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This Week

We developed our applications of step and impulse functions to beam equations. Relevant notes p.22 – 50

In the tutorial we worked on the sample test.

Next Week

We have a tutorial on Thursday. Please take this opportunity to nail down the differential equations. On the final exam there will be both a full question on beam equations and a full question on second order linear differential equations. Hence if you are comfortable with the material that is examinable in the test, feel free to move onto some of the exercises on beam equations.

Test Date

Tuesday 13 March at 6.45 p.m.

Timetable Changes

We are now going to schedule ourselves as follows:

Week 6: – & Tutorial

Week 7: Lecture/Test & –

Week 8: Lecture & Lecture

Week 9: Tutorial & Lecture

Week 10: Tutorial & Lecture

Week 11: – & Lecture

Week 12: Tutorial & Lecture

Sample Test Answers

Here I give you links to how I checked answers quickly using Wolfram Alpha. It takes Mathematica code (they are the same company) and will probably decipher your own stab at code also. Note that Wolfram Alpha gives us a lot more information than we need but that is the beauty of the thing really.

Question 1 — note there is a small typo here it should be 16y rather than just 16.

Question 2 — it’s not evaluating the constants using the boundary conditions for some reason… the answer is y(x)=-\frac{1}{9}e^{-8x}+\frac{1}{9}e^x

Question 3

Question 4 — the boundary conditions yield y(x)=-\frac{55}{2}e^{2x}+\frac{52}{3}e^{3x}+5x+\frac{25}{6}.

Question 5 — what is \theta here and how do we write (x-2)\theta(x-2)?

Question 6 — again we need to realise that the notation here is different to ours. Applying the boundary conditions we get y(x)=3[x-8]^3-3[x-2]^3+54x.