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## Main Question or Discussion Point

Is there a resource that is just a walkthrough of various kinds of problems one might get and the ways to solve them?

I'm not talking about the basics from the calc and difEQ series (u substitution, partial fraction decomposition, trig substitutions, trig power reduction, integration by parts; separation of variables, integration factors, exact equations, characteristic roots, laplace transforms), but rather more advanced things.

The only examples I know are residue integration, the basic nonlinear equation (not sure what to call it, but it's d^2y/dt^2=f(y), and the trick is to substitute dF(y)/dy for f(y), multiply each side by dy/dt, and then do some multivariable chain rule tricks before getting a sloppy integral with a root as the answer), using eigenvectors to solve the characteristic equation, and the multivariable and polar transformations to solve the Gaussian integral. There have to be way more that I'm unfamiliar with, even at the level any undergraduate can understand.

Is there a database of all these techniques, especially helping for a broader understanding of how to condense these techniques into easily derivable knowledge in nice packages?

I'm not talking about the basics from the calc and difEQ series (u substitution, partial fraction decomposition, trig substitutions, trig power reduction, integration by parts; separation of variables, integration factors, exact equations, characteristic roots, laplace transforms), but rather more advanced things.

The only examples I know are residue integration, the basic nonlinear equation (not sure what to call it, but it's d^2y/dt^2=f(y), and the trick is to substitute dF(y)/dy for f(y), multiply each side by dy/dt, and then do some multivariable chain rule tricks before getting a sloppy integral with a root as the answer), using eigenvectors to solve the characteristic equation, and the multivariable and polar transformations to solve the Gaussian integral. There have to be way more that I'm unfamiliar with, even at the level any undergraduate can understand.

Is there a database of all these techniques, especially helping for a broader understanding of how to condense these techniques into easily derivable knowledge in nice packages?