How much time should I leave to learn this?

[appianway]

I'm supposed to learn all of this to a high standard by early January. I'm probably going to go into school and complete the work there so that I can ask the specialist maths teacher questions if I want an explanation of the proofs, so I'd like an idea of how many days I should designate to this task.

Anyway, here's a list of the material that I'm supposed to learn. I don't do specialist maths, so I haven't covered complex numbers or vector calculus before. I'd really appreciate any estimations of the time that I'll need... I don't want to go to school for too little or too much time!

Functions:

Polynomial and rational functions
Exponential functions
Logarithmic functions
The natural base
Changing base
Solving exponential equations
Trig functions (including all of that cosec jazz)

Vectors:

Basic Vector Operations
Sum and difference of vectors
Multiplication by a scalar
Components of vectors
Vector products (dot products and cross vector products)

Complex Numbers

Calculus:

Limits
Differentiation
Partial differentiation
Algebraic manipulation of differentials
Integration
More difficult integration: substitution, integration by parts, recurring integrals
Taylor Series
Differential Equations

Calculus in Higher Dimensions:

Multivariate Integration
Line Integrals
Area and Volume Integrals
Integration in Polar Coordinates (two dimensional, spherical and cylindrical)
Centre of Mass
Moment of Inertia

[EvangelionZeta]

Why are you learning all this if you're not doing Spesh?

Anyway, Functions should take you a week and a bit of good working if you're dedicated.  Can't comment on the rest.

[appianway]

I already know all of the functions because of Methods... but I was hoping that it wouldn't take more than 4 days or so >.<

Apparently I need this for Physics Olympiad. We're having a quiz on it (in conjunction with our preparatory physics work) at the beginning of the summer school...

[EvangelionZeta]

Oh wait, you do Methods.

Scratch that, Functions will take like a day or two then.

All the Calculus stuff won't take much longer either, then.

:p

[humph]

A lot of that stuff is university level maths, so I'd start studying soon Well, a fair bit of the limits and higher dimensional calculus is. The first half shouldn't take too long, it's just stuff covered in spec.