Numerical and computational methods with Python by

Office hours

2023-10-19 21:05:38 UTC

Hi, I can’t find the office hour information.

Can you check what is wrong with my code please ? This is from the last lecture in Week 4.

2023-10-20 16:51:33 UTC

Practical 2 Hand-in

2023-10-20 21:00:38 UTC

I noticed in the Practical 2 paper, it mentions, 'Please hand in your answers to Questions 1, 4, 7, and 11 before the start of the practical.'

Could you provide some clarification on the process for this? Should we print out the .ipynb file or handwrite our answers?

Section 2.5

2023-10-21 13:15:02 UTC

I copied the notes, however I get that "x0" is not defined. Can you see what is wrong with my code?

Also, is it "safe" to import all the codes from the mpmath package as *? Here I used the code "import mpmath as mp" instead.

page 36

2023-10-21 15:07:38 UTC

For the matrix A, where did the summation over j go? As there are still indices in j for f_j(x_i)

Lecture notes p44.

2023-10-22 13:08:46 UTC

Hi, I am quite confused about the equation (4.20) where it says ‘by combination’. Would you please explain how this combination is taken out? Thank you.

class test scope

2023-10-23 10:24:06 UTC

Hi, may I ask which weeks will be covered in class test ?

Class Test Practice

2023-10-23 20:00:01 UTC

Hello, could you please provide us with questions from previous years’ class tests and their solution in order to help with our preparation?

Thank you very much in advance!

Week 3 content

2023-10-24 16:37:35 UTC

I didn't understand the secant method or Bisection method when we went through it in the lectures. Is there any resources you would recommend for a better understanding?

2023-10-25 13:45:30 UTC

where is the google colab notebook where we did the algorithm for fitting ?? i believe it was possibly lecture 8

Chebyshev points

2023-10-25 22:48:42 UTC

Please can you share the google collab notebook named lagrange polynomials from the lecture of Tue Oct 17? I cannot seem to see it on KEATS.

Practical 2 Solutions

2023-10-30 13:05:40 UTC

Please could you upload the answers to the practical 2 sheet?

Final Exam

2023-11-02 16:36:05 UTC

Hi, what will be on the final exam? Or is that dependent on what is covered in class. Thanks

Class Test

2023-11-06 11:25:02 UTC

Can you please upload class tests from previous years with solutions please ? Thank you.

Possible typo in the secant method

2023-11-07 16:38:54 UTC

Hello, I was doing exercise 5 in the lecture notes, and I was using the secant method which gave me the wrong answer (I believe that the top is supposed to be the $x_{n-2}$ term minus the $x_{n-1}$ term. the secant method in the notes is different from the one on wikipedia (which gives the right answer). https://en.wikipedia.org/wiki/Secant_method

Class Test Information

2023-11-08 10:58:32 UTC

hi, I wanted to ask if we will have access to any material for the class tests on 13h December. Like will we be given a cheat sheet or something

Week 4 coding sheet

2023-11-08 11:29:32 UTC

Hi, I can't find the google colab notebook for week 4 (Fitting Data). Am I missing something?

Coding Practice

2023-11-08 13:52:00 UTC

Could you post the coding practice for the class test as mentioned at the start of Tuesday's lecture?

Tutorial 2

2023-11-09 16:24:32 UTC

Hi, I can't find the tutorial sheet 2 on the webpage, would you check that?

Problem Sheet Release

2023-11-11 17:32:50 UTC

Good evening,

The problem sheet for Week 7 is yet to be released (Saturday 17:30) and there are several tutorials for this on Monday. Could all the Problem Sheets and Practical Sheets be released at latest Friday after the lecture so that we have proper time to prepare.

Thankyou

2023-11-11 17:55:30 UTC

Could you clarify what an "order-1 number" is?

2023-11-14 13:05:39 UTC

Can you upload the coding practice soolutions please

My tutor has not showed up twice for the tutorial on Monday 10-11am. Is there any way to solve this ?

2023-11-14 13:10:46 UTC

I believe there is nothing wrong with my code, but why do I get a different answer for the matrix A inverse

2023-11-14 19:05:39 UTC

Coding practice and class test

2023-11-15 13:08:22 UTC

Hi, how similar is the coding practice uploaded going to look to the actual class test. Can it been looked at as a mock class test? Also what is the scope of the class test(what weeks will be covered)?

practical 2 q11

2023-11-16 11:02:55 UTC

why do we write ys=[0,3,-2,-5,3], where do these numbers come from?

week 4 not available

2023-11-16 11:49:48 UTC

it's no longer possible to mark the interim feedback as done and hence I cannot access the week 4 material. is it possible to change this so the content is made available? thank you.

2023-11-17 11:11:18 UTC

Could you link the python code for the lecture on 14 November. The recording does not show the python part of the lecture

Thank you

exam material

2023-11-18 01:17:12 UTC

Hi, I notice that there are video lecture about Monte Carlo integral under week 7 which is not covering in lectures, will these content appear in exam or will these be covered in later lecture?

Coding practice class test

2023-11-19 18:26:51 UTC

What weeks will be assessed for the class test please ?

2023-11-19 23:52:17 UTC

Can you tell me what is wrong with this please. This is Q5 of the coding practice sheet

handwritten notes

2023-11-20 10:19:15 UTC

Hi, could you upload the handwritten notes from week 7 please? it would be really helpful. Thank you

Class Test

2023-11-21 15:41:26 UTC

Hi professor, can I ask how many questions will be in the class test please?

Could you please post the code in the lecture please ? for the Monte Carlo section

2023-11-21 16:06:01 UTC

Code from Lecture Monte Carlo

2023-11-21 16:38:40 UTC

Hi, I think you uploaded the link for Gaussian Quadrature code rather than Monte Carlo code in the 'code from lecture'

Monte Carlo Code

2023-11-21 16:47:52 UTC

For anyone can't find the code, I just found them.

How do I change the color of the dots from orange and blue to other colours ?

2023-11-23 12:14:10 UTC

For the Class test, do we have to memorize the approximations for Trapezoid, Midpoint and Simpson's rules ? or will it be given.

2023-11-23 14:37:24 UTC

Hi, I still do not get how combining both equations can lead to that expression for Richardson extrapolation, please explain

2023-11-23 15:34:59 UTC

Cheat sheet details

2023-11-26 14:24:51 UTC

Hi can you please share the details of the cheat sheet

Gaussian integration

2023-11-27 20:17:38 UTC

If we have 2n+2 free parameters then how does that relate to m =0,1 .....,2n+1 for x^m.

What is Ai , a polynomial?

Coding practice

2023-11-28 12:36:52 UTC

hi, are the solutions to coding practice 2 going to be posted? Thank you!

Hi, could you upload the solutions for Coding Practice 2 please

2023-11-28 13:07:22 UTC

Hello, in the two practice coding test there are a lot of tests after the actual question. Will this form part of the class test as well or is it just for our own benefit ?

2023-11-30 13:29:57 UTC

class test

2023-12-02 22:15:55 UTC

will there be partial marks if our code isn't 100% correct but we have written some of the right parts?

Could you if possible quickly take us through a concrete example with the Jacobi Method during the next lecture please

2023-12-02 23:17:06 UTC

2023-12-03 12:30:45 UTC

does the class test cover everything until stochastic diff eqns? or does it include this chapter/further chapters.

Formula sheet

2023-12-04 14:34:48 UTC

Hi, do you mind doing a formula sheet for everything we have seen this semester ( just to make sure that we all wrote the right formulas) ?

Thanks a lot.

Class Test 22-23 Solutions Mistake

2023-12-06 10:50:04 UTC

I think that 1a is incorrect in the coded solutions as there is no cubed term. It should be:((1+np.cos(2*np.e))/(np.pi*np.pi))**3*np.exp(np.sin(5))

Lack of Mock Test

2023-12-06 11:45:38 UTC

Good morning,

I am unable to find the Mock Test which I believe we are going through on Friday. Many of us have lectures all of Thursday. Please release it so we have adequate time to prepare.

Thankyou.

For the class test, does the arguments of our functions matter? For example, if I use inter(x,xx,yy) instead of just inter(x) and get the correct result, will I be deducted marks?

2023-12-07 19:44:06 UTC

Will you upload the answer of mock classtest?

2023-12-08 14:16:57 UTC

Practical 3, Monte carlo Method

2023-12-09 16:15:21 UTC

How do we know here that we should to take (-3,3) as the interval of x and y ?

will the questions of classtest be given like paper or like the mock exam and having tests(check)? thx

2023-12-11 12:09:21 UTC

how to solve this question(21-22classtest Q4(b))??

2023-12-11 22:24:30 UTC

I wrote the same code while it showed singular matrix error

Potential mistake in solutions to 7a (Class Test 2022-2023)

2023-12-13 12:07:46 UTC

In the final statement for A[i, j] = ..., k should be iterated over range(5), not range(3), as the same range as the weighted fits function. This makes the resulting plot later on more reasonable. Also, xs has 5 elements, not 3 so it makes sense to iterate over all of them.

What topics are examinable for the January exam?

2023-12-17 10:31:03 UTC

Can you please tell us what chapters are examinable for the January test, and will you be posting a mock test for it?

2023-12-18 10:02:02 UTC

Tutorial 3

2023-12-18 16:33:53 UTC

I know this may sound trivial but why is this true please ?

Hi, is Jacobi method not examinable?

2023-12-27 07:20:07 UTC

tutorial 5 Q2

2023-12-29 12:17:19 UTC

Why is it that x' = y1 and y' = y2 here?

Final exam

2023-12-30 14:22:34 UTC

Do we have the Taylor expansion examples such as e**a's Taylor expansion in the January exam?

22/23 paper QB5 Adams Bashforth part (a)

2024-01-03 14:44:16 UTC

how do we get from 16a to b and also how do we get 17

error estimation

2024-01-03 17:05:39 UTC

I am confused about the different error estimation in derivatives and integration, in Richardson extrapolation, given f’(x) as an example, in lecture notes, G(x)=f’(x), then substitute h1=2h2 into g(h)=f(x+h)-f(x)/h and then use the Richardson formula to calculate and get f’(x)-O(h^2). But in trapezoidal method, in lecture notes it use Taylor’s expansion to calculate the integration and then minus Si to get the approximation error. I wonder why don’t we use Taylor expansion in G(x)=f’(x)? Is Taylor expansion a way to approximate function or is it an accurate ones? If it is approximate way then why do we use it to calculate the exact integral?

Also, I did not see machine error calculation in Richardson extrapolation, is it not in the scope? Or we should go for it ourselves?

ask for exam question A3 in 21-22 paper

2024-01-03 18:47:19 UTC

I wonder how to get this result.

Pastpaper 20-21 Question A1c

2024-01-04 03:10:58 UTC

The condition f(x*) != 0 is not clear to me, wouldn't f(x*) be 0 as it is the assumption, and the condition be f'(x*) !=0 & f''(x*) !=0

Solving for Euler approximation

2024-01-04 10:41:47 UTC

Do we solve Euler formula for Nth iteration yN and then we can use the idea that x/N=h and find y(N*h=x/h *h)

If we had h=b-a/N, is it valid to replace b-a with x?

20/21 paper B6

2024-01-04 12:06:44 UTC

How come we have a vector with 3 components here? I thought if it is the second derivative we would end up with vectors with only 2 components i.e. y vec = (y0, y1)?

20/21 B4 (c)

2024-01-04 12:29:15 UTC

How comes the integral in the solution is not w(x)f(x) dx = sum Ai f(xi)

20/21 B6

2024-01-04 13:02:08 UTC

how do we get to the answer c(i) from part (b) if you could explain the intermediate steps please.

19/20 B5 b ii

2024-01-04 13:12:03 UTC

Hi, could you explain how the last equality is found?

Thank you

Ask for bringing calculator

2024-01-04 14:18:18 UTC

Are we allowed to use calculator in final exam？

Richarson Extrapolation (Chapter 4.4, Page 44, Equation 4.19)

2024-01-04 17:46:46 UTC

Dear Sir,

Could you kindly explain why the error coefficient is the same when 2 different step sizes are used please?

More concretely, for G = g(h_1) + c (h_1)^p and G = g(h_2) + c (h_2)^p, I was wondering why the same coefficient c is used, instead of having 2 different coefficient, say c_1 and c_2, for each step size h_1 and h_2 respectively please?

19/20 qB5 (b)

2024-01-05 12:18:48 UTC

How do we know the integrals are equal to A0+A1 and A0-A1 ?

19/20 paper B6 (e)

2024-01-05 12:35:03 UTC

How do we know k=1, h=1 here

2024-01-05 13:08:21 UTC

you mentioned in another padlet that the answer was wrong, could you provide detailed correct solution please.

2021-2022 A2 (c) mistake

2024-01-05 13:16:13 UTC

Hi professor, I think the x_2=23/8 not 1/16

Euler method y0,y1 notation

2024-01-05 17:46:52 UTC

Hi professor, can I ask if y0 and y1 used with Euler's Method, do they correspond with y and y' or does y1 correspond with y and y2 correspond with y'?

Because I think in the tutorial we use the former notation but in the exam answer it was using the latter.

17/18 A3 and 18/19 B4 papers

2024-01-05 20:32:24 UTC

For these two questions, on the left we have round off error denominator h^2, and on the right denominator is just h. Is this because we are approximating the second derivative on the left q and the first derivative in the right q

Coding test result

2024-01-06 10:37:07 UTC

Hi when will we be getting our results for the coding test we did?

I realized that the 22-23 paper is significantly harder than those of previous years. Anybody agrees with me ?

2024-01-06 17:50:38 UTC

Answer to 2021 B5 b）

2024-01-07 13:42:56 UTC

Seems like the answer is not correct,The question "a" contains h/3, while the question "b" contains h/2, or is the question printed incorrectly?

17-18 B5(e) Gaussian Quadrature to get A0 A1

2024-01-07 21:59:15 UTC

I wonder in this question how did you get that 1=A0+A1? It wouldn't equal to integral e^x from 0 to infinity because such integral is infinite, is there a mistake in the answer?

I noticed that there was a drawing picture section in the exam. Can we use a pencil in the exam?

2024-01-08 00:00:30 UTC

18-19 B5 Gaussian Quadrature

2024-01-08 00:30:44 UTC

Can I ask if there is a mistake here? Because integral e^(-x^2)/sqrt(pi)=1/2.

18-19 Gaussian Quadrature Symmetry

2024-01-08 12:48:21 UTC

Hi professor, can you kindly explain that why the symmetry of the weight will lead to that A0=A2 and why here we only take weight x^0 and weight x^2 not x^1 please?

Gaussian Quadrature

2024-01-08 17:00:21 UTC

Hi, can I ask when do we need to calculate the moment and when do we not need to? Because I am pretty confused since in B4 2020-2021 we calculated the moment then we follow the given procedure. However for 18-19, 17-18 and 19-20, we didn't calculate the moment but directly get the orthogonal polynomial. When do we skip calculating the moment when do we not skip?

ODE

2024-01-08 18:08:54 UTC

I wonder if I choose y:=(y1,y2,y3...) will I get marks? Or are we asked to set y:=(y0,y1,y2...) start from zero when it comes to transform n differential equations to first order differential equations?

Could you update all the exam solutions so that the mistakes mentioned in the padlet are fixed?

2024-01-08 20:22:07 UTC

22/23 B6 (d)

2024-01-09 13:14:28 UTC

How do we get the calculation for N_n+1(1/2) at the bottom? ie.e where does the -1, 0, 1 used in that formula come from

18/19 B5

2024-01-09 17:27:34 UTC

How do we know that we have x -> -x symmetry and how does this mean that we can assume the polynomial is of the form x^3 + ax?

20-21 B4 (c) ii

2024-01-09 21:29:49 UTC

Hi, I think c0=2/5 not 6/15

20/21 B6(c)(ii), Dangerous Negligence of Higher Order Term

2024-01-10 05:20:31 UTC

In this problem, you are specifically asked to neglect O(h^2) and keep anything constant or to h. Here, the solution given below failed to take in consider -((ih^2)^2)/2 which will be later known to include a multiple of h, as written on my solution above.

However, this will require knowledge on sums of cubes and would be too difficult to give on an exam without hints. Would this answer be marked incorrect? Please let me know your thoughts.

class test grades

2024-01-15 15:02:18 UTC

When are we getting our class test grades please?

When are we getting our class test grades please ?

2024-01-31 11:39:37 UTC