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 Activities
Lecture
20
1:00
20:00
Formal Lectures
Scheduled Learning And Teaching Activities
Lecture
2
1:00
2:00
Revision Lectures
Guided Independent Study
Assessment preparation and completion
37
1:00
37:00
Completion of in course assignments/ examination revision
Guided Independent Study
Independent study
41
1:00
41:00
Preparation time for lectures, background reading, coursework review
Total
100:00
Jointly Taught With
Code
Title
MAS1611
Multivariate 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 Examination
120
2
A
80
N/A
Exam Pairings
Module Code
Module Title
Semester
Comment
MAS1611
Multivariate Calculus and Differential Equations
2
N/A
Other Assessment
Description
Semester
When Set
Percentage
Comment
Prob solv exercises
2
M
20
Problem-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.
