## 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.

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%.