MATH20060 Calculus of Several Variables

Academic Year 2024/2025

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, linear approximation and tangent planes to a surface, chain rule, Implicit Function Theorem, second order derivatives, critical points, maxima and minima, constrained optimisation and Lagrange multipliers method.

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Curricular information is subject to change

Learning Outcomes:

The student will be able to - sketch a level set or multidimensional graph - compute limits of multivariable functions - calculate partial and directional derivatives - find and use the linear and quadratic approximation of a function - employ the Implicit Function Theorem - find and classify critical points - optimise a function over a region or over a curve or surface.

Student Effort Hours: 
Student Effort Type Hours
Lectures

24
Tutorial

6
Autonomous Student Learning

70
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.

Tutorials take place on Fridays every second week starting from week 3.


 
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 Open Book Exam Component Scale Must Pass Component % of Final Grade
Exam (In-person): Final Exam that takes place in the exam session. n/a Standard conversion grade scale 40% No

50
Exam (In-person): Midterm Exam taking place in week 7 of the semester. n/a Standard conversion grade scale 40% No

35
Quizzes/Short Exercises: Online quizzes. n/a Standard conversion grade scale 40% No

15

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
Firtina Kucuk Tutor
Matteo Lotriglia Tutor
Brian O'Sullivan Tutor