DCU Home | Our Courses | Loop | Registry | Library | Search DCU

Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Calculus of Several Variables
Module Code MS205
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Thorsten Neuschel
Semester 2: Thorsten Neuschel
Autumn: Thorsten Neuschel
Module TeachersNil Venet
Martin Friesen
Thorsten Neuschel
NFQ level 8 Credit Rating 5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
Repeat examination
Formal Exam

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

Workload Full-time hours per semester
Type Hours Description
Lecture36No Description
Tutorial12No Description
Independent Study77No Description
Total Workload: 125

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

Assessment Breakdown
Continuous Assessment20% Examination Weight80%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Group assignmentContinuous Assessment20%As required
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
This module is category 3
Indicative Reading List

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

Programme or List of Programmes
ACMBSc in Actuarial Mathematics
AFUAge Friendly University Programme
BPMBSc in Psychology with Mathematics
BSSAStudy Abroad (DCU Business School)
BSSAOStudy Abroad (DCU Business School)
CAFMCommon Entry, Actuarial, Financial Maths
DSBSc in Data Science
HMSAStudy Abroad (Humanities & Soc Science)
HMSAOStudy Abroad (Humanities & Soc Science)
IESAStudy Abroad (Institute of Education)
IESAOStudy Abroad (Institute of Education)
SHSAStudy Abroad (Science & Health)
SHSAOStudy Abroad (Science & Health)
Date of Last Revision01-FEB-12

My DCU | Loop | Disclaimer | Privacy Statement