Module Content

The module covers
  • Multiple Integrals (8 lectures),
  • Applications of Multiple Integrals (8 lectures),
  • Line Integrals and Green's Theorem (8 lectures),
  • and explains how these topics can be applied to
  • Computing areas and volumes, quantity surveying
  • concentration of electric charge on surfaces, moments of inertia (how easy it is to spin an object), epidemiology (probability density functions),
  • studying the work done by different forces as they cause objects to move through space.
----- Pre-requisite Knowledge. It is assumed that students have taken 1st year calculus courses in differentiation and Integration along with MA211, a course on multivariate calculus with vector calculus and differentiation. Of course, not all of you are in this category. Here are the key outcomes which you might need to refresh or catch up on. Some online problems in WeBWorK will be posted here soon to allow you practice these types of problem.
  • I variable Integration (concepts + basic computations)
  • 1-variable integaration (techniques - substitution, by parts ...)
  • Multivariate Calculus (graphs of functions f(x,y)->R describing surfaces)
  • Multivariate Calculus (partial derivatives)
  • Vector Functions

Module Coordinates

  • Lecturer: Kevin Jennings
  • Lectures: Mon 11, Tyndall theatre; Wed 11, Larmor
  • Tutorials: TBA
  • Recomended text: James Stewart 'Calculus' (same recommended text as all calculus modules in years 1-3)
  • Problem sheet: available here.
  • Module Website: Information and module documents will be posted to this site, which is linked from the Blackboard MA212 Multivariate Calculus - Integration pages. Blackboard will also be used for announcements and for posting grades.

Module Assessment

  • End of semester examination: 50%.
  • Continuous assessment: 30%.
  • Communications skills: 20%.
MA212 - Calculus II: Multivariate calculus - Integral calculus. The course is based on James Stewart's textbook. There are multiple copies in the library. We cover Chapters 15 and 16 of the 6th Edition. Specifically we cover the chapter on multiple integrals (double and triple integrals); we cover the section on applications of double integrals and we then cover the chapter on vector calculus. Assessment: 30% for continuous assessment (CA). We use webwork for this. Six assignments each worth 5 marks will be set. Typically students will have 2 or more weeks to complete each assignment. 50% will be the weighting of the final written exam in May. The questions on this exam will resemble those done in class or done in the CA homeworks.

Supplementary Material and News

A model paper is available here.

Clicker opinion polling may be used in some lectures.

Lecture Notes

Lecture Notes
(click on number)

Lecture Summaries
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.