## Topic outline

### General Information

**Lectures:**Tue 09:00-10:00 Arts2 LT, Fri 12:00-14:00 Peoples Palace:Skeel LT**Tutorials:**Mon 10:00-11:00 B.R.:3.02 (tut02), Tue 12:00-13:00 Bancroft 1.13 (tut03), Tue 12:00-13:00 Bancroft 3.26 (tut04), Wed 11:00-12:00 Peoples Palace:PP1 (tut05), Fri 14:00-15:00 Bancroft:3.26 (tut01)**Office Hours:**Tuesdays 10:00-11:00 in Queen's W310 and Fridays 14:00-15:00 in People's Palace Foyer on lecture weeks**Lecture Notes:**The full Spring 2018 lectures are available for preparation prior to lectures. Lecture notes will be scanned and posted at the end of each week. The scanned notes are to be used as a supplement to the typed notes.**Coursework:**Sheets will be released on this webpage in the week to which the exercises relate. The respective sheet will be discussed in the tutorials the week after. There will be eleven coursework sheets in total, including Revision Coursework 0.The problem denoted as Homework has to be solved by

*teams of 3 students*.*Please write all three names and student numbers as well as the tutorial group information (listed above: tut01, tut02, ... , tut05) on the solution front page.**Your solution has to be submitted and collected in your corresponding tutorials. The submission deadline is the start of your tutorial in the week after the**corresponding tutorial took place.***The last tutorials will take place in week 12.****Assessment:**Total credit for this course is 90% final examination + 10% mid-term test.**Marking Criteria:**You will be given written*feedback*on your coursework solutions, however marks will not be assigned to your submissions. Although the coursework does not contribute to your final mark, weekly practice and coursework submission for feedback is*essential*to your progress in the module, as well as your understanding of my expectations prior to the midterm and final exams.**Engagement**for this module will be monitored in line with the School's student engagement policy, in particular your weekly group coursework submissions will count toward your engagement with the module; please see http://qmplus.qmul.ac.uk/mod/book/view.php?id=443872&chapterid=39753.**Literature:**The typed lecture notes supplemented by the scanned notes are self-contained. For further insight and additional practice problems (with selected solutions), the textbooks on the reading list are recommended, all of which are available in the QMUL Library; please see the link above.All

**essential information**pertaining to this module will also be made available as a pdf file shortly.### Week one

Separable 1st-order ODEs, Reducible (to be separable) 1st-order ODE (z=ax+by+c)

### Week two

Reducible (to be separable) 1st-order ODE (z=y/x), homogenous 1st-order Linear ODE, inhomogenous 1st-order Linear ODE (Variation of parameter method), Exact 1st-order ODE

### Week Three

Initial Value Problem (I.V.P), Picard-Lindelöf Theorem (existence and uniqueness of the solutions of I.V.Ps of the 1st-order ODE)

### Week Four

Obtaining the general solutions to homogeneous 2nd-order ODEs (characteristic equations), I.V.P to 2nd-order ODEs ...### Week Five

Euler type equations, Variation of paramter method for inhomogenerous 2nd-order ODEs, Educated Guess Method.

### Week Six

Introduction to B.V.P. , theorem of the existence and uniqueness of solutions of B.V.Ps, first part of Green's function method

### Week Seven and Midterm Test

The

**midterm test**for this module is on**Mon 05 Nov at 14:00**in Arts2LT (Group 1) and Mason LT (Group 2). Specials are in Bancroft: 1.02.2 and 1.02.5. If you are not sure about the location of your exam, please confirm with the school office in Queen’s building.Please ensure that you bring with you your student ID card as well as a pen or pencil. Paper will be provided.

__Preparing for the test__**There was a revision hour on****Fri 02 Nov during lecture, for which the notes are posted below.**In this lecture we discussed the range of topics covered on the midterm and gave some additional computational exercises from past midterm tests for additional practice. Answers are appended to the end of the document and complete solutions are also provided below.The test questions will cover material in lectures and lecture notes from week 1 to 5 (with solutions to the Scanned Notes Week 5 - Fri exercises provided in the Scanned Notes Week 6 - Tue). Accordingly, the test will cover all coursework problems, Parts I, II and III, up to and including Coursework 5. The best way to prepare for the test is to understand all relevant methods and results in the scanned and typed lecture notes and revision hour, as well as the coursework exercises.

__Organizational details and what to expect__The midterm test counts 10% towards your final mark for this module. The duration of the test is 40 minutes. There will be four questions. They will be such that no calculator is needed, nor is any permitted in this examination. The unauthorised use of a calculator constitutes an examination offence. A formula sheet will be provided. Note no details of method part will be provided.

If you are a student with learning disabilities and have not done so already, please contact immediately the QMUL Disability and Dyslexia Service, see http://www.disability.qmul.ac.uk/. We cannot grant you special test conditions without official approval from this service. Also, please contact the school office by e-mail.

The

**statistics of the results is**:**marks**0 - 10 11 - 20 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 81 - 90 91 - 100 **number of student**3 6 11 17 31 58 47 33 19 4 **PLEASE NOTE that this midterm was marked very generously.**### Week Eight

B.V.P of 2nd-order ODE, Green's Function Method

### Week Nine

Linearisation of ODE systems, eigenvalues, eigenvectors, solving a system of two first-order ODEs (and I.V.P of this system ) by the eigenvalues and eigenvectors.

### Week Ten

Phase portraits: visualization of the trajectories (solutions) to a ODE system corresponding to different initial conditions around the equilibrium (fixed points)

Please note there are some updates in the scanned notes in Lecture 17 (the arrows in the coordinates were missing in previous version.)

### Week Eleven

### Week Twelve

In

**week 12**, we will cover remaining details from the typed notes and summarise the module content in review and preparation for the final exam.### Final Exam

The

**final examination**for this module will be on**Wed 15 May at 10:00**in TBA; specials will be in TBA. If you are not sure about the location of your exam, please confirm with the Maths School Office in Queen’s building.The final exam counts 90% towards your final mark for this module. The duration of the test is 2 hours. There will be five questions which are a combination of theory and application (i.e., proofs and calculations). They will be such that no calculator is needed, nor is any permitted in this examination. The unauthorised use of a calculator constitutes an examination offence. A formula sheet will be provided;

**the formula sheet that will appear on your final exam is provided below (labeled 'Appendix')**.For your final exam, the marking criteria give credit both for (clearly explained) method and final answer.

Please ensure that you bring with you your Student ID card as well as several pens or pencils and erasers. Paper will be provided.

__Preparing for the test__**There will be a Q-Reviewed Revision Lecture on****Thu 25 Apr 09:00-11:00 in G. O. Jones, for which the notes are posted below.**In this lecture we will discuss the range of topics covered from Week 7 onward in the module and give examples from past finals for additional practice. Solutions are outlined at the end of the scanned document.**Exam questions will cover material from Lectures, scanned and typed Lecture Notes and Courseworks from Weeks 1 to 12. Accordingly, the best way to prepare for this exam is to understand all relevant methods and results in the scanned and typed Lecture Notes, as well as**__all parts__of the Coursework exercises (Parts I, II and III) and additional exercises from the past finals.__Past Final Exams__**The exams below are meant to be used for additional practice only and do not necessarily reflect the exact content or emphasis of your final exam.**- No solutions will be made available for the 2014 and 2018 exams. These are for you if you want to test the ‘real thing’ without any safety net.
- For the 2015 and 2016 exams, solutions are available below. For the 2017 exam please see the revision lecture.
**More solutions (to Exams or Coursework exercises) will not be made available.**

**PLEASE NOTE:**Information about your final other than what is provided here and during the Revision Lecture will not be given out to students! Particularly, I will not give specific exam hints to single students via e-mail or otherwise. This would not be fair towards all the other students.