MTH 164 "Multidimensional Calculus"

Instructor Information:

Course Number

Class Time



Office Hours



MW 1230-1345

115 Harkness Hall

Yu Zeng

W 2-4pm, Hylan 1006


TR   1400-1515

203 Meliora Hall

Michael E. Gage

T 11am-noon, T 4pm-5, F 9:30am-11, Hylan 1010


MW 1400-1515

108 Goergen Hall

Xuwen Chen

MW 1245-1345 or by appointment, 1018 Hylan Building

TA and Recitation Information:


Recitation Time



Office Hours








Hylan 101

Hylan 305

Hylan 102

Shouman Das

W 1800-1900 @ Hylan 713







Hylan 305

Hylan 201

Hylan 1101

Murat Guner

M 1430-1530 @ Hylan 715







Hutch 138

Todd 202

Hylan 101

Robert Magnus

W 1400-1500 @ Hylan 718



Hylan 102

John Buckley

M 1800-1900 @ Carlson 2nd floor by windows



Hylan 101

Alex Johnson

W 0900-1000 @ B&L 374



Morey 501

Christopher Langfield

W 1530-1630 @ Carlson Basement


Webwork TA


Mark Auden

F 1200-1300 @ B&L 374

Recitation and workshop sign-ups will open Thursday, January 19th at 6:00pm. To sign up for a workshop or recitation, go to your blackboard page. In the top right corner, under My Organizations, you will see Spring 2017-Recitation-MTH164. Click that. You will be taken to an instruction page. Please note that you may only select one recitation time. If you have made a mistake, you will have to be manually deleted from your incorrect choice before you can choose again. (See the instruction page on how to do this.) This will lead to delays, and your desired time might fill up. So choose carefully the first time. Double-check before you click.


Equations of lines and planes, quadric surfaces, space curves, partial derivatives, linear approximation, directional derivatives, extrema, Lagrange multipliers, double/triple integrals including cylindrical and spherical coordinates. Line, surface, and volume integrals, divergence theorem, Stokes' theorem.


MTH 143, 162, or 172.


Stewart's Calculus (Early Transcendentals) 8th edition. (It is the same as 141-143 and 161-162. Older editions of the textbook are fine.)


Webwork 20%, Quizzes 10%, Midterm 1 20%, Midterm 2 20%, Final 30%. (We do not grade attendance since we are in college. For your information, in a recent course’s first midterm, 9 out of 10 students who regularly go to classes got an A, while only 1 out of 9 students who studies by themselves got the same grade.)


Webwork is assigned every week on Wednesday, starting 2/1. It is due in one week. We drop the lowest two webwork grades of each student's webwork grades (including zeros for unsubmitted assignments).

You are advised to enter Moodle and Webwork through you blackboard account.


There will be 7-10 quizzes total in the semester. The schedule of quizzes depends on the intensity of the material, that is, the beginning does not have many quizzes, but as the course progresses, we will have weekly quizzes. MAKE UP QUIZZES WILL NOT BE GIVEN UNDER ANY CIRCUMSTANCES. However, in recognition of the fact that unavoidable issues sometimes arise, the lowest two quiz grades of each student's quiz grades (including zeros for unsubmitted quizzes) will be dropped when calculating final semester grades.


Midterm I will be at Hutchinson 141 from 0800 to 0930 on 03/02/2017. Materials covered is up to 02/23/2017. So you have one week to review. The complain period for Midterm I is 03/06-03/23/2017 (Two weeks not counting spring break). Please go to your professor’s office hour during this period to check if you have been graded according to the grading guideline. After 03/23/2017, even you were graded wrong, no corrections will be made. (Without a deadline, nothing gets done.)


Midterm II will be at Hutchinson 141 from 0800 to 0930 on 04/06/2017. Materials covered is up to 03/30/2017. So you have one week to review. The complain period for the Midterm II is 04/10-04/19/2017. Please go to your professor’s office hour during this period to check if you have been graded according to the grading guideline. After 04/19/2017, even you were graded wrong, no corrections will be made. (Without a deadline, nothing gets done.)

The Final is scheduled at 1600, Monday, May 8. Location: TBA. The final will have part I and part II. If, in part I of the final, you get a higher score than your lowest midterm, then the score in part I of the final replaces that lowest midterm score of yours.

Course policies

1.      We use absolute grading system. The cut-offs are 85% for A, 80% for A-, 75% for B+, 65% for B,  60% for C+, 55% for C, 50% for C-, 40% for D. That is, if everyone gets above 85%, then everyone gets an A. To help students’ GPA, there is a wider range of B and there is no B- or D+. To protect students who get “on the edge” scores, like 84.9% in all exams, we do not use letter grade until the final total garde.

2.  Grading of exam problems are done step by step according to the grading guideline. Away from multiple choices, the final answer of every exam problem has no points so you do not need to worry about a wrong simplification or miscalculation at the last step. If a problem has multiple steps and one makes a computational mistake in a middle step, then one receives half of the credit of the leftover steps only if the method in the leftover steps is correct and will yield a correct answer if the previous computational mistake was not made.

3. If you have a schedule conflict at a midterm time, please notice your instructor at least two weeks ahead so that we can schedule your an earlier exam.

4. If you miss one midterm, don’t worry about it because part I of the Final will count towards that automatically. If you miss the Final with valid excuses like illness or emergency, you must notify the instructor and provide supporting documentation which verifies your excuses as soon as possible. A make-up will be given in one week of the original final. If you miss the final without a valid excuse or supporting documentation, you will receive a score of 0 on the final and no make-up will be given.

5. Incomplete "I" grades are almost never given. The only justification is a documented serious medical problem or a genuine personal/family emergency. Falling behind in this course or problems with workload on other courses are not acceptable reasons.

6. You are responsible for knowing and abiding by the University of Rochester's academic integrity code. Any violation of academic integrity will be pursued according to the specified procedures.

7. It is University of Rochester policy to provide reasonable accommodations to students who have a documented disability (e.g., physical, learning, psychiatric, vision, hearing, or systemic) that may affect their ability to participate in course activities or to meet course requirements. Students with disabilities are encouraged to contact the Center for Excellence in Teaching and Learning and their instructor for a confidential discussion of their individual need for academic accommodations. The Center for Excellence in Teaching and Learning is located in 1-154 Dewey Hall.

8. Solely per student request, we are uploading old exams for information. Please keep in mind that the old exmas MAY NOT represent the new exam and the actual exam MAY NOT contain problems similar to the old exams. The textbook, quizzes, and webwork are still the best sources of exam materials. Download

Please notify your instructor of any need for accommodations as early as possible, as it may not be possible to honor accommodation requests made less than one week before an exam.

Weekly schedule:

Week of


Suggested Exercises

Related Book Sections


Three-Dimensional Coordinate Systems; Vectors

12.1: 7-17 odd, 23, 29, 41

12.2: 19, 21, 23, 27

12.1, 12.2


The Dot Product; The Cross Product

12.3: 3, 5, 7, 15, 17, 19, 23, 29, 39, 41, 43

12.4: 1, 3, 5, 7, 19, 29, 31

12.3, 12.4


Equations of Lines and Planes; Vector Functions and Space Curves

12.5: 1 (all), 3, 5, 13, 19-39 odd, 45, 51, 53, 55, 57

13.1: 3, 5, 21-26, 27, 41, 43

12.5, 13.1


Derivatives and Integrals of Vector Functions; Arc Length (Up to tangent vector; curvature is optional); Functions of Several Variables;

13.2: 9-25 odd, 35, 37, 49

13.3: 1, 3, 5, 15, 23

14.1: 13, 15, 17, 32, 43, 47, 59-64, 65, 67

13.2, 13.3, 14.1


Limits and Continuity, Partial Derivatives

14.2: 5-15 odd, 19, 29, 31

14.3: 15-37 odd, 43, 53, 55, 59, 63, 65, 67, 71

14.2, 14.3


Tangent Planes and Linear Approximations; The Chain Rule

14.4: 1, 3, 5, 11, 13, 17, 19, 21

14.5: 1-33 odd

14.4, 14.5


Directional Derivatives and the Gradient Vector; Maximum and Minimum Values

14.6: 7-29 odd, 41, 43, 45, 51

14.7: 1, 5-19 odd, 29, 31-49 odd

14.6, 14.7


Lagrange Multipliers; Double Integrals over Rectangles; Iterated Double Integrals

14.8: 3-11 odd, 21, 29-39 odd

15.1: 11, 13, 15-34 odd, 37-43 odd, 47-50 odd

14.8, 15.1


Double Integrals over General Regions; Double Integrals in Polar Coordinates

15.2: 1-9 odd, 15-21 odd, 23-32 odd, 45-58 odd

(From here on out, you are adviced to do every single problem in the book.)

15.3: 1-31 odd, 39

15.2, 15.3


Triple Integrals; Triple Integrals in Cylindrical Coordinates; Triple Integrals in Spherical Coordinates

15.6: 3-21 odd, 29-34 odd, 53, 55a

15.7: 1-6 all, 9, 17-29 odd

15.8: 1-6 all, 9, 15, 19-29 odd, 35, 39, 41

15.6, 15.7, 15.8


Change of Variables in Multiple Integrals; Vector Fields; Line Integrals

15.9: 1-5 odd, 15-19 odd

16.1: 1, 5, 11-14, 21, 23, 29, 31

16.2: 1-21 odd, 39

15.9, 16.1, 16.2


The Fundamental Theorem for Line Integrals; Green's Theorem

16.3: 3-23 odd



Curl and Divergence; Parametric Surfaces and their Areas

16.4: 1-11 odd, 17

16.5: 1-7 odd, 13-19 odd

16.6: 1, 13-25 odd, 33, 35, 39-49 odd

16.4, 16.5, 16.6


Surface Integrals

16.7: 5-31 odd



Stoke’s Theorem and Divergence Theorem

16.8, 16.9