MAS1613 : Multivariable Calculus
- Offered for Year: 2024/25
- Module Leader(s): Dr Stuart Hall
- 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 2 Credit Value: | 10 |
| ECTS Credits: | 5.0 |
| European Credit Transfer System | |
Aims
To introduce calculus of functions of several variables
Module Summary
This module, which continues and extends the work of MAS1612, develops many of the ideas that are needed when constructing mathematical models of phenomena in the real world. 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 functions of several variables: continuity and differentiability, partial differentiation, gradient, chain rule and Jacobian matrices
Sketching multivariable functions and level sets - by hand and using software such as Python
Taylor series in two (or more) variables, classification of stationary points
Multiple Integrals: double and triple integrals
Change of variables (including use of polar, cylindrical and spherical coordinates)
The inverse and implicit function theorems
Exact differentials
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Class |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 5 | 1:00 | 5:00 | Drop-in sessions |
| Guided Independent Study | Independent study | 53 | 1:00 | 53:00 | Preparation time for lectures, background reading, coursework review |
| Guided Independent Study | Independent study | 15 | 1:00 | 15:00 | Preparation of in course assessment |
| Total | 100:00 |
Jointly Taught With
| Code | Title |
|---|---|
| PHY1041 | Multivariable Calculus |
Teaching Rationale And Relationship
The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.
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 |
|---|---|---|---|
| Multivariable Calculus | 2 | N/A |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 2 | M | 7 | Problem-solving exercise assessments |
| Prob solv exercises | 2 | M | 7 | Problem-solving exercise assessments |
| Prob solv exercises | 2 | M | 6 | Problem-solving exercise assessments |
Formative Assessments
Formative Assessment is an assessment which develops your skills in being assessed, allows for you to receive feedback, and prepares you for being assessed. However, it does not count to your final mark.
| Description | Semester | When Set | Comment |
|---|---|---|---|
| Aural Examination | 2 | M | Problem-solving exercise assessments |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.
Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.
The coursework assignments 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/
- MAS1613's Timetable