Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Calculus of Several Variables
Module Code	MS205
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Jason Quinn Semester 2: Jason Quinn Autumn: Jason Quinn
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This module introduces students to the theory, practice and application of calculus of several variables. The module builds on the first-year module 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 module content
2. Demonstrate understanding of selected definitions from the module content
3. Prove (parts of) selected theorems from the module content
4. Solve a wide range of problems from the module content

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	36	No Description
Tutorial	12	No Description
Independent learning	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

Differential Calculus.
Limits and Continuity; directional and partial derivatives; affine approximation and derivative; chain rule; higher derivatives; mean value theorem and Taylors theorem; determination of local maxima and minima; Lagrange multipliers; statements of inverse and implicit function theorems..

Integral Calculus.
Double integrals; Fubinis theorem; Jacobians and change of variables formula; triple integrals..

Integral Theorems.
Green's theorem; statements of the Gauss theorem and the Stokes theorem..

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Course Work Breakdown
Type	Description	% of total	Assessment Date
In Class Test	Class Test 1	12%	Week 5
In Class Test	Class Test 2	13%	Week 11

Reassessment Requirement
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