MAS1603 : Multivariable Calculus and Differential Equations
- Offered for Year: 2018/19
- Module Leader(s): Dr Paul Bushby
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
|Semester 2 Credit Value:||15|
To develop an understanding of ordinary differential equations and a familiarity with relevant solution methods. To introduce the calculus of functions of several variables.
This module, which continues and extends the work of MAS1601, 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 variation of parameters.
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).
|Scheduled Learning And Teaching Activities||Lecture||34||1:00||34:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||1||9:00||9:00||Revision for class test|
|Guided Independent Study||Assessment preparation and completion||1||19:00||19:00||Revision for unseen exam|
|Guided Independent Study||Assessment preparation and completion||1||2:30||2:30||Unseen exam|
|Scheduled Learning And Teaching Activities||Lecture||1||1:00||1:00||Assignment laboratory|
|Scheduled Learning And Teaching Activities||Lecture||1||1:00||1:00||Class test|
|Scheduled Learning And Teaching Activities||Lecture||3||1:00||3:00||Problem classes|
|Scheduled Learning And Teaching Activities||Lecture||3||1:00||3:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||4||1:00||4:00||Tutorials in the lecture room|
|Guided Independent Study||Independent study||1||34:30||34:30||Studying, practising and gaining understanding of course material|
|Guided Independent Study||Independent study||5||3:00||15:00||Review of coursework assignments and course test|
|Guided Independent Study||Independent study||4||6:00||24:00||Preparation for coursework assignments|
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. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.
The format of resits will be determined by the Board of Examiners
|Written Examination||40||2||M||10||Class test|
|Module Code||Module Title||Semester||Comment|
|PHY1029||Multivariate Calculus and Differential Equations||2||N/A|
|Prob solv exercises||2||M||10||Coursework assignments|
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments will consist of one written assignment (approximately 3%), one assignment laboratory (approximately 3%) and two computer based assessments (each approximately 2%). The coursework assignments and the (in class, therefore 40 minute) coursework test 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 are thus formative as well as summative assessments.