Fall 2020 - MATH 251 D300

Calculus III (3)

Class Number: 2839

Delivery Method: Remote


  • Course Times + Location:

    Mo, We, Fr 8:30 AM – 9:20 AM

  • Exam Times + Location:

    Dec 12, 2020
    12:00 PM – 3:00 PM

  • Prerequisites:

    MATH 152; or MATH 155 or MATH 158 with a grade of at least B. Recommended: It is recommended that MATH 240 or 232 be taken before or concurrently with MATH 251.



Rectangular, cylindrical and spherical coordinates. Vectors, lines, planes, cylinders, quadric surfaces. Vector functions, curves, motion in space. Differential and integral calculus of several variables. Vector fields, line integrals, fundamental theorem for line integrals, Green's theorem. Quantitative.


This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable.

Math 251 D300 (Prime) Special Lectures

The Department of Mathematics is offering a section of MATH251 Calculus III which is designed for students who have shown mastery of the concepts covered in Calculus I and II and who are interested in lectures that present the ideas that go beyond the textbook basics. Many of these ideas show how the calculus naturally leads into many of the upper-division math courses. This special experience is designed for students whose plans include further math classes (MATH322, MACM316, MATH314 especially). Mathematics program majors and minors are especially encouraged to participate.

The prime section (D300) will have classes at the same time as section D100, MWF 8:30am-9:20am, but will meet in a separate venue. Both sections, D100 and D300, will cover the same course topics and will have the same midterms and final exam. The section D300 will have an alternate set of weekly assessments. Promotional video link

To participate in the Prime D300 lectures ...
1)  if you have a grade of A or better in MATH152, you may directly register into MATH 251 D300; or
2)  all others, who are not eligible for direct enrollment to the Prime lectures (including those from MATH155 & MATH158), must register for MATH251 D100 AND complete the following questionnaire. Questionnaire link

Students selected for these special lectures (Section D300) based on their questionnaires will be notified by e-mail prior to the first lecture, and informed about the (virtual) class location. It is expected that prime students will maintain the high D300 standards throughout the semester. Students in difficulty may be transferred to D100 without penalty

Topics covered 

Vectors and Geometry of Space:  
  • Three Dimensional Coordinate System 
  • Vectors 
  • The Dot Product 
  • The Cross Product 
  • Equations of Lines and Planes 
  • Cylinders and Quadric Surfaces

Vector Functions:  
  • Vector Functions and Space Curves 
  • Derivatives and Integrals of Vector Functions 
  • Arc Length and Curvature 
  • Motion in Space

Partial Derivatives:  
  • Functions of Several Variables 
  • Limits and Continuity 
  • Partial Derivatives 
  • Tangent Planes and Linear Approximations 
  • The Chain Rule 
  • Directional Derivatives and the Gradient Vector 
  • Maximum and Minimum Values 
  • Lagrange Multipliers and Constrained Maximum and Minimum Problems

Multiple Integrals: 
  • Double Integrals over Rectangles 
  • Iterated Integrals 
  • Double Integrals over General Regions 
  • Double Integrals in Polar Coordinates 
  • Applications of Double Integrals 
  • Triple Integrals 
  • Triple Integrals in Cylindrical Coordinates 
  • Triple Integrals in Spherical Coordinates 
  • Change of Variables in Multiple Integrals  

Vector Calculus:  
  • Vector Fields 
  • Line Integrals 
  • The Fundamental Theorem for Line Integrals 
  • Green's Theorem

Course Delivery

  •  Lecture: synchronous- lectures will be held at fixed times, on-line
  • Midterm(s): synchronous; date: TBA
  •  Final exam: synchronous; date: TBA


  • Quizzes 10%
  • Online Homework 5%
  • Midterm 1 17.5%
  • Midterm 2 17.5%
  • Final Exam 50%


Students should be aware that they have certain rights  to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to  the options discussed in class at the beginning of the semester.


  • Access to strong and reliable internet.
  • Ability to scan documents (phone app acceptable)
  • Access to webcam and microphone (embedded in computer sufficient)



Calculus: Early Transcendentals, 8th Edition Textbook, by James Stewart, packaged with Multi-term Enhanced WebAssign [Text + EWA/eBook]

*Please Note: If you have purchased the above package within the last 5 years, do not purchase again!

ISBN: 9781305597624

Registrar Notes:


SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html


Teaching at SFU in fall 2020 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112).