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PHY1029 : Multivariate Calculus and Differential Equations

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 use functions of many variables, learn a variety
of coordinate systems and learn how to solve simple differential equations.

Outline Of Syllabus

Partial differentiation: stationary points, chain rule.
Integration: Polar, spherical and cylindrical coordinates. Double integration; change of variables; line integrals.
Differential equations: Partial and ordinary; linear and non-linear; homogeneous and non- homogeneous. Solving ODEs: direct integration; separation of variables. First-order differential equations: separable, homogeneous and general linear. Second-order differential equations: Constant coefficients.

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 ActivitiesLecture12:002:00Assignment Laboratory
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class Test
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem 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
Guided Independent StudyIndependent study118:0018:00Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study52:0010:00Review of courseworkassignments and class test
Guided Independent StudyIndependent study44:0016:00Preparation for Coursework Assignments
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.

Assessment Methods

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

Description Length Semester When Set Percentage Comment
Written Examination1202A80unseen
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 assignments
Prob solv exercises2M10Course test
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. Written assignments, CBA's and an assignment laboratory of approximately equal weight (worth approximately 10% in total) and one class test (worth approximately 10% in total) allow the students to develop their problem solving techniques, to practise the methods learnt in the module and to receive feedback; this is thus formative as well as summative assessment.

Reading Lists