Mathematics Department publishes a list of Mathematics graduate students who are willing to tutor students; copies are available on the second floor of Van Vleck Hall, next to the elevators.

Location: Varies; many tutors will meet in Van Vleck Hall: some will meet off-campus.
Cost: Fees vary from tutor to tutor; typical costs are $20 to $30 per hour.






·        See the Guide’s to Rules, Rights and Responsibilities.



By enrolling in this course, each student assumes the responsibilities of an active participant in UW-Madison’s community of scholars in which everyone’s academic work and behavior are held to the highest academic integrity standards. Academic misconduct compromises the integrity of the university. Cheating, fabrication, plagiarism, unauthorized collaboration, and helping others commit these acts are examples of academic misconduct, which can result in disciplinary action. This includes but is not limited to failure on the assignment/course, disciplinary probation, or suspension. Substantial or repeated cases of misconduct will be forwarded to the Office of Student Conduct & Community Standards for additional review. For more information, refer to



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