# 2020/21 Undergraduate Module Catalogue

## PHYS1300 Maths 2- Multivariable Calculus

### 10 creditsClass Size: 255

Module manager: Dr Thomas Moore
Email: T.A.Moore@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2020/21

### 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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Example Class 11 1.00 11.00 Office Hour Discussions 11 1.00 0.00 Lecture 22 1.00 22.00 Private study hours 68.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 101.00

10 assignments.

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment Assignment Assignments submitted during semester and work during examples classes 10.00 Online Assessment Online Mid-Term Assessment 30.00 Total percentage (Assessment Coursework) 40.00

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

Exams
 Exam type Exam duration % of formal assessment Online Time-Limited assessment 48 hr 00 mins 60.00 Total percentage (Assessment Exams) 60.00

Students will have to complete an online assessment 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. The assessment will not take 48 hours to complete, but students will have a 48 hour time period in which to complete it. Students are required to pass all assessments for this module in order to pass the module overall.

### Reading list

The reading list is available from the Library website

Last updated: 12/10/2020 15:48:24

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