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Unformatted text preview: MAT 320 Fall 2007 Review for Final Note: Final is cumulative, so use the Midterm 2 Review and the Midterm 1 Practice Exam as well as the material below. • Theorem: be able to apply • Theorem : and know what goes into the proof • Theorem : and be able to prove. § 7.1 Understand the parallelism between the definition of “ f is Riemann integrable on [ a, b ] with integral L ” and, for example, “the sequence ( a n ) is convergent with limit L .” Basic: Theorem 7.1.2 The integral is unique. Understand examples (c) and (d) on p.198, and understand the elementary Theorem 7.1.4 . Also Theorem 7.1.5 , and review Example 7.1.6 (Thomae’s function on [0 , 1] is in R ([0 , 1]). § 7.2 Theorem 7.2.1 (Cauchy Criterion) important because it gives a definition of “ f integrable on [ a, b ]” that does not involve the value of R b a f . Theorem 7.2.3 - “Squeeze Theorem” used in proof of Theorem 7.2.6 : If f is continuous on [ a, b ] then f ∈ R ([ a, b ]). Theorem 7.2.7 : If f is monotone on [ a, b ] then f ∈ R ([ a, b ]). Theorem 7.2.8 (Additivity Theorem) etc....
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- Fall '10
- Mathematical Series, Riemann