As a mathematics graduate with focus on programming we did a whole lot of coding of some mathematical statements (as well as proving them), but yet rarely giving real life examples and applications for given statements.
So for my future work i would like to learn some of the applications (mostly in electronics, programming, physics...) and get some references where i can continue to learn so that - given a problem i can correlate that to something i have learned before.
I am most interested in applications for these fields:
- Interpolation (Hermite, multidimensional, Newton, Spline ...)
- Approximation ( Least squares, uniform approximation,..)
- Numerical methods for solving differential equations
- Numerical methods for finding eigenvalues and eigenvectors
Numerical Methods for solving non-linear equations
- Integration by curve, surface
- Integrals with parameters
- Fourier series,Fourier transformation,Fourier integral
- Uniform convergence (for sequence of functions, series, integrals)
Weierstrass function, Riemann zeta function
- Lebesgue measure, Lebesgue integral
- Radon - Nikodym theorem , derivate
- Monotone convergence theorem, dominant convergence theorem
Lp spaces, norms
- Cauchy integral theorem
- Picard's theorem
- Laurent series ...
References, books, websites - anything will do, just as long as there are multiple examples (also the more on the side of programming (algorithms, problem solving) and electronics the better)