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I'm currently taking a course in Multivariable Calculus at my University and would appreciate any recommendations for a textbook to supplement the lectures with. Thus far the relevant material we've covered in a Single Variable course at around the level of Spivak and some Linear Algebra around the level of Strang (Linear Algebra and its Applications). For reference we are concurrently studying some more analysis in R but now around the level of Rudin's PMA (though I do not think this has impacted the design of this module at all).

The content of the course is as follows:

• Continuous Vector-Valued Functions

• Some Linear Algebra

• Differentiable Functions

• Inverse Function Theorem and Implicit Function Theorem

• Vector Fields, Green’s Theorem in the Plane and the Divergence Theorem in R^3

• Maxima, minima and saddles

We are also told that at the end of the module we should be able to:

From my experience the module started off with a fairly theoretical flair - which remained present throughout the entirety of the material on differentiation. We started by studying a small but requisite amount of norms, metrics and topologies which was then used in our treatment of differentiation - especially the inverse and implicit function theorems (which receive a lot of emphasis in this module). We then moved on to the integration section of the course which was, by contrast, more computational in flair. It still seemed to me to be at a higher level than seen in books such as Stewart but this was mostly by the nature of the exercises given and presentation of the subject matter as opposed to the content itself.

- Demonstrate understanding of the basic concepts, theorems and calculations of multivariate analysis.

- Demonstrate understanding of the Implicit and Inverse Function Theorems and their applications.
- Demonstrate understanding of vector fields and Green’s Theorem and the Divergence Theorem.
- Demonstrate the ability to analyse and classify critical points using Taylor expansions.

If any further information would help please feel free to ask and thank you to anyone who takes the time to assist me with this search!

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# Calculus Multivariable calculus without forms or manifolds

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