MATA37H3 Lecture Notes - Lecture 1: Summation, Associative Property, Riemann Sum
Document Summary
Mata37 - lecture 1 - syllabus, sigma notation, and area approximation. Course information: instructor: dr. kathleen smith, email: smithk@utsc. utoronto. ca, of ce: ic 458, hours: 4 pm - 5 pm: grading scheme: Sigma notation (chapter 4. 1: review from calculus i, chapter 4. 1, de nition of sigma notation (see page 318): If ak is a real-valued function of k, then am + am+1 + + an 1 + an = M is the starting value, and n is the end value. 4(cid:88) k=1 ak = ak + ak k=m+1 k=1: ex. 4(cid:88) (2ak + 3bk) ak = 7, bk = 10, a0 = 2, nd. = 2 ak + 3 bk k=0. = 2(a0 + k=0 ak) + 3 k=0 k=0. = 2(2 + 7) + 3(10) = 2(9) + 3(10) = 48: useful formulas: k=1 n(cid:88) n(cid:88) n(cid:88) n(cid:88) k=1 k=1 k=1. 2 k2 = k3 = n(n + 1)(2n + 1) 27 n3 k2) = lim n n(cid:88) k=1.
