Exercises for mathematics 4D/N

On this page you will find exercise sets and solution proposals, as well as administrative information regarding the exercise activities.

In total, 12 exercise sheets will be provided. In order to get access to the exam, you have to get 8 exercise sheets approved. It is, however, strongly recommended that you complete all exercise sets.

In each exercise sheet there will be 4 problems: in order to get the sheet approved you need to solve all of them, but only two will be graded.

Approvals from previous semesters

If you have fulfilled the exercise requirements a previous semester (in either of the courses TMA4130, TMA4125, or TMA4135, you do not have to do so again. If you want confirmation that you have a registered approval from previous semesters, you need to contact eksamen@math.ntnu.no.

Submissions: time and place

The solutions should be handed in in ovsys. Please hand in a pdf-file with the solutions of the analytical problems and either jupyter notebooks (.ipynb) or python files (.py) for the programming problems. The exercise sets will be published on Monday of the week in the column "Publication week" and the deadline is always midnight 23:59 on the dates given below (the Friday of the week after).

The answers of the analytical problems should contain enough details so that it is clear how a solution has been obtained. For the programming problems, it is necessary that the code actually runs. You decide if you want to answer the questions in Norwegian or English.

You can request feedback from the student assistants through ovsys, but you need to specify which of the exercises you want feedback on (and it can not be all of them). Debugging of code will not be done.

Exercise sheets

The .ipynb files that will be provided below can be run by Jupyter Notebook. If Jupyter Notebook is not already installed, we recommend using the Anaconda distribution, a detailed installation guide for which can be found here.

In order to work with jupyter notebooks in Anaconda, follow the following steps:

(Download and install Anaconda on your computer.)
Download the jupyter notebook on your computer. We recommend to set up a dedicated working directory for Maths 4N/D.
Start the Anaconda Navigator, and launch Jupyter Notebook. This should open a new window in your web-browser, from which you can navigate to your stored notebooks or open new ones.
For your solutions to the numerical exercises, feel free to copy code parts from the provided jupyter notebooks.

Own Work

It is very important to only submit work that is your own. We want to remind you of the importance of academic integrity and the fact that copying from each other is not allowed. Respecting the intellectual property of others is a fundamental principle in maintaining a fair and honest academic environment. Copying, plagiarism, or using someone else's work without proper attribution is not only against our guidelines but also undermines the trust and integrity of our entire learning institution.

If you want specific comments on your solution, please write a small comment on where you had problems or questions in the future. Without that you will only get general comments and if there is nothing else to say than what is written in the solution, you might not get a comment at all.

Publication week - Ex. n.	Deadline	Exercise sheet	Additional Files / Remarks	Solutions
34 - Exercise 1	29/08/25	Exercise 1	1b) You can do one step at a time. \(f_y\) is the matrix consisting of \((f^j_k)_{j,k}\), so \(f_yf=(\sum_k f^j_k f^k)_j\), ergo \((f_yf)_y=\left(\frac\partial{\partial y^s}\left(\sum_k f^j_k f^k\right)\right)_{j,s}=(\sum_k f^j_{k,s}f^k+ f^j_kf^k_s)_{j,s}\) where we used the product rule…	Exercise 1 solution
35 - Exercise 2	05/09/25	Exercise 2		Exercise 2 solution
36 - Exercise 3	12/09/25	Exercise 3	exercise3_prob1_fillin.ipynb exercise3_problem3_fillin.ipynb In task 1j) a PDF is mentioned: Preliminaries.pdf	Exercise 3 solution exercise3_problem1_solution.ipynb exercise3_problem3_solution.ipynb exercise3_problem4_solution.ipynb exercise3_problem5_solution.ipynb
37 - Exercise 4	19/09/25	Exercise 4	exercise4_problem2_fillin.ipynb exercise4_problem3_fillin.ipynb exercise4_problem4_fillin.ipynb exercise4_problem7_fillin.ipynb	Exercise 4 solution exercise4_problem1_solution.ipynb exercise4_problem2_solution.ipynb exercise4_problem3_solution.ipynb exercise4_problem4_solution.ipynb exercise4_problem5_solution.ipynb exercise4_problem7_solution.ipynb
38 - Exercise 5	26/09/25	Exercise 5	Remember to use the table from formulas.pdf plenary_laplace1_fillin.pdf plenary_laplace1_complete.pdf Plenary	Exercise 5 solution
39 - Exercise 6	03/10/25	Exercise 6	Exercise 6 long plenary_laplace2_fillin.pdf plenary_laplace2_complete.pdf plenary_laplace2_complete.one	Exercise 6 solution
40 - Exercise 7	17/10/25 !!!	Exercise 7	If you want you can use the additional files exercise7_problem6_fillin.ipynb exercise7_problem11_fillin.ipynb exercise7_problem14_fillin.ipynb 1c) and 11 were changed! Have a look at the plenary for exercise 8.	Exercise 7 solution exercise7_problem4_solution.ipynb exercise7_problem6_solution.ipynb exercise7_problem7_solution.ipynb exercise7_problem8_solution.ipynb exercise7_problem9_solution.ipynb exercise7_problem11_solution.ipynb exercise7_problem14_solution.ipynb
41 - Exercise 8	17/10/25	Exercise 8	Plenary Num ODE.ipynb Plenary Num ODE - fillin.pdf Plenary Num ODE.pdf Plenary Num ODE - fillin.one Plenary Num ODE.one Plenary	Exercise 8 solution
42 - Exercise 9	24/10/25	Exercise 9	exercise9_problem7_fillin.ipynb	Exercise 9 solution exercise9_problem7_solution.ipynb
43 - Exercise 10	31/10/25	Exercise 10	Problem 4: In the exam you get point reduction if you don't state why function = series. Sorry that the plenary is a bit messy (no iPad). Plenary Plenary Fourier series - fillin Plenary Fourier series - complete plenary_fourier_series_fillin.one plenary_fourier_series.ipynb plenary_fourier_series.ipynb	Exercise 10 solution
44 - Exercise 11	07/11/25	Exercise 11	The FFT in python is np.fft.fft(signal) dft.ipynb plenary_fourier_transform_-_fillin.pdf plenary_fourier_transform_-_complete.pdf plenary_fourier_transform_-_fillin.one plenary_fourier_transform_-_complete.one plenary_fourier_transform.ipynb change name to 'audio1.wav'	Exercise 11 solution exercise11_problem4_solution.ipynb exercise11_problem10_solution.ipynb There was a mistake in task 3c when computing \(\omega_3\) for \(N=3\)
45 - Exercise 12	12/11/25 !!!	Exercise 12		Exercise 12 solution

Exercise Classes

The exercise classes start in week 35, in the following times:

Day	Time	Room	Note
Monday	8 - 10	GL-GEL EL6	Small session
Tuesday	8 - 10	GL-SB2 S8	Small session
Tuesday	16 - 18	GL-GEL EL6	Small session
Wednesday	8 - 10	GL_RFB R5	Big session, please come here.
Wednesday	14 - 16	H3 521 Sprokkit	small session (new !!!)
Wednesday	16 - 18	GL_RFB R8
Thursday	10 - 12	GL-HB H3	Small session
Thursday	16 - 18	GL-GE G1	Small session
Friday	8 - 10	GL-RFB R9