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MT2503 Multivariate 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 2, 4, 7, 9, 11), Tue and Thu [Semester 1] 9.00 am Mon (weeks 1, 3, 5, 7, 9, 12), Wed and Fri [Semester 2]

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

Module coordinator

Dr A Naughton

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

Module Staff

S1: Dr Irene Kyza; Dr Tom Elsden S2: Dr Aidan Naughton

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 extends the basic calculus in a single variable to the setting of real functions of several variables. It introduces techniques and concepts that are used throughout the mathematical sciences and physics: partial derivatives, double and triple integrals, surface sketching, cylindrical and spherical coordinates. 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 MT1002. IF MT1002 HAS NOT BEEN PASSED THEN A AT ADVANCED HIGHER MATHEMATICS, OR A AT A-LEVEL FURTHER MATHEMATICS, OR A AT BOTH A-LEVEL MATHEMATICS AND A-LEVEL PHYSICS

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5-hours lectures (x 10 weeks), 1 tutorial (x 5 weeks), 1 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 key mathematical techniques in multivariate calculus (including Taylor series, gradients, partial derivatives, implicit differentiation, double and triple integrals)
  • Identify and apply appropriate mathematical techniques to solve problems in optimisation
  • Sketch areas and volumes in 3D space
  • Design computer code to investigate and analyse problems in multivariate calculus

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/

MT2503 Multivariate Calculus

Academic year

2025 to 2026 Semester 1

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 2, 4, 7, 9, 11), Tue and Thu [Semester 1] 9.00 am Mon (weeks 1, 3, 5, 7, 9, 12), Wed and Fri [Semester 2]

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

Module coordinator

Dr I Kyza

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

Module Staff

S1: Dr Irene Kyza; Dr Tom Elsden S2: Dr Aidan Naughton

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 extends the basic calculus in a single variable to the setting of real functions of several variables. It introduces techniques and concepts that are used throughout the mathematical sciences and physics: partial derivatives, double and triple integrals, surface sketching, cylindrical and spherical coordinates. 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 MT1002. IF MT1002 HAS NOT BEEN PASSED THEN A AT ADVANCED HIGHER MATHEMATICS, OR A AT A-LEVEL FURTHER MATHEMATICS, OR A AT BOTH A-LEVEL MATHEMATICS AND A-LEVEL PHYSICS

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5-hours lectures (x 10 weeks), 1 tutorial (x 5 weeks), 1 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 key mathematical techniques in multivariate calculus (including Taylor series, gradients, partial derivatives, implicit differentiation, double and triple integrals)
  • Identify and apply appropriate mathematical techniques to solve problems in optimisation
  • Sketch areas and volumes in 3D space
  • Design computer code to investigate and analyse problems in multivariate calculus

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/

MT2503 Multivariate Calculus

Academic year

2026 to 2027 Semester 1

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 2, 4, 7, 9, 11), Tue and Thu [Semester 1] 9.00 am Mon (weeks 1, 3, 5, 7, 9, 12), Wed and Fri [Semester 2]

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

Module Staff

S1: TBD S2: 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 extends the basic calculus in a single variable to the setting of real functions of several variables. It introduces techniques and concepts that are used throughout the mathematical sciences and physics: partial derivatives, double and triple integrals, surface sketching, cylindrical and spherical coordinates. 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 MT1002. IF MT1002 HAS NOT BEEN PASSED THEN A AT ADVANCED HIGHER MATHEMATICS, OR A AT A-LEVEL FURTHER MATHEMATICS, OR A AT BOTH A-LEVEL MATHEMATICS AND A-LEVEL PHYSICS

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5-hours lectures (x 10 weeks), 1 tutorial (x 5 weeks), 1 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 key mathematical techniques in multivariate calculus (including Taylor series, gradients, partial derivatives, implicit differentiation, double and triple integrals)
  • Identify and apply appropriate mathematical techniques to solve problems in optimisation
  • Sketch areas and volumes in 3D space
  • Design computer code to investigate and analyse problems in multivariate calculus

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 basic differentiation rules: product rule, quotient rule, chain rule. Hyperbolic functions & inverse hyperbolic function: graphs, derivatives, integrals & identities.
  • Power series, including Taylor series about an arbitrary point. Limits, continuity & differentiability of functions on one variable (definitions). L’Hopital’s Rule.
  • Revision of vectors and dot product. Functions of several variables, representation as surfaces, surface sketching, and limits of functions of several variables, continuity and differentiability for functions of two variables.
  • Partial derivatives, chain rule for functions of n-variables.
  • Implicit differentiation and contours, higher order partial derivatives, derivatives in n-dimensions, tangent planes
  • Taylor series for functions of two variables. Maxima and minima.
  • Directional derivative and gradient. Lagrange multipliers.
  • Revision of integration for functions of one-variable. Double integrals. Spherical and cylindrical coordinates. Triple integrals.

MT2503 Multivariate 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 2, 4, 7, 9, 11), Tue and Thu [Semester 1] 9.00 am Mon (weeks 1, 3, 5, 7, 9, 12), Wed and Fri [Semester 2]

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

Module coordinator

Dr A Naughton

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

Module Staff

S1: TBD S2: 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 extends the basic calculus in a single variable to the setting of real functions of several variables. It introduces techniques and concepts that are used throughout the mathematical sciences and physics: partial derivatives, double and triple integrals, surface sketching, cylindrical and spherical coordinates. 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 MT1002. IF MT1002 HAS NOT BEEN PASSED THEN A AT ADVANCED HIGHER MATHEMATICS, OR A AT A-LEVEL FURTHER MATHEMATICS, OR A AT BOTH A-LEVEL MATHEMATICS AND A-LEVEL PHYSICS

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5-hours lectures (x 10 weeks), 1 tutorial (x 5 weeks), 1 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 key mathematical techniques in multivariate calculus (including Taylor series, gradients, partial derivatives, implicit differentiation, double and triple integrals)
  • Identify and apply appropriate mathematical techniques to solve problems in optimisation
  • Sketch areas and volumes in 3D space
  • Design computer code to investigate and analyse problems in multivariate calculus

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 basic differentiation rules: product rule, quotient rule, chain rule. Hyperbolic functions & inverse hyperbolic function: graphs, derivatives, integrals & identities.
  • Power series, including Taylor series about an arbitrary point. Limits, continuity & differentiability of functions on one variable (definitions). L’Hopital’s Rule.
  • Revision of vectors and dot product. Functions of several variables, representation as surfaces, surface sketching, and limits of functions of several variables, continuity and differentiability for functions of two variables.
  • Partial derivatives, chain rule for functions of n-variables.
  • Implicit differentiation and contours, higher order partial derivatives, derivatives in n-dimensions, tangent planes
  • Taylor series for functions of two variables. Maxima and minima.
  • Directional derivative and gradient. Lagrange multipliers.
  • Revision of integration for functions of one-variable. Double integrals. Spherical and cylindrical coordinates. Triple integrals.