## 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 2023/24

### 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
Students will be able to demonstrate knowledge, understanding and application of:
1. Series
2. Second-order differential equations
3. Multi-variable calculus including different coordinate systems
5. Flux, surface integrals and the divergence theorem

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

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

Resists will be in standard exam format.

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.