Reddit mentions of Advanced Engineering Mathematics

Engineer here. The Navier–Stokes equations are expressed using vector calculus.

I'd just point you to books. I highly recommend actually doing the exercises at the end of each chapter.

John Bird - Engineering Mathematics

This is a good book that doesn't assume that you've completed GCSE mathematics. It brings you up to scratch to a level of mathematics I'd expect a first year undergraduate to have. Yes, it starts with fractions. A large chunk of it is geometry and calculus, though it does touch on some statistics and matrices and complex algebra on the way there.
It ends with you being able to solve basic separable 1ˢᵗ order ODEs.

Kreyszig - Advanced Engineering Mathematics

Higher-order ODEs, Linear Algebra, Vector Calculus, PDEs, Complex Analysis, Fourier. Oh, and linear programming and optimization.

There's a recommended study guide and order in the introduction.

Knuth - Concrete Mathematics

Just thought I'd include this here, since you're a programmer. Touches on some continuous and some discrete mathematics essential for computer science.

I'm studying general engineering in the UK so I can guess that the pure maths topics you're likely to learn in the first year is: calculus 1-2, complex numbers, fourier series, solving ordinary differential equations (1st and 2nd order), vectors, matrices and also anything you covered at A-level. If you did things like M1-3, FP1-3 or C1-4 at A-level, making sure you're confident with those topics is probably more useful at this stage.

I only have one textbook, and that's Kreyszigs (it's ~1300 pages and covers A-level to Phd level engineering maths), although I wouldn't really recommend spending a lot on a textbook as it can be a bit daunting and there are plenty of resources online as long as you know which topics you want to be learning.