# 2023/24 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** 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’stheorem, 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

4. Div, grad and curl

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 |

### 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 |

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.

### Reading list

The reading list is available from the Library websiteLast updated: 02/11/2023

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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