Math 131A – Course Outline – Spring 2011•Text: Apostol,Calculus, Volume I,2nded.•Instructor: Betsy Stovall1.Introduction. Crash review of basic propositional logic and set notation. (Chapter I.2)◦On your own: Read I.1–2 with an emphasis on I.2. You will have seen much of this in115A, so our review will be brief.2.Field and order axioms, Examples and non-examples of fields. Introduction to the realnumbers. (I.3)3.Supremum and infimum. Definitions and basic properties. Completeness axiom. (I.3)4.Archimedian property. The rationals are dense in the reals. But√2∈R\Q. (I.3)5.Induction, complete induction, and well-ordering property. (I.4)6.Induction examples. Summation notation. (I.4)7.What is a function? Integrals of step functions. (Chapter 1)8.Integrals of general functions. (Chapter 1)9.Integrating monotone functions. (Chapter 1)End material for Midterm 1.10.Basic properties of the integral. (Chapter 1)Midterm 1 is Tuesday 4/19, during section.
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