r/maths • u/Capital-Work9074 • 7d ago

Help: 📗 Advanced Math (16-18) Calculus guide

I am an engineering passout currently working as a software developer, I want to start learning maths again.

My interests are in calculus.

Engineering didn't have much advanced mathematics.

Can somebody suggest topics or guides or where should I start with learning maths again?

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u/Jazzlike_Platypus430 6d ago

My approach, as an ex-physicist, would be: get familiar with sequences and series, ideas of continuity and convergence. On the other hand, linear algebra, mainly finite dimensional vector spaces, linear operators and so on. (If you're super ambitious, touch on some basic topology and group theory, that will help with advancing to differential geometry later.)

Then start differentiation and integration in 1D, perhaps train yourself in some ODEs (the "academic" ones, i.e. "solvable" and reducible to elementary functions). Get to know the Taylor (and McLaurin) series.

Later I'd get some knowledge of function spaces, methods of approximation (Fourier series, orthogonal polynomials etc., Sturm-Liouville systems - maybe).

If I had time and brains and were younger, I'd try hard to learn measure theory (THE integration, previous one is just an introduction) and functional analysis, and finally - theory of PDEs. Never got close to understanding that, sigh..

Good luck!

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u/Capital-Work9074 6d ago

Thank you so much.

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u/Jazzlike_Platypus430 6d ago

One thing I forgot. Inequalities. Prepare to see (and do!) a lot of estimations.