### The Learning Curve

From the Learning Curve:

Learning Curves: Honors: Multivariable Calculus: What textbook would you use to teach honors Calc 3?

Already rejected: Apostal for being too linear-algebra-y and Hurley for being out of print.

Too linear-alebra-y? How can a multivariable calculus textbook be too linear-algebra-y? Multivariable derivatives and integrals are linear maps in an algebra-like space, aren't they?

## 2 Comments:

At 6:07 PM, cieran said…

Agreed!

All of Apostol's books are excellent, as long as the student is up to the task (as they would be at Berkeley, or in any Honors program).

As far as the notion of too-much linear algebra, multivariate calculus can't be taught properly without a good grounding in linear algebra, so that's a red herring.

The gradient is a vector, the Hessian is a symmetric matrix, multivariate transformations inherit their local properties from the associated Jacobian matrices, etc., etc., etc. Linear algebra is an organic part of multivariate calculus, whether we like it or not!

A Honors course in multivariate calculus that doesn't include a solid grounding in the relevant linear algebraic underpinnings does

notmerit the "honors" designation!At 1:59 AM, sabera said…

Mathematics of Linear Algebra

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