Undergraduate Course: Honours Differential Equations (MATH10066)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Availability  Available to all students 
SCQF Credits  20 
ECTS Credits  10 
Summary  Core course for Honours Degrees involving Mathematics.
Higher order linear equations; Laplace transform; Systems of First Order Linear ODEs; Nonlinear systems of ODEs; Fourier Series; Intro to 3 common PDEs; SturmLiouville Theory.
Skills: Symbolic manipulation, computer algebra, graphics, final project. Platform: Maple in computer labs. 
Course description 
See reading list below for relevant textbook.
Higher order linear equations (Chapter 4 (25p) 2h) in particular const. coeffs, as motivation for systems.
Laplace transform (Chapter 6 (50p) 4h) solving const. coeffs. ODEs, step functions, impulse functions, convolution.
Systems of First Order Linear ODEs (Chapter 7 (90p) 7h) solution using eigenpairs, solution of initial value problem, matrix exponential, homog. and inhomog. systems with const. coeffs.
Nonlinear systems of ODEs (Chapter 9 (90p) 7h) classification of 2x2 systems, phase trajectory and phase portrait. Saddle, centre, node and focus, linearisation, HartmanGrobmanTheorem, vanderPol system, trapping regions, periodic solutions, PoincareBendixson Theorem.
Fourier Series (Chapters 10.110.4 (50p) 4h) periodicity, orthogonality, convergence, even/odd.
Intro to 3 common PDEs (Chapters 10.510.8, (50p) 3h) Heat eq., Wave eq., Laplace's eq., initial and boundary conditions, separation of variables.
SturmLiouville Theory (Chapter 11, (60p) 5h) eigenfunctions, eigenvalues, orthogonality, eigenfunction expansions, boundary value problems, EulerCauchy ODE, completeness, selfAdjoint differential operators.
(total 32h listed)
Skills:
Use of a selection of basic Maple commands for symbolic manipulation for computer algebra and calculus; use of 2d and 3d Maple graphics; some applications in differential equations.
(total 10h)

Entry Requirements (not applicable to Visiting Students)
Prerequisites 
Students MUST have passed:
Several Variable Calculus and Differential Equations (MATH08063)

Corequisites  
Prohibited Combinations  
Other requirements  Students must not have taken :
MATH10033 Complex Variable & Differential Equations or
MATH09014 Differential Equations (VS1) 
Information for Visiting Students
Prerequisites  None 
Course Delivery Information

Academic year 2014/15, Available to all students (SV1)

Quota: None 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 35,
Seminar/Tutorial Hours 10,
Supervised Practical/Workshop/Studio Hours 10,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
138 )

Additional Information (Learning and Teaching) 
Students must pass exam and course overall.

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%, Examination 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)  Honours Differential Equations  3:00  

Academic year 2014/15, Partyear visiting students only (VV1)

Quota: None 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 35,
Seminar/Tutorial Hours 10,
Supervised Practical/Workshop/Studio Hours 10,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
138 )

Additional Information (Learning and Teaching) 
Students must pass exam and course overall.

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%, Examination 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)  Honours Differential Equations (Semester 1 Visiting Students only)  3:00  
Learning Outcomes
1. Higher order linear equations, in particular const. coeffs, as motivation for systems
2. Laplace transform , solving const. coeffs. ODEs, step functions, impulse functions, convolution
3. Systems of First Order Linear ODEs, solution using eigenpairs, solution of initial value problem, matrix exponential, homog. and inhomog. systems with const. coeffs.
4. Nonlinear systems of ODEs, classification of 2x2 systems, phase
trajectory and phase portrait. Saddle, centre, node and focus, linearisation, HartmanGrobmanTheorem, vanderPol system, trapping regions, periodic solutions, PoincareBendixson Theorem
5. Fourier Series , periodicity, orthogonality, convergence, even/odd
Intro to 3 common PDEs: Heat eq., Wave eq., Laplace's eq., initial and
boundary conditions, separation of variables.
6. SturmLiouville Theory: eigenfunctions, eigenvalues, orthogonality,
eigenfunction expansions, boundary value problems, EulerCauchy ODE,
completeness, selfAdjoint differential operators
7. Confidence using Maple to perform symbolic manipulation in computer
algebra and calculus; use of Maple graphics.
8. Investigate issues related to differential equations.
9. Experience of working on a small individual project in Maple and reporting on the outcomes.

Reading List
Elementary Differential Equations and Boundary Value Problems, Boyce
and DiPrima, Wiley
(continuing students should already have a copy from year 2). 
Additional Information
Graduate Attributes and Skills 
Not entered 
Study Abroad 
Not Applicable. 
Keywords  HDEq 
Contacts
Course organiser  Dr Joan Simon Soler
Tel: (0131 6)50 8571
Email: J.Simon@ed.ac.uk 
Course secretary  Mrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk 

