# Modules

### MAS2801 : Vector Calculus

• Offered for Year: 2017/18
• Module Leader(s): Dr Toby Wood
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 1 Credit Value: 10 ECTS Credits: 5.0

#### Aims

To present the basic mathematical techniques needed to formulate and describe physical and mathematical problems involving vector and scalar fields in 3D space.

Module Summary
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 Poisson equations; heat and wave equations.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Tutorials in the lecture room
Guided Independent StudyIndependent study123:0023:00Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study33:009:00Review of coursework assignments and class test
Guided Independent StudyIndependent study26:0012:00Preparation for coursework assignments
Total100:00
##### Jointly Taught With
Code Title
PHY2026Vector Calculus
##### 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 studentsâ€™ 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.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A85N/A
##### Exam Pairings
Module Code Module Title Semester Comment
PHY2026Vector Calculus1N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Coursework assignments
Prob solv exercises1M10Course test
##### Formative Assessments
Description Semester When Set Comment
Prob solv exercises1MComputer 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) 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 are thus formative as well as summative assessments.