Mathematics 105– Spring 2004Problem Set 1The 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 1and 2 of Spivak’sCalculus on Manifolds. Chapter 1 is a review of basic material whichis part of the syllabus for Math 104. We’ll go through it fairly quickly. Then we’llmove on to Chapter 2, whose first four sections review material that you learned onthe computational level in multivariable calculus, Math 53, but presumably withoutproofs or perhaps even precise definitions. We’ll fill these in. In the final two sectionswe 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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Continuous function, Spivak, implicit function theorems