2005/06 Undergraduate Module Catalogue
PHYS2170 Vector Calculus and Partial Differential Equations
10 creditsClass Size: 125
Module manager: Dr P D Olmsted
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2005/06
Pre-requisitesPHYS2160 (Matrices and Vector Calculus) or equivalent
This module is not approved as an Elective
ObjectivesOn 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.
Mathematical SkillsMathematical Skills
- 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.
Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for informationLectures: 22 x 1 hour;
Examples classes: 11 x 1 hour.
Private studyHomework: 10 hours;
Study: 57 hours.
Opportunities for Formative Feedback3 assignments.
Methods of assessment
Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information1 x 2 hour examination at the end of the semester: 85%;
Marked assignments: 15%.
Reading listThe reading list is available from the Library website
Last updated: 19/04/2005
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