# Nice Resource to learn Advanced Calculus

1. Dec 8, 2013

### Septim

Greetings everyone,

I know this is not the right place for this post but I cannot post in the science education subforum so I post my question here. 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. Thanks in advance

2. May 26, 2014

### homer

D'oh, too bad this post is months old. There is an incredible resource on coursera: Massively Multivariable Online Open Calculus Class.

https://www.coursera.org/course/m2o2c2

Not sure if you can still sign up or not on coursera, but most of the meat of the course is hosted by Ohio State anyways, and Jim said he'd keep it open:

http://ximera.osu.edu/course/kisonecat/m2o2c2/course/

It's a pretty action-packed six week course on multivariable differential calc:

- First week is on $\mathbb{R}^n$ and linear maps $\mathbb{R}^n \to \mathbb{R}^m$
- Second week is on total derivative (as a linear map), partial deriviatives, gradients, and a bit about one-forms
- Third week is finite dimensional vector spaces, linear maps, eigenvectors
- Fourth week is bilinear maps, intro to the tensor product, adjoints, and ends with a really simple and cool proof of the spectral theorem
- Fifth week is on the second derivative of a map $\mathbb{R}^n \to \mathbb{R}$ as a bilinear form represented by the Hessian matrix, equality of mixed partials, optimization, and constrained optimization using Lagrange multipliers
- Sixth week is multilinear forms, kth derivatives of maps $\mathbb{R}^n \to \mathbb{R}$ as k-linear forms $(\mathbb{R}^n)^k \to \mathbb{R}$, and Taylor's Theorem.

Next September he'll likely do a continuation course on forms, building up to Stokes' Theorem.

3. Jul 31, 2014

### Alicelewis11

I think you can search on Google which you want to get regarding anything where you can find so many results which are very satisfy able.