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MST20070

Academic Year 2025/2026

Multivariable Calculus with Applications (MST20070)

Subject:
Mathematical Studies
College:
Science
School:
Mathematics & Statistics
Level:
2 (Intermediate)
Credits:
5
Module Coordinator:
Dr Harriet Walsh
Trimester:
Autumn
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This module introduces the calculus of functions of two or more real variables.

Beginning with domains, graphs, level sets and limits of multivariable functions, the module covers partial derivatives, directional derivatives and gradient vectors. It then examines critical points and optimisation of multivariable functions, including constrained optimisation using Lagrange multipliers, and the topics of linear approximation and the differential. Finally, the module covers double integrals and line integrals of functions of two variables, and explores how these notions are related.

About this Module

Learning Outcomes:

At the end of this module, students should be able to
- sketch the domain, level sets and graph of a function of two variables
- compute limits of multivariable functions, or show they do not exist
- calculate partial derivatives and directional derivatives
- determine the direction of steepest ascent and tangent plane of a function at a given point
- find and classify critical points
- maximise or minimise a multivariable function, over its domain or over a curve or surface
- find and use the linear approximation of a function
- double integrals and line integrals of functions of two variables.

Student Effort Hours:
Student Effort Type Hours
Lectures

24
Tutorial

10
Autonomous Student Learning

70
Total

104

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning.

Requirements, Exclusions and Recommendations
Learning Requirements:

Students must have completed MST10010 or MATH10350 in order to be eligible to register to the module.

Learning Recommendations:

Students are strongly recommended to take a Linear Algebra course (MST10030 or equivalent) before taking this module.


Module Requisites and Incompatibles
Pre-requisite:
MATH10350 - Calculus (MPS), MST10010 - Calculus I

Incompatibles:
MATH20060 - Calculus of Several Variables, MATH20140 - Multivariable Calculus (Sci)., MATH20240 - Mathematics for Engineers IV, MATH20290 - Multivariable Calculus for Eng

Additional Information:
Pre-requisites: MST10010 OR MATH10350.


 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): Final in person exam End of trimester
Duration:
2 hr(s)
 Standard conversion grade scale 40% No
80
 No
Quizzes/Short Exercises: Continuous assessment in form of tutorial quizzes and mid-term test Week 3, Week 5, Week 7, Week 10, Week 12 Standard conversion grade scale 40% No
20
 No

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

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Ms Niamh Fennelly Tutor
Mr Nestor Garcia Cabrera Tutor
Sarah Murphy Tutor
Timothy O'Brien-Pifer 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) - Autumn: All Weeks Fri 09:00 - 09:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks 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 Tues 14:00 - 14:50
Autumn Tutorial Offering 2 Week(s) - Autumn: Weeks 2-12 Wed 09:00 - 09:50
Autumn Tutorial Offering 3 Week(s) - Autumn: Weeks 2-12 Wed 09:00 - 09:50
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