Module: Calculus of Several Variables

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Calculus of Several Variables
Module Code	MTH1035 (ITS: MS205)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

Description

This module introduces students to the theory, practice and application of calculus of several variables. The module builds on the first-year modules on calculus of one variable. Students will learn how to differentiate and integrate functions of several variables, and how the interplay of differentiation and integration leads to the integral theorems. The module teaches essential know-how and skills to understand more advanced methods in analysis in general and in probability in particular.

Learning Outcomes

1. State selected definitions and theorems from the content
2. Prove (parts of) selected theorems
3. Demonstrate a mastery of the concepts of multivariate differential and integral calculus
4. Apply techniques of multivariate calculus to solve a wide range of problems

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	No Description
Tutorial	12	No Description
Independent Study	77	No Description
Total Workload: 125

Section Breakdown
CRN	11209	Part of Term	Semester 1
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Thorsten Neuschel	Module Teacher	Martin Friesen

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	Continuous Assessment	20%	As required
Formal Examination	End-of-Semester Final Examination	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	c,
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Topological properties of Euclidean Space and Continuity
Norms and scalar products, convergence, open and closed sets, compactness, continuous functions and properties

Differential calculus and applications
Gradient, directional derivative, total derivative, sum and product rules, chain rule, Taylor expansion, Lagrange method, optimization

Integral calculus and applications
Multivariate integrals and main properties, integral theorems

Indicative Reading List

Books:

J. Marsden and A. Tromba: 1996, Vector Calculus, Freeman,
S. Lang: 1987, Calculus of Several Variables, Springer,

Articles:
None

Other Resources

None