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PHY1029 : Multivariate Calculus and Differential Equations (Inactive)

  • Inactive for Year: 2020/21
  • Module Leader(s): Dr Gerasimos Rigopoulos
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semester 2 Credit Value: 10
ECTS Credits: 5.0


To lay the mathematical foundations for more advanced mathematics needed to describe
physical systems. Students will learn how to solve simple differential equations and how known computational tools of the calculus of functions of a single variable generalize to functions of many variables.

Outline Of Syllabus

A general introduction to differential equations: Partial and ordinary; linear and non-linear; homogeneous and non- homogeneous. First-order ordinary differential equations (ODEs): direct integration; separation of variables, homogeneous equations, general linear first order ODEs. Second-order linear ODEs: Constant coefficients, inhomogeneous equations. Partial differentiation of multivariable functions: stationary points, chain rule. Integration of multivariable functions: Double and triple integration, change of variables, polar, spherical and cylindrical coordinates.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture231:0023:00Formal lectures
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Guided Independent StudyAssessment preparation and completion12:002:00Unseen Exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class Test
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture61:006:00Problem classes
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Tutorials in the lecture room
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Guided Independent StudyIndependent study44:0016:00Preparation for Coursework Assignments
Guided Independent StudyIndependent study115:0015:00Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study52:0010:00Review of coursework assignments and class test
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. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. The small group tutorials allow students to improve their understanding of fundamental material and to develop mathematical presentation skills. Office hours 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.

Assessment Methods

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

Description Length Semester When Set Percentage Comment
Written Examination1202A80unseen exam
Written Examination402M10Class test
Exam Pairings
Module Code Module Title Semester Comment
MAS1603Multivariable Calculus and Differential Equations2N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M10Coursework assignment
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. One written assignment and one mid-semester class test allow the students to develop their problem solving techniques, to practise the methods learnt in the module and to receive feedback; this assessment has a secondary formative purpose as well as a primary summative purpose.

Reading Lists