01:640:251 - Multivariable Calculus

General Information:

01:640:251 Multivariable Calculus (4 Credits)  

This course covers multi-variable and vector calculus. Topics include analytic geometry of three dimensions, partial derivatives, optimization techniques, multiple integrals, vectors in Euclidean space, and vector analysis.

Prerequisite: CALC2 (Math 152, 154, or 192).


Thomas' CALCULUS Early Transcendentals, 14/e,  by Joel Hass, Christopher Heil, and Maurice Weir. Pearson Education. ISBN: 9780134639543 

MyMathLab access with etext: ISBN: 9780135901403

MyMathLab access can be purchased directly from Pearson.

Standard Syllabus, and Homework


Information for Instructors

Information for instructors


Lecture Topics & textbook homework for Math 251 

This is a very rapid plan of study. A great deal of energy and determination will be needed to keep up with it. Modifications may be necessary. Periodic assignments (Maple labs, workshops, etc.) may be due at times, and additional problems may be suggested.

The text is the 14th edition of Thomas' CALCULUS Early Transcendentals, by Joel Hass, Christopher Heil, and Maurice Weir. Pearson Education. ISBN: 9780134639543 

Lecture Topics and Suggested Textbook Problems for 640:251
LectureTopic(s) and text sectionsSuggested Homework
1 12.1 Three Dimensional Coordinate Systems
12.2 Vectors
12.1/ #3,9,15,16,21,23,39,59
12.2/ #9,19,23,25,31,41,47
2 12.3 The Dot Product 
12.4 The Cross Product 
12.3/ #3,13,18,19,22
12.4/ #7,15,21,23,27,33,35,45
3 12.5 Lines and Planes in Space
12.6 Cylinders and Quadric Surfaces
12.5/ #6,6,9,23,27,31,37,41, 47, 57
12.6/ #1-12, 13, 15, 21, 25
4 13.1 Curves in Space and Their Tangents 13.1/ #1,15,19,23, 31
5 13.2 Integrals of Vector-Valued Functions, Projectile Motion 13.2/ #3,5,8,11,15,19
6 13.3 Arc Length in Space 13.3/ #5,9,13,15
7 14.1 Functions of Several Variables
14.2 Limits and Continuity in Higher Dimensions
14.1/ #6,6,9,15-18,27,31,41,58,59
14.2/ #11,15,20-22,31,47,48,53,59
8 14.3 Partial Derivatives
14.4 The Chain Rule
14.3/ #9,14-18,27,3046,67
14.4/ #7,28,29,33,39,44
9 14.5 Directional Derivatives and Gradient Vectors
14.6 Tangent Planes and Differentials
14.5/ #3-6,9,10,21,28,29,31
14.6/ #5,9,13,19,21,31
10 14.7 Extreme Values and Saddle Points 14.7/ #13,19,29,33,35,43,45,62
11 14.8 Lagrange Multipliers 14.8/ #1,5,9,13,17,21,29
12 15.1 Double and Iterated Integrals Over Rectangles
15.2 Double Integrals over General Regions
15.1/ #7,11,13,18,23,27,29,36
15.2/ #1-8,12,15,18,23,29,35,38,43,53
13 15.3 Area by Double Integration
15.4 Double Integrals in Polar Form
15.3/ #6-8,16,18,21
15.4/ #1-6,9,11,16,23,25,28,35
14 15.5 Triple Integrals in Rectangular Coordinates 15.5/ #3,6,17,21,27,28,37,45
15 Catch up & Review  
16 15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.7/ #3-7,13-17,25,31,38,47,59,65
17 15.8 Substitution in Multiple Integrals 15.8/ #1,3,6,7,9
18 16.1 Line Integrals of Scalar Functions 16.1/ #1-9,14,15,25,26,29,35,36
19 16.2 Vector Fields & Line Integrals: Work, Circulation, Flux 16.2/ #3,7,11,14,15,18,25,27,29,30,35,39,40,57,59
20 16.3 Path Independence, Conservative Fields, Potentials 16.3/ #3,5,9,11,19,22,25,29,31
21 16.4 Green's Theorem in the Plane 16.4/ #2,5,9,13,16,17,21,29,31,37
22 Catch up & Review  
23 16.5 Surfaces and Area 16.5/ #1,7,11,13,15,27,41,43
24 16.6 Surface Integrals 16.6/#3,5,6,17,23,26,28,43
25 16.7 Stokes' Theorem 16.7/ #5,7,11,19,23,28
26 16.8 The Divergence Theorem & A Unified Theory 16.8/ #9,11,13,15,27,28
27 Catch up & Review  
28 Catch up & Review  


Exam Protocols

The exams will be administered on MyLab  on Mondays. Each midterm will be 50 minutes long, but the time window for accessing and completing the exam will be 9:00pm-11pm. The exams are open notes. Tablets, calculators, phones, or other electronic devices is not allowed during the exams.  

Midterm 1:  Monday, February 15

Midterm 2:  Monday, March 8

Midterm 3:  Monday, April 5

Midterm 4:  Monday, April 26

Final Exam: to be announced


MyLab - Online Homework

Students are required to purchase access to MyLab Math to complete the online homework, and possibly quizzes and exams. The MyLab assignments are similar to the exercises in the official list of HW exercises. (The official HW exercises are not handed in for grading but instead form a significant, but not exhaustive, portion of your study guide for the course.) Each assignment will have a specific due date set by the professor, and these assignments must be completed online.

How to use MyLab properly:
If you take shortcuts like trying to find answers to MyLab problems from various "homework help" web services without solving all of the problems yourself in their entirety, then your performance on exams will suffer. Instead, use the built-in help tools within MyLab. This online homework exists primarily to give you feedback on your ability to calculate correct answers at early stages of the learning process. The homework is not intended to measure your mastery of the material; only the midterm exams and final exam measure mastery. Without doing well on the exams, it is impossible to pass the course, even with a perfect score on the homework. So be sure to take full advantage of MyLab to get as much feedback as possible on your problem-solving skills.

Getting started with MyLab:

  • You will be able to access your MyLab course directly through your Canvas site for Math 251.
  • In your Canvas site, navigate to MyLab and Mastering and follow the on-screen instructions to create a Pearson account (or link an existing Pearson account) to your Canvas account.
  • You will automatically be enrolled in the MyLab course.
  • If you switch to a different section of Math 251, you can enroll in your new section's MyLab course by following these same instructions.

Student support for MyLab:

  • System Requirements
    MyLab works on a series of pop-up screens. You MUST enable pop-ups when working in MyLab. For help on how to do this, as well as make sure your browser is up to date, use the link above.
  • How to Use MyLab on a Mobile Device
    This video shows you how to set up your mobile device with any necessary browser add-ons and apps to use MyLab properly. 
  • Pearson Support Database
    Use the above link to search Pearson's database for support topics (e.g., resetting password).
  • Contact Support
    Use the above link to contact technical support. Fill out the required form and you will be immediately connected to a support agent based on your issue.
  • Pearson sales representative:
    Melissa Blum is our Pearson Sales representative. If you are having technical issues, please first contact Technical Support. If you are still having issues after contacting Technical Support, please email Melissa Blum with the Incident Number you received from working with Technical Support. You must have an Incident Number for Melissa to be able to help.

Other information about MyLab:

  • MyLab is an interactive, online homework system. The assignments follow the lecture topics.
  • Questions are algorithmically generated to give each student their own random versions of the questions.
  • After entering an incorrect answer, students are given helpful feedback and hints. Most exercises will also include learning aids, such as guided solutions and sample problems.
  • You have three attempts to get an answer correct. If you use all three attempts, you will be told the correct answer and given a new, random version of the same problem. There is no limit to the number of versions of a particular problem you can be given. So you are strongly encouraged to work on a problem until you get the correct answer. There is no penalty for the number of attempts taken.


Matlab Computer Labs

We will have some computer labs to show how technology facilitates the learning of certain calculus concepts. These were primarily designed for Matlab, since you can use the Rutgers license to download it for free. However, you may also use Maple or Mathematica to work on these assignmets. More information about them will be given during at the beginning of the Spring Semester.

Grading Weights

ComponentWeight -- 400 points total
Quizzes 30 points (7.5% of grade)
Reading Assignments 10 points (2.5% of grade)
Homework [MyLab] 40 points (10% of grade)
Computer Labs 20 points (5% of grade)
Midterm exams 50 points each, 200 total (12.5% each, 50% total)
Final exam 100 points (25% of grade)


Disclaimer: Posted for informational purposes only

This material is posted by the faculty of the Mathematics Department at Rutgers New Brunswick for informational purposes. While we try to maintain it, information may not be current or may not apply to individual sections. The authority for content, textbook, syllabus, and grading policy lies with the current instructor.

Information posted prior to the beginning of the semester is frequently tentative, or based on previous semesters. Textbooks should not be purchased until confirmed with the instructor. For generally reliable textbook information—with the exception of sections with an alphabetic code like H1 or T1, and topics courses (197,395,495)—see the textbook list.