Fall 2022 - MATH 251 D200

Calculus III (3)

Class Number: 4155

Delivery Method: In Person


  • Course Times + Location:

    Sep 7 – Dec 6, 2022: Mon, Wed, Fri, 8:30–9:20 a.m.

  • Exam Times + Location:

    Dec 14, 2022
    Wed, 8:30–11:30 a.m.

  • Prerequisites:

    MATH 152 with a minimum grade of C-; 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.


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 (D200) will have classes at the same time as section D100, MWF 8:30am-9:20am, but will meet in a separate venue. All sections, D100, D200, D300, will cover the same course topics and will have the same midterms and final exam. The Prime section (D200) will have an alternate set of weekly assessments. 

Three of our MATH faculty chat about this special lecture series in this Zoom-recorded meeting from 2020 - login with your SFU credentials (your computing ID without the @sfu.ca and your password).

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 Calc 3 Prime Questionnaire.

Students selected for these special lectures (Section D200) based on their questionnaires will be notified by e-mail prior to the first lecture. It is expected that prime students will maintain the high 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


  • 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.


This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient). 

Some workshop hours may be offered in virtual (Zoom) format. See your Canvas course for more details on workshop hours.



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


Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Registrar Notes:


SFU’s Academic Integrity website 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