I am going back to school and preparing my first-semester course which is so-called "engineering maths". I used to be a physics major 5 years ago and had ok-ish knowledge in calculus, but now the part of my calculus brain is shiny as a piece of metal; I have forgotten 90% of it.
I have exactly a month left to prepare for it, but I am a bit confused about where to start and where are these topics lie in;
*Vector calculus, including Gauss’ and Stokes’ Theorems;
*sequences and series;
*Fourier series, Laplace transforms;
*systems of homogeneous ordinary differential equations, including phase plane and linearization for nonlinear systems;
*second-order partial differential equations and separation of variables.
Given only one month time, where is the best to start and what is the best materials for learning and practising? I am doing the single variable course from MIT, but it's taking too long and makes me want to hurry to vector calculus; ironically I worry about the sort of gap among these topics and a single variable. I know it is not realistic given a short period but at least I would want to study in a correct order that covers all the topic above.
I am both excited and worried about studying maths again because I want to do well instead of just passing with Bs as I did in undergraduate.
Thanks for reading and you're much appreciated!
If you can find a copy of Engineering Mathematics by A.J.M. Spencer (and others) (Van Nostrand, 1977), don't hesitate to get it. It was my undergraduate text in my 3rd year of my elec. eng. degree course back in the early 1980s. It has everything you need, not just for your 1 month re-acquaintance with the material, but should be a constant companion over the rest of your course.
If it had not been for this book, I would have failed my exam on 2nd-order partial differential equations.
I recently got a second-hand copy of it, replacing the old one I had, and it is just as good as I remember it.
There may be newer (and hence more modern) books available nowadays, but I won't be able to comment on them.