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
- Fall 2021 Technology Requirements
- Lecture Topics
- MyLab - Online Homework
- Matlab Assignments
- Grading Weights
- Exam Protocols
- There is a Canvas course site for each lecture group where all grades, exam reviews, syllabus, etc., are posted. You can access your Canvas course at https://canvas.rutgers.edu/.
- Information for Instructors
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 (matlab 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|
|Lecture||Topic(s) and text sections||Suggested Homework|
|1||12.1 Three Dimensional Coordinate Systems
|2||12.3 The Dot Product
12.4 The Cross Product
|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
|8||14.3 Partial Derivatives
14.4 The Chain Rule
|9||14.5 Directional Derivatives and Gradient Vectors
14.6 Tangent Planes and Differentials
|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
|13||15.3 Area by Double Integration
15.4 Double Integrals in Polar Form
|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|
More details about the exams will be posted on this website as the semester progresses. In principle, the dates are:
Short Exam: Monday, September 27
Midterm 1: Monday, October 18
Midterm 2: Sunday, November 14
Midterm 3: Monday, December 6
Final Exam: TBA.
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: firstname.lastname@example.org
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.
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.
|Component||Weight -- 500 points total|
|Classwork||100 points (20% of grade)|
|Short Exam||40 points (8% of grade)|
|Midterm 1||60 points (12% of grade)|
|Midterm 2||90 points (18% of grade)|
|Midterm 3||60 points (12% of grade)|
|Final exam||150 points (30% of grade)|
Extra problems : if you have finished working on the practice exams and additional review material provided by your instructor, you may want to check this list of problems if you want to do additional practice problems. Some of these are more conceptual in nature, so they may be useful to enhance your understanding of the course material.
Respondus Practice : solutions to the respondus practice assignment
Material related to the September 27 Short Exam
- For this exam we will be usingRespondus. Typically it takes between 5 and 10 minutes for the authentication process to be completed before you can start working on the exam.
- For example, if you finish being authenticated by Respondus at 9:15 pm, then you would be done with the short exam at 9:50 pm, and then you would have 20 minutes (until 10:10 pm) to upload your work to the canvas site. On the other hand, if someone started the exam later and finishes being authenticated by Respondus at 9:35 pm, then you would be done with the short exam at 10:10 pm, and then you would have until 10:30 pm to upload your work to the Canvas site.
- We encourage everyone to start the exam process as soon as possible and email your professor immediately if you are running into any technological issues(loosing access to the exam because of poor internet connectivity, etc).
- Uploading your work and Academic Integrity:
The sections of the book for the Sep 27 short exam are:
- Section 12.1: Three-Dimensional Coordinate Systems
- Section 12.2: Vectors
- Section 12.3: The Dot Product
- Section 12.4: The Cross Product
- Section 12.5: Lines and Planes in Space
- Section 12.6: Cylinders and Quadric Surfaces
- Section 13.1: Curves in Space and their tangents
- Section 13.2: Integrals of Vector Functions; Projectile Motion
- Section 13.3: Arc Length in Space
Dear 251 student,
- This midterm will again use Respondus.
- We encourage everyone to start the exam process as soon as possible and email your professor immediately if you are running into any technological issues
- Uploading your work and Academic Integrity:
The sections of the book for the Oct 18 midterm are:
- Section 14.1: Functions of Several Variables
- Section 14.2: Limits and Continuity in Higher Dimensions
- Section 14.3: Partial Derivatives
- Section 14.4: The Chain Rule
- Section 14.5: Directional Derivatives and Gradient Vectors
- Section 14.6: Tangent Planes and Differentials
- Section 14.7: Extreme Values and Saddle Points