Exam 2012
Final Results
The final grades have been sent to the secretary.
I got the permission to display them here:
| |
10001 | C |
10002 | C |
10003 | C |
10004 | A |
10005 | E |
10006 | D |
10007 | C |
10010 | B |
10011 | E |
10015 | F |
10020 | B |
10021 | A |
10022 | A |
10023 | C |
10025 | B |
10026 | C |
10027 | B |
10029 | A |
10030 | C |
10031 | D |
10033 | F |
10034 | A |
10035 | C |
10037 | D |
10038 | C |
10039 | F |
10040 | C |
10041 | A |
10042 | B |
10043 | C |
10044 | A |
10045 | A |
10046 | B |
10049 | C |
10050 | C |
10051 | B |
10052 | A |
10053 | A |
10055 | C |
10057 | A |
Statistics
The statistics are as follows:
Congratulations to you all!!!
It has been a great pleasure for me to have you as student this year. I wish you a good continuation!
Solutions
Standard Mistakes
Some comments on the classical mistakes:
A Lagrange polynomial is a polynomial which is one at one of the interpolation points, and zero at the other ones; there is no such thing as a "interpolating Lagrange polynomial
many made a sign mistake for the Newton's method; Newton's method is (notice the sign in front of \(F(x_n)\): \[ F'(x_n) ∆x = - F(x_n) \]
To my surprise many did mistakes in 5b; in particular, many found solutions that were not defined for \(ε=0\), or even when \(ε\) converges to zero; this is incorrect: see the solution
by far the hardest question was 5c); only a few of you did it correctly; I have written a very detailed solution
Grading
The grading of the exam is finished, but you will have to wait for the final grade, because those grades have to be consolidated with the project grades. You should get your grade during this week though.
Statistics
Only one student has made an error-free exam.
Average points for each question (in percentage):
Question | Average (%) |
1a | 75 |
1b | 89 |
2 | 84 |
3a | 87 |
3b | 54 |
4a | 72 |
4b | 69 |
5a | 89 |
5b | 64 |
5c | 21 |
The exam will take place on Friday 08.06.2012, 15:00–19:00.
Exam Rules
The only printed material allowed is the official course book by Cheney and Kincaid.
The notes on the FFT algorithm will be printed out along with the exam sheet, so you do not have to take them with you.
No hand-written notes are allowed.
you are not allowed to write anything else than you name, anywhere in the book
you may mark pages with paper marks (lapper) without annotation or by dog-earings (eselører)
you may mark text in the book by underlining/highlighting it (understreking/overstreking)
Things to know for the exam
Fixed point theorem
Newton's method to find root of equations: how to use it in various cases, what are its limits
Fundamental theorem of interpolation: there is a unique polynomial of degree \(k\) which interpolates through \(k+1\) points
Lagrange polynomials
Neville formula: build an approximation polynomial from two other interpolation polynomials
Neville algorithm to compute the value of an interpolation polynomial without know the polynomial
Newton's divided differences
Interpolation Error formula: what it means, how to use it, what are its limits.
Interpret a log-log graph
Use Taylor's formula to show the order of a given approximation formula
Richardson's extrapolation algorithm
Gauss Elimination
Cost of Gauss Elimination
Gauss Elimination is equivalent to an LU decomposition
Iterative Methods: Jacobi and Gauss-Seidel methods
Linear fixed point methods
Two different formulae for integration: one quadrature formula and one integration formula
Be able to compute quadrature formula weights
Order of quadrature formula
Gauss Points
Be able to use the Fast Fourier Transform algorithm
Past Exams