MAS1607 : Multivariable Calculus & Differential Equations
- Offered for Year: 2020/21
- Module Leader(s): Dr Paul Bushby
- Lecturer: Dr Magda Carr
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
| Semester 2 Credit Value: | 20 |
| ECTS Credits: | 10.0 |
Aims
To develop an understanding of ordinary differential equations and a familiarity with relevant solution methods. To introduce the calculus of functions of several variables.
Module summary
This module, which continues and extends the work of MAS1605, develops many of the ideas that are needed when constructing mathematical models of phenomena in the real world. Many such models are formulated in terms of ordinary differential equations, and this module introduces the methods that are needed to solve problems of this type. The world where we live is multi-dimensional - three-dimensional if we consider spatial dimensions alone, or four-dimensional if we treat time as another variable. It is therefore essential to develop tools to describe and model objects and processes that occur in multi-dimensional spaces. In order to do this we require multidimensional calculus. This module introduces the partial derivative, and the multiple integral, as well as power series in two or more variables.
Outline Of Syllabus
Introduction to ordinary differential equations (ODEs): terminology and examples.
First-order ODEs: separable equations, homogeneous equations, integrating factor. Existence and uniqueness of the initial value problem for first-order ODEs, singular points and integral curves of first-order ODEs.
Second-order ODEs: homogeneous equations with constant coefficients, particular integrals for inhomogeneous equations, method of reduction of order.
Introduction to functions of several variables: partial differentiation, gradient, chain rule and Jacobian matrices.
Taylor series in two (or more) variables, classification of stationary points.
Multiple Integrals: double and triple integrals, change of variables (including polar coordinates).
Teaching Methods
Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 9 | 1:00 | 9:00 | Synchronous On Line Material |
| Structured Guided Learning | Lecture materials | 36 | 1:00 | 36:00 | Non Synchronous Activities |
| Guided Independent Study | Assessment preparation and completion | 30 | 1:00 | 30:00 | Completion of In Course Assessment |
| Scheduled Learning And Teaching Activities | Small group teaching | 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 |
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. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. 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.
Student should consult their individual timetable for up-to-date delivery information.
Assessment Methods
Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.
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 | 60 | In Class Test |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Written exercise | 2 | M | 20 | N/A |
| Written exercise | 2 | M | 20 | N/A |
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/
- MAS1607's Timetable