2022/23 Undergraduate Module Catalogue

PHYS1300 Maths 2- Multivariable Calculus

10 creditsClass Size: 255

Module manager: Dr Julian Pittard
Email: J.M.Pittard@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2022/23

Pre-requisite qualifications

'A' Level Physics and Maths or equivalent

This module is not approved as a discovery module

Objectives

Series, including : l’Hopital’s rule, convergence of sequences and series, Taylor’s
theorem, Taylor and MacLaurin series, Introduction to Fourier series
Second order differential equations with constant coefficients, applications to
mechanics and simple harmonic motion
Multi-Variable calculus, including: partial differentiation, stationary points of multivariable
functions, multiple integration, multiple variable calculus in Cartesian, polar,
cylindrical and spherical coordinate systems
The ‘del’ operator including: the gradient of scalar fields, the divergence and curl of
vector fields, the Laplacian, the del operator in Cartesian, cylindrical and spherical
polar coordinate systems
Flux and the Divergence theorem including: the definition of flux across a surface,
evaluating flux through surface integrals, introduction to the Divergence theorem for
flux across closed surfaces

Learning outcomes
Manipulate numerical and other quantitative information, and apply manipulative skills to the solution of problems.

Skills outcomes
Basic mathematical skills in pure mathematics
Ability to solve differential equations
ability to model a physical problem

Syllabus

Series, including : l’Hopital’s rule, convergence of sequences and series, Taylor’s theorem, Taylor and MacLaurin series, Fourier theorem, Fourier series

Second order differential equations, including homogeneity, general solutions to homogeneous differential equations, particular integrals, applications to mechanics and simple harmonic motion


Multi-Variable calculus, including : partial differentiation, stationary points of multi-variable functions, multiple integration, multiple variable calculus in Cartesian, cylindrical and spherical polar coordinate systems

The ‘del’ operator including: the gradient of scalar fields, the divergence and curl of vector fields, the Laplacian, the del operator in Cartesian, cylindrical and spherical polar coordinate systems

Flux and the Divergence theorem including: the definition of flux across a surface, evaluating flux through surface integrals, the Divergence theorem for flux across closed surfaces

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	33	1.00	33.00
Private study hours			67.00
Total Contact hours			33.00
Total hours (100hr per 10 credits)			100.00

Opportunities for Formative Feedback

10 assignments.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	Regular coursework	20.00
Total percentage (Assessment Coursework)		20.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	80.00
Total percentage (Assessment Exams)		80.00

Students will have to complete an in-person exam at the end of the module. This will take place during the examinations period at the end of the semester and will be time bound. Students must submit a serious attempt at all assessments, in order to pass the module.

Reading list

The reading list is available from the Library website

Last updated: 08/02/2023

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