UCEAP Differential Equations Course Description
School of Mathematics & Statistics, University of Glasgow
November 14, 2014
Course description
This 10 credit course 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.
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. 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.
Running over an eight-week period parallel with a separate 10 credit 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).
Learning goals and outcomes
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 a 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.
Specifically, at the end of the course a student will 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;
• understand the linearisation technique;
• classify singularities according to their stability;
• use differential equations as mathematical models.
Teaching style
There will be a mix of traditional lectures and ‘flipped’ classroom environment, with an emphasis
on independant learning on the part of the student. Students will be required to complete
reading and diagnostic quizzes in advance of attending classes.
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Prerequisites
Normally a student should have completed at least one semester of single variable calculus.
Corequisites
Students must be enrolled in both the UCEAP Linear Algebra and UCEAP Mathematical
Thinking & Communication courses.
Topics covered on weekly basis
The course will cover the following material with the numbering corresponding to the course
textbook.
• Chapter 1 — Introduction to Differential Equations (DEs)
– Definitions and Terminology (§1)
– Initial-Value Problems (§2)
– DEs as Mathematical Models (§3)
• Chapter 2 — First-Order DEs
– Solution Curves Without a Solution (§1)
– Separable Equations (§2)
– Linear Equations (§3)
– Solutions by Substitutions (§5)
• Chapter 3 — Modelling with First-Order DEs
– Linear Models (§1)
– Non-linear Models (§2)
– Modelling with Systems of First-Order DEs (§3)
• Chapter 4 — Higher Order DEs
– Preliminary Theory-Linear Equations (§1)
– Reduction of Order (§2)
– Homogeneous Linear Equations with Constant Coefficients (§3)
• Chapter 5 — Modelling with Higher-Order DEs
– Linear Models: Initial-Value Problems (§1)
– Linear Models: Boundary-Value Problems (§2)
• Chapter 8 — Systems of Linear First-Order DEs
– Preliminary Theory: Linear Systems (§1)
– Homogeneous Linear Systems (§2)
– Non-homogeneous Linear Systems (§3)
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• Chapter 10 — Plane Autonomous Systems
– Autonomous Systems (§1)
– Stability of Linear Systems (§2)
– Linearisation and Local Stability (§3)
The precise ordering of topics may be subject to change as appropriate.
Contact hours
In total there will be 28 contact hours comprising lectures, mini-lectures, problem sessions/
tutorials and guided learning. There will also be 14 optional ‘drop-in’ hours where students can
ask questions of lecturers and tutors. This will be shared between the three available UCEAP
Summer School courses (Linear Algebra, Differential Equations and Mathematical Thinking &
Communication).
Estimated/expected independant study and homework hours
For this course students should expect to work 9–10 hours per week independant of contact
hours. In total across the three courses of the UCEAP Summer School students should expect
to have a full 40 hour working week.
Reading lists (required)
Differential Equations with Boundary-Value Problems, International 8th Edition, Zill & Wright,
Cengage Publishers
(Please note: Textbooks are in general less expensive in the UK and furthermore we work together with the
publisher to secure the lowest possible prices for our students. The textbook will be available on campus to
purchase on arrival in both e-book and physical versions — please purchase the textbook after arriving in
Glasgow to ensure getting the correct version.)
Cost in UK = 50-60 GBP
Assessment information
50% final exam
20% handwritten weekly feedback exercises
20% e-assessed weekly assignments
10% engagement (based on participation and not grade acheived with weekly quizzes, pre-class work, peer
assessed participation in group work, etc.)
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