PHY2026 : Vector Calculus
- Offered for Year: 2017/18
- Module Leader(s): Dr Toby Wood
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semester 1 Credit Value:
To present the basic mathematical techniques needed to formulate and describe physical and
mathematical problems involving vector and scalar fields in 3D space.
Describing geometric objects and fields in multiple dimensions requires some basic mathematical
tools. This course (together with MAS2802) introduces the tools that are needed to apply calculus to
problems in three dimensions.
This module explains how we can mathematically define curves and surfaces in three-dimensional
space, and how we can calculate their properties, such as tangent, length and area. We also
introduce the concepts of scalar fields (e.g. temperature, pressure, density) and vector fields (e.g.
velocity and electromagnetic fields). To describe these objects and quantities we must generalize
the principles of calculus to multi-dimensions. This course introduces the mathematical language
and concepts that are needed to study continuous media, fluids, and electromagnetism.
Outline Of Syllabus
Scalar and vector fields; double and triple integrals; parametric representations of curves and
surfaces; tangent vector and line integrals; normal vector and surface integrals; differential operators
(gradient, divergence, curl, and Laplacian);
suffix notation and the summation convention; operators in spherical and cylindrical coordinates;
Gauss', Stokes' and Green's theorems; Laplace and Poisson equations; heat and wave equations.
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||3||1:00||3:00||Problem classes|
|Guided Independent Study||Assessment preparation and completion||1||13:00||13:00||Revision for unseen Exam|
|Guided Independent Study||Assessment preparation and completion||1||2:00||2:00||Unseen Exam|
|Scheduled Learning And Teaching Activities||Lecture||25||1:00||25:00||Formal lectures|
|Scheduled Learning And Teaching Activities||Lecture||1||1:00||1:00||Class test|
|Guided Independent Study||Assessment preparation and completion||1||6:00||6:00||Revision for class test|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||4||1:00||4:00||Tutorials in the lecture room|
|Guided Independent Study||Independent study||1||23:00||23:00||Studying, practising and gaining understanding of course material|
|Guided Independent Study||Independent study||3||3:00||9:00||Review of coursework assignments and class test|
|Guided Independent Study||Independent study||2||6:00||12:00||Preparation for coursework assignments|
Jointly Taught With
Teaching Rationale And Relationship
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving
general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the
theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow
students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an
opportunity for more direct contact between individual students and the lecturer.
The format of resits will be determined by the Board of Examiners
|Prob solv exercises||1||M||5||Coursework assignments|
|Prob solv exercises||1||M||10||Course test|
|Prob solv exercises||1||M||CBAs|
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments will consist of two written assignment of approximately equal weight. The coursework assignments, the (in class) coursework test and the formative CBAs allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback;these are thus formative as well as summative assessments.