Course Catalogue

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This course introduces general theory and methods for solutions covering: First and second

order differential equations, separation of variables, linear differential equations, systems of first

order equations, nonlinear differential equations and stability.

Running over an eight-week period parallel with a separate course on Linear Algebra, the

courses are divided into two four-week blocks with one-third of the material of this course being

covered in the first and two-thirds of the material being covered in the second (For the Linear

Algebra course the opposite is true). In total there will be approximately 29 contact hours comprising lectures, problem sessions/tutorials and guided learning.

Normally a student should have completed at least one semester of single variable calculus.

None

Students must be enrolled in both the Linear Algebra Summer School and Scotland, the City of Glasgow and the Origins of the Modern World courses.

Description of Summative Assessment: 

Assessment: Unseen examination (50%) 90 minutes exam paper consisting of 6 short written questions.  Course work consists of handwritten assignments (20%) and online assignments (20%); a further 5% will come from participation (as opposed to grades) in weekly quizzes and other assigned work, with a final 5% coming from oral assessment and presentation, including group work.

Reassessment: In accordance with the University's Code of Assessment reassessments are normally set for all courses which do not contribute to the honours classifications. For non honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students, and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions are listed below in this box.

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non-Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

Because of the timing of the summer school, there is no opportunity for reassessment to be timetabled within the same academic session.

The aim of the course is to give students a good basic understanding of the theory and methods

of finding solutions for differential equations and to introduce them to applications of differential

equations in modelling and stability problems. The course will provide both a comprehensive

foundation of basic differential equations theory and practice for a broad range of subjects in

Science & Technology. This is an opportunity for students to focus their efforts and accelerate

their learning over the summer vacation period.

The course will use a variety of traditional and computerised assessment methods to provide

regular feedback to both the students and tutors in order to both empower students to gauge

their progress and to customise the course to the their needs.

By the end of the course, students should be able to

_ find solutions to certain classes of linear differential equations;

_ find solutions to systems of linear differential equations using eigenvalues and eigenvectors;

_find solutions to certain classes of nonlinear differential equations;

_ apply the linearisation technique;

_ classify singularities according to their stability;

_ use differential equations as mathematical models.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.  The final grade for the course will

be comprised of 50% final exam and 50% continuous assessment. Students will be required to

have a passing grade in both halves of the course assessment in order to secure an overall pass.