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hw1 - Mathematics 105 Spring 2004 Problem Set 1 The first...

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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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