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6 Pages

120131-T-DeepSeaSed-Terrigenous-A.R

Course: GLG 244, Spring 2012
School: Miami University
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of 2/12/12! Consilience unity knowledge; confluence of knowledge and understanding In 1968, the following observations were "known" In 1968, the following observations were "known" 1! 2/12/12! 4800 4800 Water Depth Water Depth 2! 2/12/12! Water Depth Water Depth Better estimate of M.O.R. 3! 2/12/12! 1000 km 42 years 1000 million km 42 million years How many cm...

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of 2/12/12! Consilience unity knowledge; confluence of knowledge and understanding In 1968, the following observations were "known" In 1968, the following observations were "known" 1! 2/12/12! 4800 4800 Water Depth Water Depth 2! 2/12/12! Water Depth Water Depth Better estimate of M.O.R. 3! 2/12/12! 1000 km 42 years 1000 million km 42 million years How many cm per year? 1000 m 62 million years 4! 2/12/12! How many cm per year? cm/1000 years? 1000 m 62 million years Terrigenous material to the ocean: How does it get there? Pre-Katrina 5! 2/12/12! Point Source of sediment Which rivers? How much sediment? END Tuesday, January 31, 2012 6!
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Miami University - GLG - 244
1/31/12Convection in the EarthComposite idea of forces of plate tectonics: Push Pull DragTrujillo and Thurman, 2010Trujillo and Thurman, 2010Trujillo and Thurman, 2010EarthquakesEnd of Lecture 12-01-2411/31/12EarthquakesBi enofo fZneTrujil
Miami University - GLG - 244
1/31/12ca. 1915Fig. 3-3, p. 51Overlaps (red) Underlaps (blue)Overlaps (red) Underlaps (blue)Is there a fit of the continents, or not?Is there a fit of the continents, or not?http:/www.indiana.edu/~geol116/11/31/12PATTERNS ?END LECTURE 12-01-19
Miami University - GLG - 244
1/19/12!Pinnipeds (Pinnipedia)!(fin-footed)!1. Seals: ! (Phocidae)! earless! claws!Mark R. Boardman! http:/animals.nationalgeographic.com/animals/photos/seals-and-sea-lions/!Pinnipeds (Pinnipedia)!(fin-footed)!2. Sea Lions:! (Otariidae) ! eared! lo
Miami University - GLG - 244
1/19/12BATHYMETRYObservations (facts) Patterns Synthesis Hypotheses or Theory(explanation grounded in data and patterns of data)REMOTE SENSING:Indirect methods of "seeing"REMOTE SENSING:Indirect methods of "seeing"Echosoundingtelevision, telephon
Miami University - GLG - 244
1/19/12BATHYMETRYObservations (facts) Patterns Synthesis Hypotheses or Theory(explanation grounded in data and patterns of data)Goals and ObjectivesUnderstand what methods were used historically and are used today to make observations about the bathy
Miami University - GLG - 244
Miami University - GLG - 244
1/19/12Oceanography GLG 244 Spring, 2012interdisciplinary Complex and ComplicatedCredibilityConsilienceComplex + Complicatedindirect ways of knowing (instrumentation) scientific system (not scientists) statisticsConsiliencelinkage of facts and
MIT - MATH - 18.100B
Problem Set 3, 18.100B/C, Fall 2011Michael Andrews Department of Mathematics MIT October 1, 20111Let X be a metric space and E X. Let cl(E) denote the closure of E and let int(E) denote the interior of E.aWe proved on the last sheet (problem 2) that
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Final exam review sheet Most of the final will consist of problems from this list. 1. Prove that R2 is not the union of a countable family of lines. 2. Problem 10 from page 44. 3. Let E R be uncountable. (a) Prove that E has
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011First midterm review sheet The first midterm covers all the material from chapters one and two, except for the appendix to chapter one. On the midterm you will be asked to give the proof, or a part of the proof, of one or two
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Second midterm review sheet The second midterm covers all the material from chapters 3 5, and you may use results from chapters 1 5 without proof. Most of the midterm will consist of problems from this list. You will not be a
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Problem Set 1 Due September 15th at 4 pm in room 2-108. Hand in parts 1, 2 and 3 separately. Put your name and whether you are registered for 18.100B or 18.100C on each part. Part 1 1. Let m and n be positive integers with no
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Problem Set 2 Due September 22nd at 4 pm in room 2-108. Hand in parts 1, 2 and 3 separately. Put your name and whether you are registered for 18.100B or 18.100C on each part. Part 1 1. Problem 15 from page 23. Students regist
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Problem Set 3 Due September 29th at 4 pm in room 2-108. Hand in parts 1, 2 and 3 separately. Put your name and whether you are registered for 18.100B or 18.100C on each part. Part 1 1. Let X be a metric space and E X. Let cl(
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Problem Set 4 Due October 13th at 4 pm in room 2-108. Hand in parts 1, 2 and 3 separately. Put your name and whether you are registered for 18.100B or 18.100C on each part. Part 1 1. Problem 1 from page 78. 2. Let X be a comp
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Problem Set 5 Due October 20th at 4 pm in room 2-108. Hand in parts 1, 2 and 3 separately. Put your name and whether you are registered for 18.100B or 18.100C on each part. Part 1 1. (a) Prove that if (an )nN is a bounded seq
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Problem Set 6 Due October 27th at 4 pm in room 2-108. Hand in parts 1, 2 and 3 separately. Put your name and whether you are registered for 18.100B or 18.100C on each part. Part 1 1. Problem 9 from page 79. 2. Suppose (an )nN
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Problem Set 7 Due November 3rd at 4 pm in room 2-108. Hand in parts 1, 2 and 3 separately. Put your name and whether you are registered for 18.100B or 18.100C on each part. Part 1 1. Let X and Y be metric spaces and f : X Y a
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Problem Set 8 Due November 17th at 4 pm in room 2-108. Hand in parts 1, 2 and 3 separately. Put your name and whether you are registered for 18.100B or 18.100C on each part. Part 1 1. Problem 15 from page 115. 2. Problem 16 f
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Problem Set 9 Due December 1st at 4 pm in room 2-108. Hand in parts 1, 2 and 3 separately. Put your name and whether you are registered for 18.100B or 18.100C on each part. Part 1 1. Problem 10, parts a c, from page 139. Hint
MIT - MATH - 18.100B
18.100B and 18.100C Fall 2011Problem Set 10 Due December 8th at 4 pm in room 2-108. Hand in parts 1, 2 and 3 separately. Put your name and whether you are registered for 18.100B or 18.100C on each part. Part 1 1. Let K : [0, 1] [0, 1] R be continuous, an
MIT - MATH - 18.100B
Problem Set 1, 18.100B/C, Fall 2011Michael Andrews Department of Mathematics MIT September 21, 20111Let m and n be positive integers with no common factor. Prove that if m/n is rational, then m and n are both perfect squares, that is to say there exist
MIT - MATH - 18.100B
Problem Set 2, 18.100B/C, Fall 2011Michael Andrews Department of Mathematics MIT September 21, 20111Problem 15 from page 23. Let a = (a1 , . . . , an ), b = (b1 , . . . , bn ) Cn . Putn n nA=i=1|aj |2 , B =j=1|bj |2 and C =j=1aj bj .Then it wa
Minnesota - MATH - 5525
Math 5525: Spring 2010 Introduction to Ordinary Differential EquationsInformation on Final Exam: Tuesday, May 11, 2010Time and place: Tuesday, May 11, 10:30 am 12:30 pm, AmundH 240. There will be 8 problems. No books, no notes. Calculators are permitted
Minnesota - MATH - 5525
Math 5525: Spring 2010 Introduction to Ordinary Differential Equations: Homework #1 (due on February 10). 100 points are divided between 10 problems, 10 points each. #1. Find a second-order equation of the form a(x)y +b(x)y +c(x)y = 0, which has solutions
Minnesota - MATH - 5525
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations: Homework #2 (due on March 10). 100 points are divided between 8 problems. #1. (10 points). Find the solution of the problem xy + 4y + x = 0. satisfying the initial condition y(1) = 0
Minnesota - MATH - 5525
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations: Homework #3 (due on March 31). 100 points are divided between 6 problems. #1. (10 points). Let y(x) be a solution of the problem y = sin y, y(0) = a R1 = (-, ),which is defined on R
Minnesota - MATH - 5525
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations Homework #4 (due on Wednesday, April 28). 100 points are divided between 5 problems, 20 points each. You can use without proof statements of Problems in the textbook. #1. Find the bou
Minnesota - MATH - 5525
nnswwtL.r-+n *t'L.tf,f(Yn',cfw_ =-t+UXL\ ol cfw__ e ;-T*_* f 2q+)x-6+xzc - c &" L)a+(x"-2*)g = e &=x'-|x " 4= \-*,-, (=Ax-T* -dN =C 't+*v?tu-fr\l I Ci. t4 tcfw_-dN T^'t4cfw_+ "U*&lv-'l-*l- trc + C a*.#ttt 't-.l-L I r , -cfw_-r -1-l.l-
Minnesota - MATH - 5525
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations: Homework #2. Problems and Solutions #1. Find the solution of the problem xy + 4y + x = 0. satisfying the initial condition y(1) = 0. Solution. The corresponding homogeneous equation
Minnesota - MATH - 5525
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations: Homework #3. Problems and Solutions #1. Let y(x) be a solution of the problem y = sin y, y(0) = a R1 = (-, ),which is defined on R1 . Show that y(x) is a monotone function on R1 , e
Minnesota - MATH - 5525
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations: Homework #4. Problems and Solutions #1. Find the bounded continuous functions p1 (x), p2 (x), . . . , pn (x) with minimal possible n, such that the function x3 y(x) = sin x - x + 6 s
Minnesota - MATH - 5525
Math 5525. May 11, 2010. Final Exam. Problems and Solutions. Problem 1 (10 points) Find the general solution of the problem dy y 2 - x2 x = + . dx xy y Solution. dy y 2 - x2 x y = + = , dx xy y x v= y x = v+x dv = v, dx dv = 0, dx v = C, y = Cx.Problem 2
Minnesota - MATH - 5525
Math 5525. April 14, 2010. Midterm Exam 2. Problems and Solutions. Problem 1. Find the general solution of the equation xy - (2x + 1)y + (x + 1)y = 0. Note that one of two linearly independent solutions is y1 (x) = ex . Solution. By Abel's formula, the Wr
Minnesota - MATH - 5525
Math 5525: Introduction to Ordinary Differential EquationsSyllabus: Spring 2010Class Times and Location: 2:30 pm 3:20 pm MWF, AmundH 240. Instructor: Mikhail Safonov, VinH 231, tel: 625-8571, email: safonov@math.umn.edu http:/www.math.umn.edu/safonov Of
Minnesota - MATH - 3283
MATH 3283W. Sequences, Series, and Foundations: Writing Intensive. Spring 2009Homework 1. Problems and Solutions I. Writing Intensive Part 1 (5 points). Check whether or not each of the following statements can be true for some values ("true" or "false")
Minnesota - MATH - 3283
MATH 3283W. Sequences, Series, and Foundations: Writing Intensive. Spring 2009Homework 3. Problems and Solutions I. Writing Intensive Part 1. Let f (x) be a continuous function on the segment [0, 1]. Show that f is uniformly continuous on [0, 1], which m
Minnesota - MATH - 3283
These notes by Mikhail Safonov serve as a supplementary material to the textbook by Weyne Richter "Sequences, Series and Foundations. Math 2283 and 3283W"Sequences, Series and FoundationsChapter 1. Truth, Falsity and Mathematical Induction1 Truth Table
Minnesota - MATH - 5615
Math 5615H. Name (Print)October 5, 2011.Midterm Exam.60 points are distributed between 5 problems. You have 50 minutes (2:30 pm 3:20 pm) to work on these problems. No books, no notes. Calculators are permitted, however, for full credit, you need to sho
Minnesota - MATH - 5615
Math 5615H. Name (Print)November 16, 2011.2nd Midterm Exam.60 points are distributed between 5 problems. You have 50 minutes (2:30 pm 3:20 pm) to work on these problems. No books, no notes, except for: Appendix A. Exponential and Logarithmic Functions
Minnesota - MATH - 5615
Appendix A. Exponential and Logarithmic FunctionsFor fixed b > 1, the function bx was defined in Exercise 6 on p.22 in the textbook "Principles of Mathematical Analysis" by W. Rudin. It satisfies bx > 0, and (E1). bx+y = bx by for real x, y. In particula
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #1 (due on Wednesday, September 14). 50 points are divided between 5 problems, 10 points each. #1. Prove that 6 and 2 + 3 are NOT rational. #2. Let A and B be bounded sets in R. Consider the algeb
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #2 (due on Wednesday, September 21). 50 points are divided between 5 problems, 10 points each. #1. Let F be a field. Show that there exist not more that two different solutions solutions of the eq
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #3 (due on Wednesday, September 28). 50 points are divided between 5 problems, 10 points each. #1. Let A := cfw_a1 , a2 , . . . be a set of real numbers defined as follows: a1 = 1, Find sup A. #2.
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #4 (due on Wednesday, October 5). 50 points are divided between 5 problems, 10 points each. #1. Let f be a mapping of A to B. Show that for each B1 B and B2 B, their inverse images satisfy the pro
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #5 (due on Wednesday, October 12). 50 points are divided between 5 problems, 10 points each. #1. Show that for an arbitrary sequence E1 , E2 , . . . of sets, the set ( n=1 k=n) Ek is contained i
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #6 (due on Wednesday, October 19). 50 points are divided between 5 problems, 10 points each. #1. Show that for an arbitrary set E in a metric space (X, d), the set E of its limit point is closed.
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #7 (due on Wednesday, October 26). 50 points are divided between 4 problems. You can use the following Theorem which was proved in class. Theorem. A subset K of a metric space (X, d) is compact in
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #8 (due on Wednesday, November 2). 50 points are divided between 4 problems. #1. (12 points). Let 0 < x1 = a < x2 = b be arbitrary real number, and let 1 xn := (xn-2 + xn-1 ) for n = 3, 4, 5, . .
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #9 (due on Wednesday, November 9). 50 points are divided between 4 problems. #1. (10 points). Using partial-fraction decomposition 1 A B C = + + , n(n + 1)(n + 2) n n+1 n+2 show that the series n
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #10 (due on Wednesday, November 16). 50 points are divided between 4 problems. #1. (12 points). The sequence cfw_an is defined by a1 = 0, and an+1 = 2an /2 for n = 1, 2, 3, . . . .Prove that cfw
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #11 (due on Wednesday, November 23). 50 points are divided between 4 problems. #1. (12 points). Find S :=n=1 n . 2nHint. One can try to rewrite 2S in terms of S, or use Theorem 3.41 with an = 1
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #12 (due on Wednesday, November 30). 50 points are divided between 5 problems, 10 points each. #1. Let aj and bj,k be real numbers defined for all j, k = 0, 1, 2, . . ., such that j=0|aj | A = c
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #13 (due on Wednesday, December 7). 50 points are divided between 4 problems. #1. (10 points, Exercise 2 on p.98). If f is a continuous mapping of a metric space X into a metric space Y , prove th
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I.Fall 2011Homework #1. Problems and short Solutions. #1. Prove that 6 and 2 + 3 are NOT rational. Proof. If p := 6 Q, then p2 = 6, and we get a contradiction in the same way as in Example 1.1 in the textbook. If q :
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I. Homework #2. Problems and Solutions.Fall 2011#1. Let F be a field. Show that there exist not more that two different solutions solutions of the equation x x = 1. Is it possible that there is only one solution to t
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I. Homework #3. Problems and Solutions.Fall 2011#1. Let A := cfw_a1 , a2 , . . . be a set of real numbers defined as follows: a1 = 1, and ak+1 = 1 + ak for k = 1, 2, . . . . Find sup A. Solution. By induction, 1 ak <
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I. Homework #4. Problems and Solutions.Fall 2011#1. Let f be a mapping of A to B. Show that for each B1 B and B2 B, their inverse images satisfy the properties (i) f -1 (B1 B2 ) = f -1 (B1 ) f -1 (B2 ), Proof. (i) We
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I. Homework #5. Problems and Solutions.Fall 2011#1. Show that for an arbitrary sequence E1 , E2 , . . . of sets, the set lim inf En :=n n=1 k=nEkis contained inlim sup En :=n n=1 k=nEk .Proof. For arbitrary
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I. Homework #6. Problems and Solutions.Fall 2011#1. Show that for an arbitrary set E in a metric space (X, d), the set E of its limit point is closed. Proof. Let p be a limit point of E . Then r > 0, the set Gr := Nr
Minnesota - MATH - 5615
Math 5615H: Introduction to Analysis I. Homework #7. Problems and Solutions.Fall 2011You can use the following Theorems which were discussed in class. Theorem 1. A subset K of a metric space (X, d) is compact in X if and only if every infinite subset E