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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Calculus of Several Variables & Fourier Anlys
Module Code MS244
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Ronan Egan
Semester 2: Ronan Egan
Autumn: Ronan Egan
Module TeachersRonan Egan
NFQ level 8 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

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. Infinite dimensional vector spaces, in teh context of Fourier Series, will be considered also. 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.

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 and apply selected definitions and theorems.
5. Calculate trigonometric Fourier Series of elementary functions defined on finite intervals and sketch the periodic extensions of such functions.

Workload Full-time hours per semester
Type Hours Description
Lecture42Students 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.
Tutorial18Students will show their solutions to homework questions and will receive help with and feed-back on these solutions.
Independent Study129.5Corresponding to each lecture students will devote approximately 1.5 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 to solving homework problems which are to be discussed in that tutorial.
Total Workload: 189.5

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 as directed line segments, their addition and scalar multiplication. Frames of reference and coordinates. The inner product, cross product and their applications.

Parametrized curves. Level sets and their parametrizations.

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

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

Function spaces. Orthogonal projections onto finite dimensional spaces. Calculation of Trigonometric Fourier Series, Bessel's inequality, Parseval's identity. Fourier Transforms.

Assessment Breakdown
Continuous Assessment50% Examination Weight50%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Loop Quizn/a10%n/a
In Class Testn/a20%n/a
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

    Other Resources

    Programme or List of Programmes
    APBSc in Applied Physics
    PANBSc Physics with Data Analytics
    PBMBSc Physics with Biomedical Sciences
    PHABSc in Physics with Astronomy

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