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MT2506 Vector Calculus

Academic year

2025 to 2026 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 8

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

12.00 noon Mon (weeks 1, 3, 5, 7, 9, 12), Wed and Fri

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof D G Dritschel

Prof D G Dritschel
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Prof David Dritschel, Dr Stefania Lisai

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module introduces students to some of the fundamental techniques that are used throughout the mathematical modelling of problems arising in the physical world such as grad, div and curl as well as cylindrical and spherical coordinate systems. Fundamental theorems such as Green's Theorem, Stokes' Theorem and Gauss's Divergence Theorem will also be studied. It provides the foundation for many of the modules available in applied mathematics later in the Honours programme. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2503

Assessment pattern

2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 hours of lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examples class (x 5 weeks)

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Understand the geometrical meanings of gradient, divergence and curl
  • Determine appropriate basis vectors in a variety of common coordinate systems
  • Be able to differentiate basis vectors both in space and in time
  • Perform line, surface and volume integrals of vector-valued functions
  • Generate the directed surface area element for a general surface
  • Apply Stokes' and Gauss' theorems

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics please consult the School Handbook, at /mathematics-statistics/students/ug/module-choices-2000/

MT2506 Vector Calculus

Academic year

2026 to 2027 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 8

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

12.00 noon Mon (weeks 1, 3, 5, 7, 9, 12), Wed and Fri

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof D G Dritschel

Prof D G Dritschel
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

TBD

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module introduces students to some of the fundamental techniques that are used throughout the mathematical modelling of problems arising in the physical world such as grad, div and curl as well as cylindrical and spherical coordinate systems. Fundamental theorems such as Green's Theorem, Stokes' Theorem and Gauss's Divergence Theorem will also be studied. It provides the foundation for many of the modules available in applied mathematics later in the Honours programme. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2503

Assessment pattern

2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 hours of lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examples class (x 5 weeks)

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Understand the geometrical meanings of gradient, divergence and curl
  • Determine appropriate basis vectors in a variety of common coordinate systems
  • Be able to differentiate basis vectors both in space and in time
  • Perform line, surface and volume integrals of vector-valued functions
  • Generate the directed surface area element for a general surface
  • Apply Stokes' and Gauss' theorems

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics see our Module choices at 1000 and 2000 level page.

Syllabus

  • Revision of modulus, dot and scalar products (& derivation of cosine formula).
  • Grad and directional derivatives of a scalar field; calculation of div and curl of vectors, and curl curl of a vector; verification of identities for div and curl of (scalar times vector); div and curl in cylindrical coordinates; derivatives of unit vectors in spherical coordinates; identity div curl = 0.
  • Parametric line integrals in the (x,y) plane; potential function use in line integrals (result depends upon starting and finishing points only).
  • Surface integrals of: scalars in spherical coordinates; vectors (in cartesians) using the method of projection; vectors in cylindrical coordinates.
  • Green's Theorem in (x,y) with parametric integration; Stokes' Theorem in cartesian and spherical coordinates; Gauss' Divergence theorem in cartesian and cylindrical coordinates.