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