Math 131A – Course Outline – Spring 2011 • Text: Apostol, Calculus, Volume I , 2 nd ed. • Instructor: Betsy Stovall 1. 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 in 115A, so our review will be brief. 2. Field and order axioms, Examples and non-examples of ﬁelds. Introduction to the real numbers. (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.
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This note was uploaded on 09/23/2011 for the course MATH 131 taught by Professor Eskin during the Spring '10 term at UCLA.