Global Opportunities

### PHY1029 : Multivariate Calculus and Differential Equations

• Offered for Year: 2022/23
• Available to incoming Study Abroad and Exchange students
• Module Leader(s): Dr Gerasimos Rigopoulos
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 2 Credit Value: 10 ECTS Credits: 5.0

#### Aims

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; 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 ActivitiesLecture201:0020:00Formal Lectures
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Guided Independent StudyAssessment preparation and completion371:0037:00Completion of in course assignments/ examination revision
Guided Independent StudyIndependent study411:0041:00Preparation time for lectures, background reading, coursework review
Total100:00
##### Jointly Taught With
Code Title
MAS1611Multivariate Calculus and Differential Equations
##### 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.

#### Assessment Methods

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

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
##### Exam Pairings
Module Code Module Title Semester Comment
MAS1611Multivariate Calculus and Differential Equations2N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M20Problem-solving exercises
##### Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignment allows 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 assessment has a secondary formative purpose as well as a primary summative purpose.