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LSU - EE - 3220
google_ad_url = ';google_date = new Date();google_random = google_date.getTime();google_org_error_handler = window.onerror;function quoted(str) cfw_return (str != null) ? '"' + str + '"' : '"';function google_encodeURIComponent(str) cfw_if (typeof
BYU - CHIN - 201
01/06/2012Every Chinese character is made up of a number of strokes, or single movements of the pen or writing brush. The order and direction in which the strokes are made are very important in producing uniform characters, and learning the basic rules o
BYU - CHIN - 201
01/14/2012
BYU - CHIN - 201
01/20/2012
BYU - CHIN - 201
02/03/2012??
Xiamen University - FIN - 201
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Xiamen University - FIN - 201
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Xiamen University - FIN - 201
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Xiamen University - FIN - 201
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Xiamen University - FIN - 201
5. 6.() 1.( ) 2. 3. () 1. 2. () 1. (1) (2) (3) (4) (5) (6) (7)2. (1) (2) (3) (4) 3. (1)(2) (3)" () () 1. (1) (2) (3) 2. (1) (2) 3. (1) (2) (3) 4. (1) (2) (3) (4) 5. (1) (2) (3) 6.
Xiamen University - FIN - 201
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Xiamen University - FIN - 201
2. 3. 4. * 1. 2. 3. 1. * * * * 15-1 15-2 15-3 15-4 2. 3.
UMass Lowell - CS - 91.304
91.304 Foundations of Computer ScienceChapter 0 Lecture Notes Prof. David Martin and Prof. Giam Pecelli (with modifications by Prof. Karen Daniels)This work is licensed under the Creative Commons Attribution-ShareAlike License. To view a copy of this li
UMass Lowell - CS - 91.304
91.304 Foundations of (Theoretical) C (Th ti l) Computer S i t ScienceChapter 5 Lecture Notes (Remainder) David Martin (with modifications by Karen Daniels) dm@cs.uml.edu With thanks to Giam PecelliThis work is licensed under the Creative Commons Attrib
UMass Lowell - CS - 91.404
UMass Lowell Computer Science 91.404Analysis of AlgorithmsProf. Karen DanielsFall, Fall 2011Heap Lecture Chapter 6 Ch tUse NOTES feature to see explanation accompanying some slides. PseudoPseudo-code is from Cormen et al. textbook.Heap BasicsStruct
UMass Lowell - CS - 91.404
UML CSAnalysis of Algorithms 91.404 (section 201) Homework Set #1Fall, 2011Assigned: Friday, 9/2Due: Wednesday, 9/14 (start of lecture)This assignment covers textbook material in Chapters1-2.Note: Refer to course web site for homework policies. Reme
UMass Lowell - CS - 91.404
UML CSAnalysis of Algorithms 91.404 (section 201) Homework Set #2Fall, 2011Assigned: Wednesday, 9/14Due: Wednesday, 9/21 (start of lecture)This assignment covers textbook material in Chapters1-3.Note: Refer to course web site for homework policies.
UMass Lowell - CS - 91.404
UML CSAnalysis of Algorithms 91.404 (section 201) Homework Set #3Fall, 2011Assigned: Wednesday, 9/21Due: Wednesday, 9/28 (start of lecture)This assignment covers textbook material in Chapters 1-4.Note: Refer to course web site for homework policies.
UMass Lowell - CS - 91.404
UML CSAnalysis of Algorithms 91.404 (section 201) Homework Set #4Fall, 2011Assigned: Friday, 9/30Due: Wednesday, 10/5 (start of lecture)This assignment covers textbook material in Chapters 1-5.Note: Refer to course web site for homework policies. Pl
UMass Lowell - CS - 91.404
UML CSAnalysis of Algorithms 91.404 (section 201) Homework Set #5Fall, 2011Assigned: Friday, 10/7Due: Friday, 10/14 (start of lecture)This assignment covers textbook material in Chapters 1-6.Note: Refer to course web site for homework policies. Plea
UMass Lowell - CS - 91.404
UML CSAnalysis of Algorithms 91.404 (section 201) Homework Set #6Fall, 2011Assigned: Monday, 10/17Due: Monday, 10/24 (start of lecture)This assignment covers textbook material in Chapter 7. Note: Partial credit for wrong answers is only given if work
UMass Lowell - CS - 91.404
UML CSAnalysis of Algorithms 91.404 (section 201) Homework Set #7Fall, 2011Assigned: Wednesday, 10/31Due: Monday, 11/7 (start of lecture)This assignment covers textbook material in Chapter 8. Note: Partial credit for wrong answers is only given if wo
UMass Lowell - CS - 91.404
UML CSAnalysis of Algorithms 91.404 (section 201) Homework Set #8Fall, 2011Assigned: Wednesday, 11/9Due: Friday, 11/18 (start of lecture)This assignment covers textbook material in Chapters 10-11. Note: Partial credit for wrong answers is only given
UMass Lowell - CS - 91.404
UML CSAnalysis of Algorithms 91.404 (section 201) Homework Set #9Fall, 2011Assigned: Monday, 11/21Due: Monday, 12/5 (start of lecture)This assignment covers textbook material in Chapters 12-13. Note: Partial credit for wrong answers is only given if
UMass Lowell - UML - 84.314
Skoog Chapter 7Components of Optical InstrumentsGeneral Design of Optical Instruments Sources of Radiation Wavelength Selectors Sample Containers Radiation Transducers (Detectors) Signal Processors and Readouts Fiber OpticsOptical spectroscopic based o
UMass Lowell - UML - 84.314
Chapter 26: An Introduction to Chromatographic Separations Column Chromatography Migration Rates Distribution Contstants Retention Times Selectivity Factor Zone Broadening & Column Efficiency Optimizing Performance ResolutionIntro to Chromatography C
UMass Lowell - MATH - 491
Any questions about the exam? Homework? Maple? Final exam vs. final project Return exam Give overall comments: 1. Read everything before you start. Some of you didn't realize that when I ask for a formula for a sequence, I want a closed form formula, not
UMass Lowell - MATH - 491
TODAY: Short recurrence for counting lattice paths by q-weight Number partitions Short recurrence for counting lattice paths by q-weight Warm-up: combinatorial interpretation of (a choose b) b = a (a-1 choose b-1) Consequence: (a choose b) = (a/b) (a-1 ch
UMass Lowell - MATH - 491
Collect homework, and comments on how to improve the homework Any questions about the homework or the material? TODAY: Paths in DAGs Counting paths by multiplying matrices Domino tilings again Weighted enumeration A finite DAG (directed acyclic graph) is
UMass Lowell - MATH - 491
Math 491, Problem Set #11 (due 10/21/03)1. Let cn be the number of domino tilings of a 3-by-2n cylinder, obtained by gluing together the left and right sides (of length 3) of a 3-by-2n rectangle. Express the generating function c1 x + c2 x2 + c3 x3 + . .
UMass Lowell - MATH - 141
James Propp Office: OH 428C Phone: 978-934-2438 (not a good way to reach me except during office hours) Email: JamesPropp -at- gmail -dot- com Course web-page: http:/jamespropp.org/141/ Classroom: Pasteur 408 Meeting time: MonWedThuFri, 11:00-11:50 Welcom
UMass Lowell - MATH - 141
[Go around with names] [If there are new students:] Say your name Describe your academic and non-academic interests Say why you signed up for the course Say a little about your math background (esp. calculus) Talk about your best and worst math experience
UMass Lowell - MATH - 141
For graphing problems, you have to show work (e.g., plot specific points). You won't get much credit if it looks like you could have just copied your picture from the output of a graphing calculator. Key concepts of section 1.1: Function, domain, range In
UMass Lowell - MATH - 141
For Friday: Read section 1.2 Is everyone getting the email? Get contact info for new students. Reminder: You will derive the maximum benefit from (and enjoyment of) class discussions if you have done the reading ahead of time. Class meetings are where we
UMass Lowell - MATH - 141
[Collect students' notes on 1.2. Allow one day's grace: "You can hand them in on Monday."] [Remind them that the homework on section 1.1 is due on MONDAY.] The graph of y = f(x) = 1/sqrt(1x2) looks like2 .52 .01 .51 .00 .5 2 112Is the function f
UMass Lowell - MATH - 141
[Go around with names] [Hand out time sheets] Section 1.2 What's the main point of section 1.2? .?.Functions that crop up in the real world can be represented or at least approximated by functions that are algebraically built up from some universal build
UMass Lowell - MATH - 141
[Go around with names] [Collect notes on 1.3] [Hand out time sheets] Preparation for section 1.3: Quantifiers Last time we saw that the negation of the proposition "All good people like dogs" is "Some good people dislike dogs" i.e. "At least one good pers
UMass Lowell - MATH - 141
Section 1.3: The notion of limit Stewart's first definition: We write limxa f(x) = L and say "the limit of f(x), as x approaches a, equals L" if we can make the values of f(x) arbitrarily close to L by taking x to be sufficiently close (but not equal) to
UMass Lowell - MATH - 141
Section 1.3: The notion of limit (continued) [Discuss Example 9 on page 32 two ways: in terms of the picture, and in terms of strategies for Adam and Eve.] The limit of f(x) as x approaches a may be undefined, e.g., limx0 1/x. The existence of the limit,
UMass Lowell - MATH - 141
[Collect summaries of section 1.4] [Hand out time-sheets for assignment #3] Section 1.3: The notion of limit (continued) Claim (see Example 1 from p. 24): If A(h) = 4.9(10+h) for all h 0, limh0 A(h) = 49. Bad proof: "Just plug in h = 0." What's wrong with
UMass Lowell - MATH - 141
Section 1.3: The notion of limit (continued) For the function f(x) = x sin 1/x (defined for all x0) do we have limx0 f(x) = 0?0.4 0.3 0.2 0.1 0.4 0.2 0.1 0.20.20.4.?. Yes. What's Eve's strategy? .?. Eve wins by taking = . Check: For every x satisfyi
UMass Lowell - MATH - 141
[Take formal attendance]Campbell,David Young DeFilippo,James W Durkee,Zachary Martin Durrenberger,Marcelle Denise Gandevia,Munish Munir Graceffa,Erin R Kelly,Maureen Catherine Medeiros,Daniel Raposo Morris,John Patrick Theriault,Matthew Robert Vaughan,St
UMass Lowell - MATH - 141
One-sided limits: Suppose f(x) is a function defined for all values of x close to but less than a; that is, suppose there exists r > 0 such that f(x) is defined whenever x < a with |x a| < r. Then we say that limxa f(x) = L iff there for every > 0 there e
UMass Lowell - MATH - 141
[Hand out time sheets] Prof. Tibor Beke will substitute for me on Thursday and Friday of this week. Section 1.5: Continuity Key concept: Continuity. A continuous function is one that satisfies the direct substitution property limxa f(x) = f(a). Main point
UMass Lowell - MATH - 141
Section 1.5: Continuity (continued) Theorem 1.5.7: If limxa g(x) = b and limxb f(x) = c, then limxa f(g(x) = c, provided that the function f is continuous at b. Note that in the statement of the theorem, we could have written "f(b) = c" instead of "limxb
UMass Lowell - MATH - 141
Section 1.6: Limits involving infinity Key idea: Even though infinity isn't a real number, it can be useful as a way of indicating how functions behave. E.g., for f(x)=1/x2, according to our earlier definition, limx0 1/x2 is undefined, but we find it usef
UMass Lowell - MATH - 141
[Discuss True-False problems on page 70.] 1. "If f is a function, then f(s+t) = f(s) + f(t)." .?. False. Example: f(x) = x2, s = t = 1. Note however that it IS true that (f+g)(t) = f(t) + g(t); that's the definition of f+g. 2. "If f(s) = f(t), then s = t.
UMass Lowell - MATH - 141
[Hand out time-sheet; 241 too!] Revised due-date for assigment #5: 10/10 is a holiday! So it's due 10/12. Don't feel bad about making mistakes on the True/False questions! They're designed to be tricky. Better to make these mistakes now (and thereby learn
UMass Lowell - MATH - 141
Algebra review (preparing for chapter 2): (a2 b2)/(a b) = a + b (a3 b3)/(a b) = a2 + ab + b2 (a4 b4)/(a b) = a3 + a2b + ab2 + b3 (a5 b5)/(a b) = a4 + a3b + a2b2 + ab3 + b4 etc. (a + b)2 = 1a2 + 2ab + 1b2 (a + b)3 = 1a3 + 3a2b + 3ab2 + 1b3 (a + b)4 = 1a4 +
UMass Lowell - MATH - 141
For next Wednesday, read section 2.3. Last time we looked at the function f(x) = x|x|:42-2-112-2-4which can also be described by the two-part formula cfw_x2 if x < 0, f(x) = cfw_ cfw_x2 if x 0. We showed last time that f(x) is differentiable at x
UMass Lowell - MATH - 141
For Thursday, read section 2.4. "Paradox": "Solve x2 = 1. We get x = +1 and x = 1. So 1 = x = 1, implying 1 = 1." .?. An equation is only true (or false) in a context and in a domain of validity. Ignore the context and domain of validity and you may get n
UMass Lowell - MATH - 141
Unfinished business from section 2.2: We saw last time that the continuous function cfw_ x sin 1/x cfw_ cfw_0 is not differentiable at x=0.0.4 0.3 0.2 0.1for x 0 and for x = 0- 0.4- 0.2 - 0.1 - 0.20.20.4Now consider the function f(x) = cfw_ x2 sin
UMass Lowell - MATH - 141
Hand out practice exam. Paradox: Write x2 = x + x + . + x (x added to itself x times). Differentiating both sides, we get 2x = 1 + 1 + . + 1 (1 added to itself x times), or 2x = x. What's going on? .?. The equation x2 = x + x + . + x is valid only when x
UMass Lowell - MATH - 141
[Hand back homework and hand out practice test solutions.] What's the main idea of section 2.6? . Implicit differentiation: To differentiate y with respect to x, you don't always need to write y explicitly in the form f(x); it can be enough to write an al
UMass Lowell - MATH - 141
Questions about the midterm exam? Reminder: Your cheat sheet must be WRITTEN or TYPED by you. The exam will cover up through (and including) section 2.5 (the chain rule). True-false questions on pages 138139: 1. "If f is continuous at a, then f is differe
UMass Lowell - MATH - 141
Hand back homework, collect section notes Section 2.8: Linear approximation and differentials Main idea? .?. Derivatives are good for finding approximate values of functions If f is a differentiable function in the vicinity of x = a, then: for x a, the (u
UMass Lowell - MATH - 141
Section 2.8: Linear approximation and differentials (concluded): Section 2.8, Problem 24: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a hemispherical dome with diameter 50 m. Solution: For a hemispher
UMass Lowell - MATH - 141
Puzzle from Monday's lecture: Does there exist an irrational number r such that rsqrt(2) is rational? Hint: The answer is in Wednesday's lecture (sort of!). Solution: We can easily prove that either r = sqrt(2) or r = sqrt(2)sqrt(2) works, but the proof w
UMass Lowell - MATH - 141
Section 3.2: Inverse functions and logarithms (concluded) Fact: If f is an increasing function then f is one-to-one. (Note: Here "increasing" means "strictly increasing".) Proof: If x1, x2 are in the domain of f with x1 < x2, then since f is increasing, f
UMass Lowell - MATH - 141
Last time we saw one way to compute the derivative of xx with respect to x. Another method we can apply is logarithmic differentiation: (d/dx) ln f(x) = f (x) / f(x) That is, if f(x) > 0 on some open interval I, then ln f(x) is differentiable with derivat
UMass Lowell - MATH - 141
Section 3.4: Exponential growth and decay (concluded). Interest If you put $100 in the bank and it's compounded yearly with 12% annual interest, after 1 year you get your original $100 plus $12 interest, for a total of $100 times 1.12 = $112. If your mone