PHY1029 : Multivariate Calculus and Differential Equations
- Offered for Year: 2019/20
- Module Leader(s): Dr Gerasimos Rigopoulos
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
|Semester 2 Credit Value:||10|
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.
|Scheduled Learning And Teaching Activities||Lecture||6||1:00||6:00||Problem classes|
|Guided Independent Study||Assessment preparation and completion||1||13:00||13:00||Revision for unseen exam|
|Scheduled Learning And Teaching Activities||Lecture||23||1:00||23:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||1||6:00||6:00||Revision for class test|
|Guided Independent Study||Assessment preparation and completion||1||2:00||2:00||Unseen Exam|
|Scheduled Learning And Teaching Activities||Lecture||1||1:00||1:00||Class Test|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||4||1:00||4:00||Tutorials in the lecture room|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||12||0:10||2:00||Office hours|
|Guided Independent Study||Independent study||4||4:00||16:00||Preparation for Coursework Assignments|
|Guided Independent Study||Independent study||1||15:00||15:00||Studying, practising and gaining understanding of course material|
|Guided Independent Study||Independent study||5||2:00||10:00||Review 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.
The format of resits will be determined by the Board of Examiners
|Written Examination||120||2||A||80||unseen exam|
|Written Examination||40||2||M||10||Class test|
|Module Code||Module Title||Semester||Comment|
|MAS1603||Multivariable Calculus and Differential Equations||2||N/A|
|Prob solv exercises||2||M||10||Coursework 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.