### MAS2104 : Introduction to Vector Calculus

• Offered for Year: 2015/16
• Module Leader(s): Dr Toby Wood
• Owning School: Mathematics & Statistics
##### Semesters
 Semester 1 Credit Value: 10 ECTS Credits: 5.0
##### Pre Requisites
Code Title
MAS1041Mathematical Methods A
MAS1042Mathematical Methods B
MAS1141Analytical Geometry and the Foundations of Differential Equations
MAS1142Modelling with Differential Equations

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#### Aims

To present the basic mathematical methods needed in the formulation of both physical and mathematical problems involving vector and scalar quantities in 3D space.

Module Summary

The development of mathematical representations of physical and thought models, and their solutions, requires some basic mathematical tools. This course (with MAS2105) introduces the various ideas that are needed in order to describe and formulate problems in three dimensions. Thus MAS2104 provides the important links between the calculus and (3D) vectors: the vector calculus.

#### Outline Of Syllabus

Vector Calculus: scalar and vector functions and fields; gradient, divergence and curl; spherical and cylindrical coordinates; curves, tangent vectors and review of line integrals; surfaces, normal vectors; surface and volume integrals; Gauss' and Stokes' Theorems.

#### Learning Outcomes

##### Intended Knowledge Outcomes

Students will know basic methods required to model scalar and vector fields in multidimensional space; they will know various ways to define such geometric objects such as curves, surfaces and volumes; they will know basic operators of vector calculus (gradient, divergence, curl, etc.); they will know the fundamental integral theorems (Gauss' and Stokes' theorems).

##### Intended Skill Outcomes

Students will be able to describe and analyse curves, surfaces and volumes, to perform rather complicated transformations of scalar and vector fields, and they will gain confidence in evaluating path, surface and volume integrals. They will be able to calculate the basic vector calculus, and to apply the fundamental integral theorems.

• Cognitive/Intellectual Skills
• Numeracy : Assessed
• Self Management
• Personal Enterprise
• Problem Solving : Assessed
• Interaction
• Communication
• Written Other : Assessed

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture61:006:00Problem classes
Guided Independent StudyAssessment preparation and completion111:0011:00Revision for unseen Exam
Guided Independent StudyAssessment preparation and completion11:301:30Unseen Exam
Scheduled Learning And Teaching ActivitiesLecture221:0022:00Formal lectures
Guided Independent StudyAssessment preparation and completion55:0025:00Written assignments and CBAs
Scheduled Learning And Teaching ActivitiesDrop-in/surgery61:006:00Drop-ins in the lecture room
Guided Independent StudyIndependent study51:005:00Assignment review
Guided Independent StudyIndependent study121:3021:30Studying, practising and gaining understanding of course material
Total100:00
##### Jointly Taught With
Code Title
MAS3104Introduction to Vector 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. Drop-ins are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. Office hours 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 Examination901A90unseen
##### Exam Pairings
Module Code Module Title Semester Comment
MAS3104Introduction to Vector Calculus1N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Written assignments and computer based assessments
##### Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. Coursework assignments (approximately 5 assignments of approximately equal weight) 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; this is thus formative as well as summative assessment. The coursework assignments may be written assignments, computer based assessments or a combination of the two, and in the case of combined assessments the deadlines for the two parts will not necessarily be the same.

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