===== Problems from the textbook =====
These are from the 10th edition of the book; see the scans if you have another.

  * **19.3:** 3 ([[http://www.math.ntnu.no/emner/TMA4123/2015v/scan/816.pdf|scan]] - the problem that begins with "Quadratic interpolation")
  * **19.5:** 4, 7, 8 ([[http://www.math.ntnu.no/emner/TMA4123/2015v/scan/836.pdf|scan]])


===== Old exam problems ===== 

The following old exam problems are
taken from TMA4135, a course that is almost identical to
TMA4123/TMA4125. The problems could just as well have been from a TMA4123/TMA4125 exam.

  * **{{:tma4135:eksamen:tma4135_10h.pdf|Fall 2010}}:** 1
  * **{{:tma4135:eksamen:tma4135_11k.pdf|Continuation/summer 2011}}:** 5
  * **{{:tma4135:eksamen:tma4135_14h.pdf|Fall 2014}}:** 2


===== Programming problem 1 (harder than problem 2) ===== 

Make a Matlab function that does interpolation either using Lagrange's
method or Newton's divided differences (hint: due to its recursive
nature, you might find Newton's divided differences easier to implement if we
ignore performance concerns((A naive implementation, which is fine
here, will compute most coefficients several times. The interested student might
want to consider memoization, but that's certainly not neccessary
here!)).)

Test your function by finding the polynomial that interpolates the following values:

| \(x\)    | -1.5     | -0.75      | 0        | 0.75     | 1.5 | 
| \(f(x)\) | -14.1014 | -0.931597  | 0.000000 | 0.931597 | 14.1014 |

The values are samples of the \(\tan\) function; plot your interpolation polynomial together with \(\tan\) on \([-1.5, 1.5]\).

===== Programming problem 2 (easy) ===== 

Make a Matlab function that approximates integrals using Simpson's
method. Table 19.4 on Kreyszig's page 829 is a good starting point. Use your function to approximate \(\int_{-1}^1 e^{-x^2}\, \mathrm{d}x\) (an integral that is impossible to compute analytically).

===== Voluntary repetition problems =====

  * **[[http://www.math.ntnu.no/emner/TMA4122/2010h/exam/TMA4125_V08.pdf|TMA4122 exam from the spring of 2008]]**: problem 2