# Past Papers

Exam Problems Solutions Remarks
Autumn 2020 pdf pdf
Summer 2020 pdf TMA4125_exam_q_7.py pdf In the solution problem 3, a factor $\sqrt{2\pi}$ is missing in the convolution theorem. The final answer should be $\sqrt{a\pi} e^{-\frac{x^2}{4a}}$.
Spring 2020 pdf pdf There is a sign error in the solution of problem 2b. At the end, it should be $(1-(-1)^n)$ instead of $1+(-1)^n$.
Autumn 2019 pdf pdf
Summer 2019 pdf pdf The solution of problem 8 is wrong. What is implemented there is an explicit Euler method, not an implicit one.
Spring 2019 pdf pdf
Autumn 2018 pdf(norsk) , pdf(english) pdf Here is a more detailed solution of Problem 2a.
Spring 2018 pdf pdf
Aug-17 pdf pdf 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 pdf pdf
Autumn 2016 pdf pdf
Aug-16 pdf pdf
Spring 2016 pdf pdf
Autumn 2015 pdf pdf
Spring 2015 pdf pdf
Autumn 2014 pdf pdf 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.
Autumn 2013 pdf pdf
Autumn 2012 pdf
Spring 2011 pdf pdf In problem 4b, the ODE should have been y''-6y'+9y=0.
Autumn 2010 pdf pdf
Spring 2010 pdf pdf
Autumn 2009 pdf pdf
Spring 2009 pdf pdf
Autumn 2008 pdf pdf
Spring 2008 pdf pdf
Autumn 2007 pdf pdf 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.
Autumn 2006 pdf pdf
Spring 2006 pdf pdf 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.

You can find more past papers at: https://wiki.math.ntnu.no/tma4130/2011h/gamle_eksamensoppgaver