congratulations! im glad you got an offer! what are you thinking in terms of firm/insurance choices now?
Same!! I'm so happy!! It's my joint first choice... i have 2 that i cant choose between uni wise but the grade requirements have determined their order.... So leeds will be my firm and lancaster my insurance.... :/
Do we need to know modulus argument form? I dont see what it is?? When we use brackets for intervals whats the difference between () and []?? And finally parametric forms.......the c and t and a....ahhh!!!! They confuse me!
Do we need to know modulus argument form? I dont see what it is?? When we use brackets for intervals whats the difference between () and []?? And finally parametric forms.......the c and t and a....ahhh!!!! They confuse me!
Thanks
You need to know mod/arg form. It's basically a way of representing x + iy. If you imagine a complex number x + iy on an Argand diagram (where the y-axis represents the imaginary plane and the x-axis the real plane), the modulus is the "length" of the line from the origin to your point on the plane.
For example, taking the complex number 3 + 4i, the modulus of that is the length needed to get from (0, 0) to (3, 4). So the root of 32+42 which is 5.
The argument of a complex number is the angle it makes between the positive real axis and the line of the complex number. Using the earlier example of 3 + 4i, the argument will be arctan(4÷3) just using basic trigonometry. Bear in mind, the argument θ must be between −π and π. So it's negative below the x-axis and positive above.
You also need to know the "modulus-argument" form of a complex number - that is x+iy=r(cos(θ)+isin(θ)) where r is the modulus and theta the argument. You don't need to know how to derive this.
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As far as concerns brackets for the intervals used in interval bisection etc. in FP1, you only need to use the form []. I believe the difference between [] and () is that [] includes the upper and lower limits, whereas () doesn't - but I may be mistaken here. Check out the symbols at the back of your text book - there's a full page of them and it should tell you what these mean.
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With the parabolic functions, it always goes that y2=4ax So if you get y2=36x then a = 9. (a, 0) is the focus of the parabola and x = -a is the directrix.
They express the x and y coordinates in hyperbolas and parabolas in parametric form. Whereas in Cartesian two-dimensional form, you use just the x and y variables, parametric form brings in a third variable - t or c or whatever you want it to be, and x and y are both functions of that third variable. By muddling these around and equation x and y using t, you can get rid of it and find the equation in Cartesian form - but it's usually horrid, thus the need for parametric form.
That's all I can think of off the top of my head. Your best bet is to go over the FP1 book on those sections as I'm sure it's much easier to understand than my poor explanations and use of Latex are :P Hope I've helped to some extent.
One last thing: do you do anything with the mod arg form once put into that form? Or is it just a way of presenting the information?
I still dont really get parametric when finding the eqn of a tangent etc but i'll have a look......
Do we need to know any proofs that you know of? (derivation ones not proof by induction (ch7))
It may ask you to express a complex number in mod-arg form, or vice versa (going the other way, simply expand the brackets on it - really easy). You don't do anything more with that til FP2.
Have you done (I think) C4 yet? That covers implicit differentiation and provides a much more elegant way of finding the eqn to the tangent in the parabola questions. Otherwise, here's how you do it:
y2=4ax[br][br]y=2ax21[br][br]dxdy=ax2−1
Then put in your x coordinate to get the gradient of the tangent at that point. Then use the equation y−y1=m(x−x1) Stick in the gradient as m then x and y coordinates as x1 and y1 and off you go!
I don't think you need any knowledge of proofs except for induction in FP1.
It may ask you to express a complex number in mod-arg form, or vice versa (going the other way, simply expand the brackets on it - really easy). You don't do anything more with that til FP2.
Have you done (I think) C4 yet? That covers implicit differentiation and provides a much more elegant way of finding the eqn to the tangent in the parabola questions. Otherwise, here's how you do it:
y2=4ax[br][br]y=2ax21[br][br]dxdy=ax2−1
Then put in your x coordinate to get the gradient of the tangent at that point. Then use the equation y−y1=m(x−x1) Stick in the gradient as m then x and y coordinates as x1 and y1 and off you go!
I don't think you need any knowledge of proofs except for induction in FP1.
Thank you thank you thank you!! I dont feel too bad about this exam actually...... No i havent done C4 yet....just finished C3 (exam on monday was hell) Are you doing the exam on monday?
Thank you thank you thank you!! I dont feel too bad about this exam actually...... No i havent done C4 yet....just finished C3 (exam on monday was hell) Are you doing the exam on monday?