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; Non-linear systems of ODEs; Fourier Series; Intro to 3 common PDEs; Sturm-Liouville 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.
Non-linear systems of ODEs (Chapter 9 (90p) 7h) classification of 2x2 systems, phase trajectory and phase portrait. Saddle, centre, node and focus, linearisation, Hartman-Grobman-Theorem, van-der-Pol system, trapping regions, periodic solutions, Poincare-Bendixson Theorem.
Fourier Series (Chapters 10.1-10.4 (50p) 4h) periodicity, orthogonality, convergence, even/odd.
Intro to 3 common PDEs (Chapters 10.5-10.8, (50p) 3h) Heat eq., Wave eq., Laplace's eq., initial and boundary conditions, separation of variables.
Sturm-Liouville Theory (Chapter 11, (60p) 5h) eigenfunctions, eigenvalues, orthogonality, eigenfunction expansions, boundary value problems, Euler-Cauchy ODE, completeness, self-Adjoint 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)
Pre-requisites |
Students MUST have passed:
Several Variable Calculus and Differential Equations (MATH08063)
|
Co-requisites | |
Prohibited Combinations | |
Other requirements | Students must not have taken :
MATH10033 Complex Variable & Differential Equations or
MATH09014 Differential Equations (VS1) |
Information for Visiting Students
Pre-requisites | None |
High Demand Course? |
Yes |
Course Delivery Information
|
Academic year 2015/16, 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 2015/16, Part-year 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. Non-linear systems of ODEs, classification of 2x2 systems, phase
trajectory and phase portrait. Saddle, centre, node and focus, linearisation, Hartman-Grobman-Theorem, van-der-Pol system, trapping regions, periodic solutions, Poincare-Bendixson 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. Sturm-Liouville Theory: eigenfunctions, eigenvalues, orthogonality,
eigenfunction expansions, boundary value problems, Euler-Cauchy ODE,
completeness, self-Adjoint 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: |
Course secretary | Mr Brett Herriot
Tel: (0131 6)50 4885
Email: |
|
© Copyright 2015 The University of Edinburgh - 27 July 2015 11:35 am
|