MAS2801 : Vector Calculus
- Offered for Year: 2019/20
- 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. These tools are essential in many branches of applied mathematics, including fluid dynamics (MAS2803).
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 wave equations.
|Scheduled Learning And Teaching Activities||Lecture||25||1:00||25:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||1||6:00||6:00||Revision for class test|
|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||1||1:00||1:00||Class test|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||12||0:10||2:00||Office hours|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||6||1:00||6:00||Problems classes and drop-ins|
|Guided Independent Study||Independent study||1||22:00||22:00||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: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.
The format of resits will be determined by the Board of Examiners
|Written Examination||40||1||M||10||Class test|
|Prob solv exercises||1||M||5||Coursework assignments|
|Prob solv exercises||1||M||Computer based assessments|
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, therefore 40 minute) coursework test and the formative computer based assessments 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 assessments have a secondary formative purpose as well as their primary summative purpose.