## Topic outline

### Q-Review Lecture Recording

### General Information

**Lectures:**Tue 13:00-15:00 (Bancroft:Mason-LT), Wed 10:00-11:00 (Bancroft:Mason-LT)**Tutorials:**Wed 09:00-10:00 (G.O.Jones:UG1, tut

**02**), 11:00-12:00 (Maths: MB-204, tut**03**),12:00-13:00(Maths: MB-204, tut**06**);Thu 10:00-11:00 (Bancroft:1.02.6, tut

**04**), 11:00-12:00 (Bancroft:David Sizer LT, tut**01**),12:00-13:00(Eng:3.25, tut**05**);**Office Hours:**Wed 13:00-14:00 (Math Building 116), on lecture weeks (Week 1 to 6, 8-12)**Lecture Notes:**The full spring 2018 lectures are available for preparation prior to lectures. However, the lecture notes can be updated in term. Hand written lecture notes will be scanned and posted before 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. I encourage all students to start to learn and check your computational answers using MAPLE, Mathematica, MATLAB, etc. For example, there are free Mathematica licenses for students in QMUL. Click here for the QMUL Mathematica software webpage. Using these softwares is a fun practice and will help you to visualise your solutions. It will be very useful if you later plan to do UG or Master projects in math, physics, biology, finance and others fields using differential equations.You will do fortnightly individual submission of courseworks.

*Please write your names and student numbers as well as the tutorial group information (listed above: tut01, tut02, ... , tut06) on the solution front page.***Your solution has to be submitted and collected in****your corresponding tutorials.**I will announce the submission deadline in the beginning paragraph of each coursework sheet*.***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, 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 coursework submissions will count toward your engagement with the module; please see here.**Examinations:**The midterm test will take place in week 7. The final exam supposedly some time in Jan. There will be a revision lecture in week 12. Detailed information of how to prepare for both examinations will be provided in due time. Previous exam papers are available in QMPlus.Please note since 2018 fall term, we have big changes in exam forms of this module. In the exams before 2018, questions were mainly focused on solving differential equations. We would like to explain more examples and also how to draft your solutions in our lectures. This will be important for applying what you learned from this module in practice and for modules based on differential equations in your later study. Accordingly, students are also expected to be able to write down differential equations of real systems, sketch solutions of differential equations, state basic definitions and theorems, and etc. The concrete requirements will be explained during lectures as well as in the revision week (week 12).

**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.### Course work & Tutorial Timetable

Here is the time table of course work sheets for MTH 5123, 2019 Autumn. Any modification will be updated later in term.

There are in total 11 course work sheets. You do not need to submit anything for course work 0 and 10. For the rest 9 course work sheets, you will do 5 submissions, where you combine homework questions of every two course work sheets in one file and submit together. The deadline to submit your homework problems is given in front of each coursework sheet. Please only use this time table as a guideline.

Released Course work sheet (CW)

Tutorials to cover

Homework

Problems submission

Written feedback to pick up in tutorials

Week 1

CW0,1

no tutorials

No tutorials

No tutorials

Week 2

CW2

CW0,1

/

/

Week 3

CW3

CW2

/

/

Week 4

CW4

CW3

CW1+2

/

Week 5

CW5

CW4

/

CW1+2

Week 6

CW6

CW5

CW3+4

/

Week 7

Reading week, Midterm exam,

none

No tutorials

No tutorials

CW3+4, No tutorials, pick up from school office

Week 8

CW7

CW6

/

/

Week 9

CW8

CW7

CW5+6

/

Week 10

CW9

CW8

/

CW5+6

Week 11

CW10

CW9

CW7+8

/

Week 12

Revision week, none

CW10

CW9

CW7+8

There are no homework problems to submit in CW10.

Feedbacks of CW9, pick up from school office after week 12

### 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, Revision for Mid-term Exam

### Week Seven and Midterm Test

This is a draft guideline of our midterm test. It will be updated in time if changes made before the test.

The

**midterm test**for this module is on**Tue 5 November 2019 at 13:30**.**The test will last for 40 mins.**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__**If time allows, t**here will be a short revision**during our week6 lecture.**In this lecture we will discuss the range of topics covered on the midterm. You should prepare your questions before week 6 tutorials, if you have any difficulties about what our module content from week 1 to week 5. Please do come to week 6 tutorials to get help on exam preparation.**The test questions will cover material in lectures and (typed and scanned) lecture notes from week 1 to 5. 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 , as well as the coursework exercises.__Organisational details and what to expect__The midterm test counts 10% towards your final mark for this module.

**There will be 4 section of questions.****No calculator**is permitted in this examination. The unauthorised use of a calculator constitutes an examination offence. An appendix 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 will be released afterwards**: (237/261 took the test)**marks**0 - 10 11 - 20 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 81 - 90 91 - 100 **number of student**0 0 4 5 16 24 20 49 79 40 **PLEASE NOTE that midterm exam will be simpler than the final exam. Make sure that you can participate the midterm exam. Otherwise, your midterm results will be calculated as 0, and can maximum get 90% of the final grade based on your final exam. For details, please confirm with the school office.**### Week Eight

Autonomous Systems, Dynamical Systems, Phase portrait (sketching trajectories in phase plane with arrows on trajectories), Equilibria

This 10 mins video gives a good summary of our lectures from Week 8-10. Please watch this in advance and try to understand the details over next 3 weeks. Phase portrait sketching is very important and examinable in our final exam.

### 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.

This 10 mins video gives a good summary of our lectures from Week 8-10. Please watch this in advance and try to understand the details through our lectures between week 8 to 10. Phase portrait sketching is very important and examinable in our final exam.

### Week Ten

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

This 10 mins video gives a good summary of our lectures from Week 8-10. Please watch this in advance and try to understand the details through our lectures between week 8 to 10. Phase portrait sketching is very important and examinable in our final exam.

### 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 exam counts 90% towards your final mark for this module. The duration of the test will be 2 hours without further announcement. 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 will be provided some weeks before the exam (labeled 'Appendix')**.For your final exam, the marking criteria give credit both for (clearly explained) method and final answer.

**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 and additional exercises from the past finals.**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.