Math 318b: ANALYSIS II
(Fall 1997)
ASSIGNMENTS AND IMPORTANT NOTICES
Assignment 1 (due in class on Fri 1/30)
Readings: Study Bartle section 29 and first half of section 30.
Problems to hand in: Bartle 29.B, 29.D, 29.J and 29.K (a unique grade will be given to these two), 29.O, 30.D.
Note that you will find hints for some of these problems in the back of the book.
Assignment 2 (due in class on Fri 2/6)
Readings: Study Bartle sections 30 and 31 (skip the Riesz Representation theorem).
Problems to hand in: Bartle 30.A, 30.J, 30.P, 30.Q, and problem assigned in class on Wed 2/28.
Note that you will find hints for some of these problems in the back of the book.
Assignment 3 (due in class on Fri 2/13)
Readings: Finish Bartle section 31 (you can skip the integral form for the remainder and the proof of the Riesz Representation theorem) and study section 32.
Problems to hand in: Bartle 31.B and 31.E (a unique grade will be given to these two), 31.J, 31.M, 31.N, 32.A.
Note: Problem 32.A will be collected together with Assignment 4 (on Fri 2/20), instead of with Assignment 3.
Assignment 4 (due in class on Fri 2/20)
Readings: Finish Bartle section 32 and study section 34.
Problems to hand in: Bartle 32.A, 32.C,32.D, 32.E(c) and 32.F(f) (a unique grade will be given to these two), 32.J.
Note:
The midterm on Fri 2/27 will be a closed book and closed notebook exam and will cover the material from Bartle sections 29, 30, 31, 32, and 34.
Homework will not be collected on Fri 2/27. Here are some suggested problems for section 34: from pb. A to problem D, and pb. F.
Assignment 5 (due in class on Fri 3/6)
Readings: Study Bartle section 35 and first half of 36.
Problems to hand in: Bartle 34.C; 34.G, 34.H, and 34.I (a unique grade will be given to these three); 35.A and 35.B (a unique grade will be given to these two); 35.R.
Assignment 6 (due in class on Fri 3/20)
Readings: Study Bartle section 36 (except double series and the proof of Thm. 36.13) and section 37 up to page 322 inclusive (you can skip Thm. 37.8 and 37.9).
Problems to hand in: Bartle 36.B and 36.C (a unique grade will be given to these two); 36.G (note that the sequence (z_n) of your example should still converge to 0; only the hypothesis of decreasing should be dropped), 37.C, 37.G, 37.J.
Assignment 7 (due in class on Fri 3/27)
Readings: Study Bartle section 37 up to page 324 (you can skip Thm. 37.8, 37.9, 37.18 and 37.19) and first half of section 38.
Problems to hand in: Bartle 37.N and 37.O (a unique grade will be given to these two), 31.Q (except the last sentence regarding the relation between the mean and the mean square quasi-norms), 38.B, 27.P and 38.C (a unique grade will be given to these two).
Assignment 8 (due in class on Fri 4/3)
Readings: Study Bartle section 38 up to Theorem 38.11 inclusive.
Problems to hand in: problem assigned in class, and Bartle 38.E, 38.M.
Note: There are ony three problems assigned. Make sure you prove every statement very carefully, without omitting any relevant detail.
Assignment 9 (due Fri 4/10)
Readings: Study Bartle section 39.
Problems: Homework will not be collected on Fri 4/10. Here are some suggested problems for section 39: A, B, D, F.
Note:The midterm on Fri 4/10 will be a closed book and closed notebook exam and will cover the material from assignment # 5 to this assignment inclusive.
Assignment 10 (due Fri 4/17)
Readings: Study Bartle section 40 (you can skip Taylor's theorem).
Problems: Bartle 39.J, 40.E, 40.U.
Assignment 11 (due Fri 4/24)
Readings: Study Bartle section 41 up to page 386 inclusive .
Problems: Bartle 40.R, 21.P and 41.A (a unique grade will be given to these two), 41.D, 41.H.
Assignment 12
Readings: Study Bartle sections 43 and 44.
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