Old Exams
We provide these exams _as is_, that is we will not explain the steps in the solutions, but you can use these to discuss with your fellow students and train.
| Exam | Problems | Solutions | Remarks |
|---|---|---|---|
| Summer 2022 – 4N/D | pdf (incl. Solutions) | ||
| Autumn 2022 – 4N/D | There is a typo in the solution of problem 3 the \(\frac{2}{n\pi}\) should be \(\frac{4}{n\pi}\), which also means the \(2+\ldots\) in the numerator of series should be \(4+\ldots\). | ||
| Spring 2022 - 4N | pdf (incl. Solutions) | ||
| Autumn 2021 - 4N | |||
| Autumn 2020 - 4N/D | This was a home exam. | ||
| Summer 2020 - 4N/D | pdf TMA4125_exam_q_7.py | This was a home exam. In the solution problem 3, a factor \(\sqrt{2\pi}\) is missing in the convolution theorem. The final answer should be \(\sqrt{a\pi} e^{-\frac{x^2}{4a}}\). |
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| Spring 2020 - 4N | This was a home exam. There is a sign error in the solution of problem 2b. At the end, it should be \((1-(-1)^n)\) instead of \(1+(-1)^n\). |
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| Autumn 2019 - 4N/D | |||
| Summer 2019 - 4N/D | There is a sign error in the solution of problem 2b. The last line should (still) have a minus upfront, cf. also Kreyszig, p. 527 (Sec. 11.9, Example 3). The solution of problem 8 is wrong. What is implemented there is an explicit Euler method, not an implicit one. |
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| Spring 2019 - 4N | |||
| Autumn 2018 - 4N/D | pdf(norsk) , pdf(english) | Here is a more detailed solution of Problem 2a. | |
| Spring 2018 - 4N | |||
| Autumn 2017 - 4D | |||
| Summer 2017 - 4N/D | In the solution of problem 2b), the sign of k in equation (1) and (2) should be the opposite for the rest of the solution to make sense. In the solution of problem 5, the y_2 should use 0.995, and not 1 in their computation. | ||
| Spring 2017 - 4N | there is a minus sign typo in the Euler identity for the sin function in the solution of 3c. | ||
| Autumn 2016 - 4N | |||
| Autumn 2016 - 4D | |||
| Summer 2016 - 4N | |||
| Summer 2016 - 4D | |||
| Spring 2016 - 4N | |||
| Autumn 2015 - 4N | |||
| Autumn 2015 - 4D | |||
| Summer 2015 - 4D | Oppgave 6 ble glemt i LF. feil i LF i oppgave 4) bruk av formelark gir k_1=0 og y_1=y_0+(1/2)k_2 = 1,00346… |
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| Autumn 2014 - 4N | There is an error in problem 5a: The interpolation points xi should be -2,-1,0,1,2 instead of -2,1,0,1,2. |
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| Høsten 2014 - 4D | |||
| Sommeren 2014 - 4D | |||
| Autumn 2013 - 4N | |||
| Høsten 2013 - 4D | |||
| Sommeren 2013 - 4D | |||
| Autumn 2012 - 4N | |||
| Høsten 2012 - 4D | |||
| Sommeren 2012 - 4D | \(x_2^{(1)} = -3{,}0420\) og ikke \(x_2^{(1)} = 3{,}0420\) slik det står i løsningsforslaget. På tredje linje i løsningen til opppgave 6 skal siste ledd \(U_{i, j-1}\) være \(U_{i-1, j}\). Sjette linje mangler også en slutt-parentes. |
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| Høsten 2011 - 4D | En fortegnsfeil forekommer i starten av løsningen til oppgave 3a. | ||
| Sommeren 2011 - 4D | En regnefeil forekommer på tredje siste linje av oppgave 4a: \(p(3/4)\) er ikke \(3/16\), men \(9/16\). | ||
| Spring 2011 - 4N | In problem 4b, the ODE should have been y''-6y'+9y=0. | ||
| Autumn 2010 - 4N | |||
| Høsten 2010 - 4D | I den Lagrange-interpolasjonsbaserte løsningen av oppgave 1 hadde det opprinnelig sneket seg inn en \(3\) for mye på nest siste linje. Dette er nå rettet opp slik at det som står der nå, er korrekt. | ||
| Sommeren 2010 - 4D | |||
| Spring 2010 - 4N | |||
| Autumn 2009 - 4N | |||
| Høsten 2009 - 4D | |||
| Sommeren 2009 - 4D | |||
| Spring 2009 - 4N | |||
| Autumn 2008 - 4N | |||
| Høsten 2008 - 4D | |||
| Sommeren 2008 - 4D | |||
| Spring 2008 - 4N | |||
| Autumn 2007 - 4N | In problem 1, the integration should be with respect to u and not t (in other words: replace the dt in the integral by du). In the solution of problem 2b, the time dependent part should be e((1-(n/2)^2)t instead of e1-(n/2)^2 t. In problem 4b, the approximation for u' '(0.1) is 4.545 and not 5.03 as claimed in the solutions. |
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| Høsten 2007 - 4D | |||
| Sommeren 2007 - 4D | |||
| Autumn 2006 - 4N | |||
| Spring 2006 - 4N | There is an error in problem 2a: The function f is equal to 1 for π/2 < x < π, not for π/2 < x < 1. |
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| Høsten 2006 - 4D | I første setning av oppgave 3c forekommer en fortegnsfeil. | ||
| Sommeren 2006 - 4D | I oppgave 6 bruker LF feil nedre randbetingelse, \(\cos\pi x/2\). | ||
| Høsten 2005 - 4D | |||
| Sommeren 2005 - 4D | |||
| Høsten 2004 - 4D | |||
| Sommeren 2004 - 4D | Skrivefeil i løsning på oppgave 3b: Her menes \(7/y\), ikke \(7/u\). Dette er en eksamen hvor LF bare er en fasit. |
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| Høsten 2003 - 4D |
You can find more past papers at: https://wiki.math.ntnu.no/tma4130/2011h/gamle_eksamensoppgaver