Module: Calculus of Several Variables

Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title	Calculus of Several Variables
Module Code	MS221
School	School of Mathematical Sciences
Module Co-ordinator	Semester 1: Ronan Egan Semester 2: Ronan Egan Autumn: Ronan Egan
Module Teachers	Brien Nolan Ronan Egan
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

None
Array

Description

This module aims to ensure that students will have an understanding of the theory of the Calculus of Several Variables suitable for their studies in Physics. Where appropriate, theorems will be explained using arguments based on Physics rather than on formal mathematical proofs. Furthermore, it aims to develop students abilities to perform the calculations that arise in applications, especially in applications to Physics. Students will attend lectures on the course material and will work, independently, to solve problems on topics related to the course material. The students will have an opportunity to review their solutions, with guidance, at weekly tutorials. Students will be expected to work collaboratively to discuss and reflect on their learning.

Learning Outcomes

1. reformulate concepts from physics in the language of vector calculus
2. perform the calculations that arise when the calculus of several variables is used to solve problems
3. demonstrate an understanding of concepts by use of examples or counterexamples
4. state selected definitions and theorems

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	36	Students will attend lectures where new material will be presented and explained. Also attention will be drawn to various supporting material and tutorials as the course progresses.
Tutorial	12	Students will show their solutions to homework questions and will receive help with and feed-back on these solutions.
Independent Study	77	Corresponding to each lecture students will devote approximately one additional hour of independent study to the material discussed in that lecture or to work on support material when attention is drawn to such in lectures. Before each tutorial students will devote approximately three and a half hours to solving homework problems which are to be discussed in that tutorial.
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

VECTORS IN 3-SPACE
Vectors as directed line segments, their addition and scalar multiplication. Frames of reference and coordinates. The inner product, cross product and their applications.

FUNCTIONS OF ONE OR MORE VARIABLES
Parametrized curves. Level sets and their parametrizations.

DIFFERENTIAL CALCULUS
Limits, continuity, partial differentiation. The chain rule. The gradient, divergence, curl and their physical interpretations. Max/Min problems and Lagrange multipliers. Taylor's formula.

INTEGRAL CALCULUS
Line integrals, multiple integrals, surface integrals. The integral theorems. Change of variable formula for multiple integrals.

Assessment Breakdown
Continuous Assessment	50%	Examination Weight	50%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Loop Quiz	Loop quiz on standard calculus	10%	Week 3
Assignment	Homework assignment	10%	Week 5
Assignment	Homework Assignment	10%	Week 7
Written Exam	Terminal exam	70%	Week 9

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 1

Indicative Reading List

Finney, R. and Thomas, G.: 0, Calculus, Addison Wesley,

Other Resources

None

Programme or List of Programmes

AFU	Age Friendly University Programme
BSSA	Study Abroad (DCU Business School)
BSSAO	Study Abroad (DCU Business School)
HMSA	Study Abroad (Humanities & Soc Science)
HMSAO	Study Abroad (Humanities & Soc Science)
IESA	Study Abroad (Institute of Education)
IESAO	Study Abroad (Institute of Education)
PEM	BSc in Physical Education with Maths.
SE	BSc Science Education
SHSA	Study Abroad (Science & Health)
SHSAO	Study Abroad (Science & Health)

Date of Last Revision

18-JUN-08

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