Okay, so this week has been centred around tackling some advanced integration, by hand. I can tell you, that it is not easy. I have noticed that most intro calculus courses, give you tables of common integration values; and MST121, is no exception. I did spend a lot of time, trying to gain a deeper understanding of double angle formulas and general trigonometry rules, so that integration of these functions, is a little easier to grasp.
I have also touched on some differential equations, involving modelling a particle in two dimensions. There is a whole book in MST121, dedicated to these equations, which I should start to study in July.
For now, I will continue to practise differentiating and integrating, until they become second nature.
I have also been supplementing my Open University study, with the Calculus lectures, from the Teaching company. It was, 'Professor Edwards to the rescue', as his lecture on integration by substitution helped clarify a point that was really confusing and not explained well, by the O.U text.
I was struggling with a rather hashed description in the text, about the addition of constants to integrals e.g.
If you have an integral such as: x(x^2 - 1)^3 dx you need to multiply the whole thing by 1/2 when working backwards, so that you end up with the correct answer. It isn't immediately obvious why you would need to do this, and the OU text didn't explain it well. However, the video lecture gave a wonderful explanation, that made it click straight away.
Total time studied this week: 18hrs
MST121
Integration by inspection
Algebraic manipulation before integration
Position, velocity and acceleration
Completed Final draft of TMA03 question 3, using Mathcad print-outs
The Teaching Company Calculus Course
Integration by substitution
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