IVLE8: [MA1506] Final Exam

• Q1(a) Separable equation.
• Q1(b) Building model from the last sentense: "Assume that ...".
  
• Q2(a) cos^2 x - sin^2 x = cos 2x
• Q2(b) Second Order Linear ODE with constant coefficients (IVP).
  
• Q3(a) First-order ODE.
• Q3(b) Logistic model and Harvesting model, with their equilibrium point B/s and beta_2 respectively.
  
• Q4(a) Use the equation in the hint, and move y'' to left-hand-side, then integrate twice, with initial value y(0)=0 and y'(0)=0. (Answer: PL^3/(3EI)? )
• Q4(b) Unit step function, same as past-year papers.
  
• Q5(a) Partial fraction.
• Q5(b) Complicated Laplace...
  
• Q6(a) You can do Laplace one by one, or do them together. (Similar to Tutorial 9 Q1, and the two methods can be find in A./P. Leung's solution and Official solution.)
• Q6(b) Complicated Markov... But you can solve it like this (can finish in less than 3 min)
  http://www.mediafire.com/?yjwbwb2myvj.
  After you learnt Advanced mathematics, don't forget the primary mathematics.
  
• Q7(a) Remember: trace = sum of eigenvalues. So easy to get the last eigenvalue.
• Q7(b) Similar to the tutorial questions.
  
• Q8(a) You have seen this question in Mid-term and tutorial already.
• Q8(b) The easiest part of this paper.

IVLE8: [MA1506] Is The Exam Difficult?

Dear all,

Many (>20) students have asked me about the answers of the exam in the recent two hours, so I wrote some hints here (maybe not correct, I did it in

http://jinchenyuan.blogspot.com/2008/04/ivle8-ma1506-final-exam.html.

I am afraid some of you have already threw your MA1506 Lecture notes and my tutorial notes into rubbish bin after you finish your last Math module in NUS.

I still want to recommend you some wonderful books, which are useless for MA1506 exam, but useful for you in the future.

1. For Electronic Engineering Students:
BOOK NAME: Laplace Transforms for Electronic Engineers.
AUTHOR: James G. Holbrook.
PUBLISH YEAR: 1959 (I think it may be as old as your parents, )

RECOMMEND REASON: Telling you why you are required to take the tough MA1506, and making you safely get a certification and a degree of NUS if you forget everything of MA1506 from now on.
Please notice that the appendix of the book (about 50 pages) is especially useful!
DOWNLOAD LINK: http://www.mediafire.com/?td4tjjctas2.

2. For Mechanical Engineering Students:
BOOK NAME: Mechanical Engineers Handbook.
AUTHOR: Dan B. Marghitu
PUBLISH YEAR: 2001

RECOMMEND REASON: You can find that what we learnt this semester is the appendix, and with these knowledge the whole handbook is not so difficult.
DOWNLOAD LINK: http://www.mediafire.com/?lwbmzhwpype.

3. For Chemical Engineering Students:
BOOK NAME: Mathematical Modeling. A Chemical Engineer's Perspective.
AUTHOR: Rutherford Aris
PUBLISH YEAR: 1999

RECOMMEND REASON: Containing many models you may meed in the future, so just copy or make some slightly change is enough.
DOWNLOAD LINK: http://www.mediafire.com/?1ypxutvm3mt.

4. For All of you, all the books in my web page (the general part and programming part):

• Handbook of Exact Solutions for Ordinary Differential Equations, Second Edition.pdf
• K.T. Tang - Mathematical Methods for Engineers and Scientists 1: Complex Analysis, Determinants and Matrices (2007).pdf
• K.T. Tang - Mathematical Methods for Engineers and Scientists 2: Vector Analysis, Ordinary Differential Equations and Laplace Transforms (2007).pdf
• K.T. Tang - Mathematical Methods for Engineers and Scientists 3: Fourier Analysis, Partial Differential Equations and Variational Methods (2007).pdf
• K. F. Riley, M. P. Hobson, S. J. Bence - Mathematical Methods for Physics and Engineering, 2nd Edition (2002).pdf
• T. V. Karman, M. A. Biot - Mathematical Methods in Engineering (1940).pdf
• Louis Lyons - All You Wanted to Know about Mathematics but Afraid to Ask. Vol. 1 (1995).pdf
• Louis Lyons - All You Wanted to Know about Mathematics but Afraid to Ask. Vol. 2 (1998).pdf
• Erwin Kreyszig - Advanced Engineering Mathematics (2007).pdf
• Erwin Kreyszig - Advanced Engineering Mathematics (2007) Slides.pdf
• Erwin Kreyszig - Advanced Engineering Mathematics (2007) Solution and Instruction.pdf
• David McMahon - MATLAB Demystified (2007).pdf
• Jaan Kiusalaas - Numerical Methods in Engineering with MATLAB (2005).pdf
• Sergey E. Lyshevski - Engineering and Scientific Computations Using MATLAB (2003).pdf
• L. F. Shampine, I. Gladwell, S. Thompson - Solving ODEs with MATLAB (2003).pdf
• H. J. Lee, W.E. Schiesser - Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB (2003).pdf
  
  

Wish you have a happy summer vacation, and enjoy your life in NUS.

Best wishes,

Chenyuan

IVLE8: [MA1506] Tutorial, Consultation and Modelling

Dear all,

(1) I hope you have already received my file "Review of MA1506 with Examples (Slides used in MA1506 IES seminar)":

http://www.mediafire.com/?duimiq1mndn.

I already find I have missed some parts in my review, I will add them soon, please visit the webfolder later:

http://www.mediafire.com/?sharekey=cc44311791b417eb8c9e7c56ba37815f1506690de66f732b.

(2) For the last tutorial, here are two files:

• Leung's Solution Slides for tutorial 11: http://www.mediafire.com/?d5nvcg3nfj4.
• Tutorial Notes 11: http://www.mediafire.com/?cl2fd4yzpjx.
  You can find the following things in the notes:
  The method to draw a Phase Plane Diagram.
  The questions appeared in the past-year paper but not in the tutorial.

(3) In the reading week, there are plenty of Consultation slots, and for my consultation slots, you can check here:

http://jin.chenyuan.googlepages.com/ma1506consultation.

Since I received 20+ consultation emails everyday recently, I changed one slot to the MSN / Email / Telephone consultation.

If you need consultation, please reserve BY FRIDAY (APR. 25). Any slot unreserved will change to MSN / Email / Telephone consultation:

• MSN: jin.chenyuan @ hotmail.com
• Email: jin.chenyuan @ gmail.com
• Office Telephone: 6516-8974

(4) I just found a book on Modelling from internet, share with you (password: math1506):

http://www.mediafire.com/?wst1ggqoero.

This book is an DJVU file, to open the book, you need the DJVU reader (WinDjView): http://sourceforge.net/project/showfiles.php?group_id=114927.

Best wishes,

Chenyuan

IVLE8: [MA1506] Some files for Tutorial 10, 11 and 12

Dear all,

Here are the A/P Leung's solution to tutorial 10, it contains some graphics of phase plane, with the meaning I explain this afternoon, you can understand what is phase plane:

• Leung's Solution Slides: http://www.mediafire.com/?ncyudud9mk1.
• Fibonacci sequence with some interesting examples and exercises (extract from the Bible of Computer Science): http://www.mediafire.com/?oduezcg9qdd.

We still have a tutorial next week (week 13), tutorial 11, that is really bad, here are the solutions to tutorial 11:

• Official solutions: http://www.mediafire.com/?wgz1x9mdaly.
• Ultimate solutions: http://www.mediafire.com/?zlmtdnhomjo.
• Tutorial notes 11 is still under revision.

If you can understand the solution from the above two files, do not suffer to come to my tutorial slot:) (of course, I will still be in the tutorial room, even there is only one student.)

In next Monday evening (14 April), I will give a seminar talk in LT3 (6pm-8pm), in which I will try to review the whole lecture notes of MA1506, with some examples. If you are interested, you can come. I think the audiences are all from MA1506 students. (I call it tutorial 12, ^_^)

I am now writing the notes for that seminar, if it is finished, I will upload it, and inform you by email.


Best wishes,

Chenyuan

IVLE8: [MA1506] Don't Be Fortune's Fool Like Romeo!

Dear all,

(1) A mistake:

I made a mistake in the ultimate solution 9 question 7, please forget the
explanation to why the rank is 2, just see my tutorial notes, that explanation
is clearer. Please check all the errors from the webpage:
http://jin.chenyuan.googlepages.com/ma1506errata.

(2) More about tutorial 9:

There is also a geometrical explanation to the last question of tutorial 9, why
the system does not have solution. (please note that in the tutorial notes
9, the explanation is algebraic, which is equivalent to geometrical one.):

• Geometrical Explanation to Question 7 can be found in the lecture notes.
  Usually, geometric meaning is much simpler to present, but algebraic meaning
  is much easier to follow.
• A./P. Leung's Solution Slides: http://www.mediafire.com/?9zninpcil2x.

(3) Solution packs of tutorial 10:

• Official Solution: http://www.mediafire.com/?1vpmud0i8m2.
• Ultimate Solution: http://www.mediafire.com/?b104lzicygj.
• Tutorial Notes: http://www.mediafire.com/?dpm42zlownd.
  This notes is just a review of chapter 6. Because I don't know what can be wriiten for this tutorial. The questions are not so difficult, if you practise enough, except for the diagonalization, which is difficult to express by words.

(4) Final exam (Consultation Schedule):

Wow, it is already tutorial 10! We are nearly killing all the tutorial bugs,
and the Final-Exam Monster is near at hand!

Some of you told me they can not understand the tutorial question, but they
were so quite in the tutorial. You need to solve your problem as soon as
possible! You can either come to my office or go to the consultation
room(E1A-03-06) in any consultation slots.

Here are the consultation schedule during the reading week:

• Science Consultation: http://www.mediafire.com/?ktkrdsj2dcd.
• Engineering Consultation: http://www.mediafire.com/?pglj2sjtjbm.
• My Consultation: http://jin.chenyuan.googlepages.com/ma1506consultation.

Don't be fortune's fool like Romeo, we need a happy ending of this module!

(5) Final exam (Past Year Paper with Solutions):

Well, here are two important passed year exam papers with their solutions:

1. 2006-2007 semester 2
   Problems: http://www.mediafire.com/?nvy5n9mynto;
   Solutions: http://www.mediafire.com/?w3zjaw1nl4w.
2. 2007-2008 semester 1
   Problems: http://www.mediafire.com/?cmh9d4a9gsw;
   Solutions: http://www.mediafire.com/?iigxjzzpnzv.

Best wishes,

Chenyuan

IVLE8: [MA1506] Tutorial Notes 8, Solution Packs 9, and Other Updates

Dear all,

(1) Here is the tutorial notes 8, I used in the tutorial this afternoon: http://www.mediafire.com/?iy4p3vyomin.


In this tutorial notes, you can find the following things, that can not be found anywhere:

• Skills, you need to be proficient in, of Chapter 5 and Chapter 6.
• Reference books for Chapter 5 and Chapter 6.
• Two different solutions to question 4.
• An systemetic approach to question 7.
• Comments and motivations of Tutorial 8 questions.

(2) Also, the solution to tutorial 9 is available in advance:

• Official solution 9: http://www.mediafire.com/?jiyz2zjmanm.
• Ultimate solution 9: http://www.mediafire.com/?jqxnexjozso.
• Tutorial notes 9: http://www.mediafire.com/?rjoijgjtmuu.

I know that you attend to numerous affairs everyday, so if you do not have time to look at the solutions and notes to tutorial 9, just leave it to me next week. :=)

For tutorial 9, it is not so difficult, I think I can finish it in half an hour.

Then for the rest time (about 20 minutes), you can ask me questions, or I can review Ch3 or Ch4 with the most important points for you. Of course, the choice depends on you.

(3) Other Updates:

• Lab 3: http://www.mediafire.com/?innmzxfumcq.
• Lab 3 solution: http://www.mediafire.com/?xtgfeg9czcs.
• A/P Leung's solution slides for tutorial 8: http://www.mediafire.com/?4ailohhdi3w.

Best wishes,

Chenyuan

IVLE8: [MA1506] Ultimate Solution 8 and the Latest Information on Final Exam

Dear all,

This is the link of Ultimate Solution to Tutorial 8: http://www.mediafire.com/?zduvkiz9jko.

After got the feedbacks from some of you, I decided to write the ultimate solutions to the rest of the tutorials, regardless of someone's remarks.

Ok, actually, this tutorial is not so difficult as the formers. If you are survived after the first three chapters, then you will have a bright future in front. Otherwise, catch up ASAP.


INFORMATION ON THE FINAL EXAMINATION:

1. The format of the examination: there are 8 questions, each question has two independent parts, and each part is worth 5 marks for a total maximum possible score of 80 marks.
2. ACCURACY is extremely important. You must write your answer clearly in the box provided for each part of a question and show your working clearly in the space provided after each part of a question. Anything which is not clearly written will be assumed to be wrong. Full marks for each part will only be given when both the answer and the working are correct. A small partial credit may be given if you are unable to get the correct answer but you can show that your working is essentially correct.
3. NO formulae list will be provided for this examination. Each student is allowed to bring into the examination hall ONE piece A4 size help sheet which must be HAND-WRITTEN (no photo copy or machine printing) and may be written on both sides. (Note: Two pieces with each piece written on one side only is NOT allowed.) Please include a short table of Laplace Transforms in your help sheet for your own use.
4. Remember to write your matriculation number (and NOT your NUSNET user-id) clearly in the space provided on the cover of the examination booklet.
5. Same policy on the use of calculators as in the mid term test.
6. Please check the module website at IVLE regularly to find the latest information on the examination.

Best wishes,

Chenyuan

IVLE8: [MA1506] Tutorial Notes 7 Part 2 (FAQ&Comments) and Tutorial 8 Official Solution

Dear all,

I have upload the second part of tutorial notes 7, This is the download link: http://www.mediafire.com/?n2m9h2zvdgz.

Like tutorial note 3, I hope ALL OF YOU have a look at this file before you starting to do the exercises of Laplace transform. The file contains the following things:

• FAQ. I hope it can clarify your misunderstanding about Laplace transfrom.
• Examples related to the tutorial questions and some other example.

There are some other materials been uploaded recently:

• Solution to Lab 2: http://www.mediafire.com/?lk0u9x24ajm.
• A/P Leung's slides for tutorial 7: http://www.mediafire.com/?jyaqypco94k.
• How to solve cubic equations (refer to tutorial 3 question 5): http://www.mediafire.com/?mscm2ndbmwa.
• Official solution to tutorial 8: http://www.mediafire.com/?yirzpy9zu00.

Have a good Friday!


Best wishes,

Chenyuan

IVLE8: [MA1506] Tutorial 7, Solutions and Notes

Dear all,

Here is the solution to tutorial 7:

Official Solution: http://www.mediafire.com/?9nztoytgwez.

Ultimate Solution: http://www.mediafire.com/?humgvwagohy.

Tutorial Notes: http://www.mediafire.com/?icyet2zmpmm, which contains the following things:

• Formula table of Laplace transform.
• Properties and theorems of Laplace transform.
• Extra Practise Exercises.

Unit Step Functions: http://www.mediafire.com/?atlg4tfmwtj. I also wrote a story to explain the meaning of "unit step function", if you have difficulties to understand and imagine what it is, you can have a look at the file.

One important thing, I want to remind you, is that: for this chapter, the tutorial questions are absolutely not enough. You need to practise a lot of exercises to have the sense of using given formulas to solve problems. Try some exercises when you have time or not have time.

Have a nice Friday and weekend!

Best wishes,

Chenyuan

IVLE8: [MA1506] Tutorial Notes 6 and Revision Slides

Dear all,

This is the tutorial notes 5: http://www.mediafire.com/?umdnjymnh13.

In this tutorial notes, you can find the following things that can not find in other files:

• Trickish skill to understand and remember the Physics formulas of chapter 3 section 7.
• The detail of tutorial question 5
• A different approach to question 5
• A different approach to question 6
• The detail of tutorial question 6 like lecture notes can be found in A/P Leung's tutorial slides: http://www.mediafire.com/?zndojvb2t5p.

Since, our final exam will cover so many chapters, it is time to start your revising. Actually, some have already started. That is a good news.

However, lecture notes is difficult to read, because there are little graphs to help you understand. You can have a look at the slides of Erwin Kreyszig's book "Advanced Engineering Mathematics" (9th Ed., 2007), which can be found here: http://www.mediafire.com/?yolmnmoznt2.

This slides are excellently made, if you want to have a look at the original book, it is here: http://www.mediafire.com/?22md4x1iidt. (The file is very big, 59.6M, it needs great patience to download it.) Moreover, the solutions and instructions to the book is also available: http://www.mediafire.com/?vuldida4nvi. The password is math1506.

If you have any question during your revision, just let me know.

Best wishes,

Chenyuan

IVLE8: [MA1506] Where is the Spam Folder

Dear all,

I hope you have seen my previous email. Some students asked me how to add me to the safe sender list these days. If the email shown in the picture below appeared in your inbox, just delete this email.

This is the answer:

First, open the “spam” folder (or called “junk email” folder) of your Email box. The following picture is an example of my NUS mailbox.

http://jin.chenyuan.googlepages.com/Spam01.JPG

Then, if you find my email in the folder, right click the email, and do a choice.

http://jin.chenyuan.googlepages.com/Spam02.JPG

Best wishes,

Chenyuan

IVLE8: [MA1506] Are you ready to HARVEST?

Dear all,

We continue to consider mathematical modelling this week. Here are some files uploaded recently:

Tutorial Notes 5: http://www.mediafire.com/?mwygfvzdyd9.

Official Solution 6: http://www.mediafire.com/?izzndajd9z7.

Ultimate Solution 6: http://www.mediafire.com/?cd2amzzntny.

The solution of tutorial 6 is greatly based on the lecture notes, I hope you are familiar with the following 3M: HARVEST MODEL; PLUG FLOW REACTOR MODEL; BALCONY MODEL. Otherwise, it is difficult to understand the questions even with their solutions.

If you have forgotten all of them, it does not matter. I will cover the most of the important points, and help you be ready to HARVEST.

However, harvest a good result in the final exam still needs your continuous effort. I have updated the consultation schedule, you can refer to: http://jin.chenyuan.googlepages.com/ma1506.

By the way, my e-mail account has been regarded as a spam mail sender by NUS, Gmail, Hotmail mailing systems.

• If you find this mail in the "Spam" folder / "Junk" folder, you can right click the mail, and choose "add sender to safe senders list".


• If you greatly agree with the mail systems, you can choose "add sender to the blocked senders list".

Last but the most important thing is: I protect all the reference books with password: "math1506", which you can download freely before. Now you need to enter the password: "math1506" before downloading.

OK. See you in the tutorial!

Best wishes,

Chenyuan

IVLE8: [MA1506] Extra Practise Exercises for Chapter 2 or Tutorial 4

Dear all,

I received many demands from your classmates these days. They want to do better in the final exam, and need extra practise exercises besides the tutorial.

Of course, one practise book is your text-book. it contains many exercises with answers. However, the book is expensive and very heavy. So, you can try the following books, which can be found from my web page: http://jin.chenyuan.googlepages.com/ma1506.

The exercises aim at Chapter 2 or tutorial 4. For chapter 3 and tutorial 5, it is really difficult to find some suitable books.



1) James C. Robinson - An Introduction to Ordinary Differential Equations (2004).pdf
Book: http://www.mediafire.com/?dowyv1190xj.
Solution: http://www.mediafire.com/?az9vdxxinn4.

For this book you can refer to the following sections: Part II. 13 Oscillations; Part II 15 Resonance.

Advantage of this book: The solutions are written in details, and Part I and Part II are exactly what you learnt in chapter 1 and chapter 2.



2) Steven G. Krantz - Differential Equations Demystified (2004).pdf
Book: http://www.mediafire.com/?fctynsnquxv.

For this book you can refer to the following sections: 2.5 Vibrations and Oscillations.

Advantage of this book: This book is straightaway, and you can easily understand what it is saying.



3) Richard Bronson, Gabriel Costa - Schaum's Outline of Differential Equations, 3rd Edition (2006).pdf
Book: http://www.mediafire.com/?5lyjtisvtjo.

For this book you can refer to the following sections: Chapter 14 Applications of Second-Order Linear Differential Equations.

This chapter match the tutorial questions very well, including the examples and the supplementary problems with answers.

For those who does not have a satisfactory mid-term result, and wants to have more practise exercises of ODEs, can have a look at this book (actually, this book is enough).
Alternatively, you can refer to my previous email here: http://jinchenyuan.blogspot.com/2008/02/ivle8-ma1506-tutorial-4-mid-term-and.html.

Advantage of this book: let you master the contents by examples and exercise.



4) Martin Braun - Differential Equations and Their Applications (1983).pdf
Book: http://www.mediafire.com/?2myzp55ssfn.

For this book you can refer to the following sections: 2.6 Mechanical Vibrations.

Advantage of this book: A famous, classic book, and clear written. Actually, many books are just copy the content of it.



5) K.T. Tang - Mathematical Methods for Engineers and Scientists 2: Vector Analysis, Ordinary Differential Equations and Laplace Transforms (2007).pdf
Book: http://www.mediafire.com/?a92fmxlmwxf.

For this book you can refer to the following sections: 5.6 Mechanical Vibrations; 5.7 Electric Circuits.

Advantage of this book: A dictionary, summarily introduce the contents you need. But not enough exercise.


Hope these books are enough for you and helpful. Enjoy the glamorous weekend without test!

Best wishes,

Chenyuan

IVLE8: [MA1506] Tutorial 5 and Mid-term Test Solutions

Dear all,

I hope you have finished all you mid-term test successfully.

Well, life goes on, and our tutorial goes on.

Here is the solution to tutorial 5:
Official: http://www.mediafire.com/?1eybbgonge8.
Ultimate: http://www.mediafire.com/?fenxycynjzp.

Another important link is: http://jinchenyuan.blogspot.com/2008/01/ivle8-ma1506-whats-new-today-update-by.html.
From this page, you can find the latest update of my site.

For the mid-term test, you can find the questions and solution here: http://www.mediafire.com/?vybunkxn5jz.

If you have any puzzles about the solutions, just let me know, and I will talk some questions in the tutorial.


Best wishes,

Chenyuan

IVLE8: [MA1506] Some Puzzles of Chapter 1

Dear all,

Here are some updating information in this week. All the contents are for the Mid-term Test.

Errata:

I found three typing errors in my tutorial notes and ultimate solutions, please have a look at this page (this page is updating when any error is found):

http://jin.chenyuan.googlepages.com/ma1506errata.

Students' Questions:

1) Some students can not understand the rule, used to find the particular solution to nonhomogeneous equations, which I mentioned in the tutorial and in tutorial notes , please have a look at the following file:

http://www.mediafire.com/?z4rziyvi3qw,
together with my tutorial notes 3:
http://www.mediafire.com/?3zbjdcljy2m.

Please remember: This rule can only applied to the equation with constant coefficients, and the right hand side is of the form:

(a) Polynomial
(b) Polynomial*e^(mx)
(c) Polynomial*sin(mx) or Polynomial*cos(mx)
(d) any linear combination of (a), (b) and (c)



For other cases,

(i) If the right hand side is not of the form (a) (b) (c) or (d), then first find the general solution y_h with right hand side being 0, then using the method of variation of parameters.

(ii) If the coefficients are not constant, we do not have effective methods to solve all the equations of variable coefficients, but for some special form we can solve it (for example Lecture notes example 25), you can find the solution here: http://www.mediafire.com/?8zwtvdgdggg.
(If you find a particular solution to the homogeneous one, you can use the method to reduce the order of the equation, and finally solve it.)

If these questions appear in the exam, I guess, the general solution to the homogeneous one will be given, then you need to use the method of variation of parameters to solve it!

(iii) If either the right hand side is not of the form (a) (b) (c) or (d), or the coefficients are not constant, then use the (i) and (ii).


2) How to solve the equation xy' = y - sqrt( x^2 + y^2 ), I mentioned a tip in tutorial notes 4.4.1, which is very important, and can be applied to this question:

http://www.mediafire.com/?unjd9tjtflb.

3) As Dr. Toh PC mentioned in his lecture, you can use Abel's identity to verify Wronskian, you can find details from wikipedia.org:

http://en.wikipedia.org/wiki/Abel_differential_equation.

4) More questions may be put into the web folder, if possible, please check it sometime later:

http://www.mediafire.com/?sharekey=cc44311791b417eb4012e8015643d9c82e81e8ebe912de5e.



By the way, NUS email system is not perform very well recently, this email is sent from IVLE, so do not reply directly.

If you need help, please use your NON-NUS email account to write to jin.chenyuan (a) gmail.com.

(If you send email to my NUS email account, I will not read your email instantaneously. There may be a delay, which is depending on my frequency "omega" of oscillation to check the email.)


With best wishes to you test!

Chenyuan

IVLE8: [MA1506] Tutorial Notes 4 and The Lecture Notes Problem

Dear all,

Here is the tutorial notes 4: http://www.mediafire.com/?3umwuz1cxzs.

For the Lecture notes Example 25, you can find the rules for Cauchy-Euler equation here: http://www.mediafire.com/?8zwtvdgdggg.

One question is why not to use the method of variation of parameters directly. The answer is the method is based on we know the general solution to the homogeneous problem, (that is, we need to know y1 and y2). So the rule in this file is to tell you how to find y1 and y2. Then you can use variation of parameters to solve it.

If you find any sentences or formula in my tutorial notes are difficult to understand, do not waste your time on thinking about it, and just send an email to me. Maybe that is just a typing error.


Best wishes,

Chenyuan

IVLE8: [MA1506] Tutorial 4, Mid-Term and Consultation

Dear all,


===================== Tutorial 4 ==============================

This is the solution to tutorial 4:
Official: http://www.mediafire.com/?evnz1yzamwt.
Ultimate: http://www.mediafire.com/?0ddhzxcifty.
Tutorial notes is in revision, and I will upload the notes in Friday evening. You can find the file in my web site: http://jin.chenyuan.googlepages.com/ma1506.

In this tutorial, we need some conclusions mentioned in the tutorial notes (chapter 2). You can also refer to the following book for this part.


===================== Mid-term ==============================


Next week is the recess week, and we do not have tutorial next week. After the recess, we are facing the mid-term. For the test, you must be familiar with all kinds of solutions mentioned in lecture notes or in my tutorial notes 2 and 3.

Besides the official practise exercises, you can also try the following excellent books (Some contents may out of syllabus, just ignore it)

1) James C. Robinson - An Introduction to Ordinary Differential Equations (2004)
Book: http://www.mediafire.com/?dowyv1190xj.
Solution: http://www.mediafire.com/?az9vdxxinn4.

You can try the following chapters and sections:
Part I: ch8, ch9, ch10(sec2)
Part II: ch12, ch14
Part III: ch19 (elective, just because your lecture notes example (chapter 1 example 25), detail in: http://www.mediafire.com/?8zwtvdgdggg.)


2) Martin Braun - Differential Equations and Their Applications (1983)
Book with answers to odd-numbered exercises:
http://www.mediafire.com/?2myzp55ssfn.

This book is a clearly written, rigorous introduction to differential equations and some excellent applications, which are just the sources of the headache word problems in the tutorial.

You can try the following chapters and sections:
Chapter 1: 1.1 - 1.8; and Chapter 2: 2.2 - 2.7


3) Steven G. Krantz - Differential Equations Demystified (2004)
Book: http://www.mediafire.com/?fctynsnquxv.

You can try the following chapters and sections:
1.7, 1.8, 1.9(elective), 2.1, 2.1, 2.3.


==================== Consultation =============================


For the face-to-face consultation information (time and venue), please refer to: http://jin.chenyuan.googlepages.com/ma1506consultation.

If you want to come, please write an email to me to reserve some slots in advance. Email Consultation is welcome everyday!


Also you can go to the public consultation slots, which is
1) in E1A-03-06
Monday, February 25, 2pm to 4pm,
Wednesday, February 27, 2pm to 4pm,
Friday, February 29, 2pm to 4pm.
2) in S16-04-35
Monday, February 25, 1pm to 3pm,
Wednesday, February 27, 3pm to 5pm,
Friday, February 29, 1pm to 3pm.


The recess week is coming. Relax and do not suffer too much about your mid-terms. Hope you have a nice week!

Best wishes,

Chenyuan

IVLE8: [MA1506] Important File, Tutorial Notes 3

Dear all,

I finished the revision of tutorial notes 3.

This is the link: http://www.mediafire.com/?3zbjdcljy2m.

I suggest all of you read this notes, together with tutorial notes 2 (http://www.mediafire.com/?3syl2ybzo2d).

The most important part is the RULE in tutorial comments for question 3.2(d).

As I mentioned in the tutorial, please DO NOT USE this rule in the exam, but FOLLOW this rule in the exam.

Best wishes,

Chenyuan

IVLE8: [MA1506] Solutions, Summarizations of ODE, and Consultation

Dear all,

Welcome back from CNY holiday! This is the information for the updating files:

Tutorial notes 2: http://www.mediafire.com/?3syl2ybzo2d.
(In the file, you can find the following materials: properties of sinh, cosh; history of ODE; Summarization of ODE part one)
Tutorial notes 3 is still under revision. I will upload the file this Friday evening, and you can find the download link form my web site: http://jin.chenyuan.googlepages.com/ma1506.

Tutorial solution 3:
Official solution: http://www.mediafire.com/?4v1mmay2ajy.
Ultimate solution (with more details): http://www.mediafire.com/?4eszbwxm9n4.

Till this week, we have already covered all the contents (Ch 1 and Tutorial 1,2,3) required in the Mid-term test, so hope you can start to prepare the test as soon as possible.
You can do the official practice exercises:
http://www.mediafire.com/?sharekey=cc44311791b417eb4012e8015643d9c89a160ea0f7e827c4,
and read your classmates' questions from here later (still empty now):
http://www.mediafire.com/?sharekey=cc44311791b417eb4012e8015643d9c82e81e8ebe912de5e.

Before the test, I plan to give you a whole day for consultation. The test is in Tuesday evening, and so I need your timetable to find a suitable schedule. I will discuss with you in the next tutorial (Tutorial 3 or Tutorial 4, depending on the time we left).

By the way, you will have your lab sections from week 5. Although I am not your lab tutor, someone asked me for solutions. So, I uploaded the solutions to lab exercises to the web site:
Lab 1: http://www.mediafire.com/?escumrzwnvn.
Solutions: http://www.mediafire.com/?dwigeidm9sl.


Best wishes,

Chenyuan

IVLE8: [MA1506] Ultimate Solutions to Tutorial 2

Dear all,

Lunar new year is coming, we do not have tutorial this Thursday and Friday.

I have finished writing out the ultimate solutions to tutorial two.

I hope you can solve all your problems in this "Old Year" ^_^, then have a good holiday.

So I uploaded the solution (Ultimate) to the web site, you can refer to the following link:

MA1506 Tutorial 2 Solutions.pdf: http://www.mediafire.com/?dmad9qmyjgj.

MA1506 Tutorial 2 Solutions (Ultimate).pdf: http://www.mediafire.com/?7zotdm1izyt.

Also, the tutorial notes for the first tutorial is available, and you can find the answer to the question that I proposed in the tutorial time. The link is http://www.mediafire.com/?8zgjyjuyjmk.

Enjoy yourself!

Best wishes,

Chenyuan