Mathematics 105– Spring 2004
Problem Set 1
The first topic of this course is differentiation of functions of several variables,
culminating in the inverse and implicit function theorems. Our test will be Chapters 1
and 2 of Spivak’s
Calculus on Manifolds
. Chapter 1 is a review of basic material which
is part of the syllabus for Math 104. We’ll go through it fairly quickly. Then we’ll
move on to Chapter 2, whose first four sections review material that you learned on
the computational level in multivariable calculus, Math 53, but presumably without
proofs or perhaps even precise definitions. We’ll fill these in. In the final two sections
we come to the inverse and implicit function theorems, which will be proved in detail.
This part of the course will take 9 or 10 lectures. The remainder of the semester will
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 Spring '04
 MichaelChrist
 Calculus, Continuous function, Spivak, implicit function theorems

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