what should i read after i've surveyed most methods in introductory numerical analysis texts? where do i go from there if i want to keep on studying numerical methods? i don't want to learn about it for any particular reason.. i just think that's what i do best and it would be good for me to learn more
>>8074533
Learn how to use a shift key
>>8074533
If I know about numerical integration can I say that I know numerical analysis?
>>8074545
can u give a good bound on ur error?
>>8074556
greater than zero in magnitude
>300k starting any job I want
>>8074533
what did you cover?
>>8074583
sounds like you're using some really shitty wuadrature then, if you can't even get it to integrate some functions exactly
>>8076004
solving systems of linear equations using gaussian elimination and some variants (eg LU and cholesky decomposition) and iterative methods, methods for finding eigenvalues, finding roots of nonlinear equations of real functions and briefly of vector fields using newton's method, approximation and interpolation of real functions, and numerical differentiation and integration
>>8078263
seems you've all the tools set up for some numerical methods for odes and later on pdes.
if you want to get more into pdes, i advice you to take some real/functional analysis, since that's the basis of finite element methods
you might also want to look up numerical linear algebra, where you study some more advanced solvers for big systems of linear equations. (very important for pdes)
>>8078297
if i'm mostly interested in statistics should i study odes and pdes anyway? i've always thought they're mostly used to solve physics problems and i don't know much physics
>>8078333
I don't have much of a backround in statistics, so unfortunately I can't tell you much about it.
Regarding the use of differential equations: You are probably right, that they pop up the most in physicist/engineering problems, but they are found everywhere in natural sciences and finance as well.
In my opinion you don't really have to know much about physics - at least I don't really do.
>>8078333
Alot of numerical computation IS solving ODE's and PDE's numerically, finding solutions to differential equations that don't have analytic solutions. alot of numerical analysis is motivated by physical applications, so you have to know a bit about where the equations come from and why people care about solving them.
There is a pair of courses from MIT, computational science and engineering 1, and mathematical methods for engineers that covers quite a lot of the applications of numerical analysis. Comp science and eng used to be called mathematical methods 1 at MIT
One occurrence of a PDE in statistics is the poisson process which is a markov process that describes the counting of random events that happen over time, like the amount of customers entering a shop at different time intervals.
ODE's come up alot in stochastic process in statistics
>>8074541
>caring about sentence structure on a chinese cartoon image board
