# MATH20060 Calculus of Several Variables

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