MAS1609 : Algebra, Multivariable Calculus & Differential Equations (Inactive)
- Inactive for Year: 2024/25
- Module Leader(s): Dr Gerasimos Rigopoulos
- Lecturer: Professor Tamara Rogers
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Your programme is made up of credits, the total differs on programme to programme.
| Semester 1 Credit Value: | 10 |
| Semester 2 Credit Value: | 10 |
| ECTS Credits: | 10.0 |
| European Credit Transfer System | |
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
Complex numbers, arithmetic, Argand diagram, polar form, de Moivre's theorem, powers and roots of unity.
Vectors: sums, products (scalar, dot, cross), equations of lines and planes, orthogonality, norm.
Linear algebra: row operations, solution of linear equations, Gaussian elimination, matrix operations, determinants, inverting matrices, eigenvectors, quadratic forms.
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 Activities | Lecture | 9 | 1:00 | 9:00 | Synchronous On Line Material |
| Guided Independent Study | Assessment preparation and completion | 30 | 1:00 | 30:00 | Completion of in course assessment |
| Structured Guided Learning | Lecture materials | 36 | 1:00 | 36:00 | Non Synchronous Activities |
| Scheduled Learning And Teaching Activities | Workshops | 9 | 1:00 | 9:00 | Present in Person |
| Structured Guided Learning | Structured non-synchronous discussion | 18 | 1:00 | 18:00 | Non Synchronous Discussion to Support Learning |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 4 | 1:00 | 4:00 | Office Hour or Discussion Board Activity |
| Guided Independent Study | Independent study | 94 | 1:00 | 94:00 | Preparation time for lectures, background reading, coursework review |
| Total | 200:00 |
Jointly Taught With
| Code | Title |
|---|---|
| PHY1035 | Algebra, Multivariable Calculus & Differential Equations |
Teaching Rationale And Relationship
Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. In addition, office hours/discussion board activity will 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
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Written exercise | 1 | M | 30 | N/A |
| Written exercise | 2 | M | 10 | N/A |
| Written exercise | 2 | M | 60 | 2 hour in class test |
Assessment Rationale And Relationship
The course assessments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS1609's Timetable