# 2005/06 Undergraduate Module Catalogue

## PHYS2170 Vector Calculus and Partial Differential Equations

### 10 creditsClass Size: 125

**Module manager:** Dr P D Olmsted**Email:** p.d.olmsted@leeds.ac.uk

**Taught:** Semester 2 (Jan to Jun) View Timetable

**Year running** 2005/06

### Pre-requisites

PHYS2160 (Matrices and Vector Calculus) or equivalent**This module is not approved as an Elective**

### Objectives

On completion of this module, students will be able to:- Convert vector field expressions from Cartesian to Polar, Cylindrical, and Spherical coordinates;

- Use the identities of vector calculus to simplify expressions;

- Evaluate integrals using the theorems of Gauss, Stokes and Green;

- Determine the Fourier series for a given function;

- Use the separation of variables technique to solve the wave equation in one dimension, Laplace's equation and the diffusion equation with appropriate boundary conditions;

- Use Fourier Series methods to solve partial differential equations of two independent variables.

**Skills outcomes**

Mathematical SkillsMathematical Skills

### Syllabus

- Scalar and vector fields; review of gradient, divergence and curl operators including various properties and identities. (Motivated by examples from fluid mechanics and electromagnetism). Review of line,surface and volume integrals.

- Integral theorems of Gauss, Stokes and Green; use of orthogonal curvilinear coordinates including spherical and cylindrical polars.

- Fourier's theorem, Fourier Series, orthogonality condition.

- Review of ordinary differential equations.

- Derivation of the wave equation in one dimension, Laplace's equation and the diffusion equation. Solution by separation of variables.

- Use of Fourier series to solve partial differential equations.

### Teaching methods

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

Lectures: 22 x 1 hour;Examples classes: 11 x 1 hour.

### Private study

Homework: 10 hours;Study: 57 hours.

### Opportunities for Formative Feedback

3 assignments.### Methods of assessment

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

1 x 2 hour examination at the end of the semester: 85%;Marked assignments: 15%.

### Reading list

The reading list is available from the Library websiteLast updated: 19/04/2005

## Browse Other Catalogues

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

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