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I need a good resource - textbook, online resource, video lecture etc.- that explains the multivariate calculus really well; the topics I want to make clear are the Hessian Matrix concept and the classification of extrema for functions of several variables, partial derivatives and identities related with them together with their proofs, some nice discussion on reciprocals of (partial) derivatives, and change of variables for multidimensional integrals and the Jacobian Matrix. These are the topics that I was able to recall at the moment. I would appreciate it if you could guide me on these matter. Any help and advice is welcome and appreciated.

Thanks in advance

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You can check out

1) Vector Calculus, linear algebra and differential forms by Hubbard and Hubbard 2) Advanced Calculus by Gerrald B Folland.

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