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MATH20060

Academic Year 2026/2027

Calculus of Several Variables (MATH20060)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
2 (Intermediate)
Credits:
5
Module Coordinator:
Assoc Professor Marius Ghergu
Trimester:
Autumn
Mode of Delivery:
Blended
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This course introduces the calculus of functions of two or more real variables. The main topics of the module are: domain of definition and level sets of several variable functions, limits and continuity, partial derivatives, tangent planes to a surface, chain rule, second order derivatives, critical points, maxima and minima, constrained optimisation and Lagrange multipliers method, line integral, double and triple integrals, Fubini and Green's theorem, change of variables.

About this Module

Learning Outcomes:

The student will be able to - compute limits of multivariable functions - calculate partial and directional derivatives - find and use the linear and quadratic approximation of a function - find and classify critical points - optimise a function over a region or over a curve or surface-compute line integrals-evaluate double and triple integral with various methods.

The United Nations identified seventeen Sustainable Development Goals (SDGs) as core to the 2030 Agenda for Sustainable Development, and UCD contributes in general to SDG 4 Quality Education. Further SDGs explored within this module if relevant are listed below. A scale of 1 - 5 indicates the extent to which the SDG is covered.


 

Student Effort Hours:
Student Effort Type Hours
Autonomous Student Learning

70

Lectures

24

Tutorial

6

Total

100


Approaches to Teaching and Learning:
The teaching will take place on campus as per UCD guidelines. Full lecture notes and full solutions to tutorials will be made available on Brightspace to students who wish to follow the module remotely.




Requirements, Exclusions and Recommendations
Learning Requirements:

MATH10350


Module Requisites and Incompatibles
Pre-requisite:
MATH10350 - Calculus (MPS)

Incompatibles:
MATH20140 - Multivariable Calculus (Sci)., MATH20240 - Mathematics for Engineers IV, MATH20290 - Multivariable Calculus for Eng, MST20070 - Multivariable Calculus


 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade Component repeat (in-module) Offered
Exam (In-person): Final Exam that takes place in the exam session. End of trimester
Duration:
2 hr(s)
Standard conversion grade scale 40% No
60
No
Exam (In-person): Midterm Exam taking place in week 7 of the semester. Week 7 Standard conversion grade scale 40% No
30
No
Quizzes/Short Exercises: Online quizzes. Week 3, Week 5, Week 7, Week 9, Week 11 Standard conversion grade scale 40% No
10
No

As part of UCD's student support, under the Additional Consideration policy, extensions may be available for the following assessments in the module: Assignment (including essay/poster), Portfolio, Reflective Assignment, Report(s), and Individual Project.


Carry forward of passed components
No
 

Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Group/class feedback, post-assessment
• Online automated feedback

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Changhong Li Tutor
Sarah Murphy Tutor

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Autumn Lecture Offering 1 Week(s) - 1, 2, 4, 6, 8, 10 Fri 09:00 - 09:50
Autumn Lecture Offering 1 Week(s) - 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12 Mon 10:00 - 10:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Wed 10:00 - 10:50
Autumn Tutorial Offering 1 Week(s) - Autumn: Weeks 2-12 Wed 12:00 - 12:50
Autumn Tutorial Offering 3 Week(s) - Autumn: Weeks 2-12 Tues 14:00 - 14:50