Module: Calculus of Several Variables

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Calculus of Several Variables
Module Code	MS205 (ITS) / MTH1035 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Thorsten Neuschel
Module Teachers	Martin Friesen
NFQ level	8	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination
Formal Exam

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

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 Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Group assignment	Continuous Assessment	20%	As required

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
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

None