What is Spivak: Definition and 166 Discussions

Spivak or Spivack is a surname of Ukrainian and Polish origin, meaning singer. It is also common among Ashkenazi Jews. The name may refer to:

Charlie Spivak (1905 or 1907–1982), American trumpeter and bandleader
David Spivak (born 1978), American mathematician
Elye Spivak (1890–1950), Soviet linguist
Gayatri Chakravorty Spivak (born 1942), Indian literary critic and professor at Columbia University
Gordon Spivack (1928–2000), American antitrust lawyer and Justice Department official
John L. Spivak (1897–1981), American communist reporter and author
Lawrence E. Spivak (1900–1994), American journalist and publisher
Lori Spivak (contemporary), Canadian jurist from Manitoba
Marla Spivak (born 1955), American entomologist and winner of the MacArthur Fellowship
Maryana Spivak (born 1985), Russian actress
Michael Spivak (born 1940), American mathematician
Mira Spivak (born 1934), Canadian politician from Manitoba; member of the Canadian Senate
Nissan Spivak (1824–1906), Bessarabian cantor and composer
Nova Spivack (born 1969), American internet entrepreneur
Oleksandr Spivak (born 1975), Russian football player of the FC Zenit Saint Petersburg Russian football club
Sidney Spivak (1928–2002), Canadian politician from Manitoba

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  1. D

    Spivak problem and question

    Homework Statement Spivak's "Calculus" Chapter 1, Problem 4v Find all numbers x for which x^2-2x+2>0 Homework Equations The Attempt at a Solution x^2-2x+2>0 x^2-2x>-2 x^2-2x+1>-2+1 (x-1)^2>-1 x\in R Would that be an adequate proof? Anything...
  2. C

    Proving f is Continuous Everywhere: Spivak Calc Problem

    Homework Statement f is a function that satisfies f(x+y)=f(x)+f(y) and f is continuous at 0. prove f is continuous everywhere Homework Equations The Attempt at a Solution its easy to see that f(0)=0 My hunch is that the only soln f= cx, and f=0; but otherwise can't make...
  3. B

    Which Calculus Book Gives Best Understanding: Spivak or Apostol?

    I am looking for a calculus book that gives the reader deep understanding of how calculus works, not just rote memorization. I have heard that the books by Micahel Spivak and Tom Apostol are good. Which of the books provides the best understanding of calculus: Spivak's or Apostol's? My parents...
  4. M

    Is the Intermediate Value Theorem Sufficient for Proving Continuity?

    I have the 4th edition of Spivak's Calculus. Problem 13(b) in Chapter 7 says: ------ Suppose that f satisfies the conclusion of the Intermediate Value Theorem, and that f takes on each value only once. Prove that f is continuous. ------- Well, what about this function: f(1) = 2 f(2)...
  5. H

    Spivak as first exposure to Calculus?

    Next year I'm going to begin studying physics as freshman and this summer I was thinking about studying Calculus on my own. Would Spivak be feasible as an introduction to calculus? I'm in Pre-Calculus right now and find it pretty easy (though I know that is not necessarily any indicator of...
  6. Z

    Spivak Calc on Manifolds, p.85

    Please forgive any stupid mistakes I've made. On p.85, 4-5: If c: [0,1] \rightarrow (R^n)^n is continuous and each (c^1(t),c^2(t),...,c^n(t)) is a basis for R^n , prove that |c^1(0),...,c^n(0)| = |c^1(1),...,c^n(1)| . Maybe I'm missing something obvious, but doesn't c(t) =...
  7. rocomath

    Prove x^n - y^n = (x-y)(x^{n-1}+x^{n-2}y+...+xy^{n-2}+y^{n-1})

    Prove the following: x^n - y^n = (x-y)(x^{n-1}+x^{n-2}y+...+xy^{n-2}+y^{n-1}) Hmm ... I factored x then -y and came out with: x^{n}+...x^{2}y^{n-2}-x^{n-2}y^{2}...-y^{n} Argh. What's up with the middle part? I'm not sure where to go from here.
  8. rocomath

    Spivak, Calculus - Where to find or is it covered?

    I just got Spivak's book a couple days ago, I've flipped through it and was looking through the Index. Does Spivak cover Related Rates or Optimization? I did not find it at all, so I am curious and wondering if it's under some other name. Thanks!
  9. D

    X + 3^x < 4 ? Spivak got me on Chap. 1

    Must be something missing from my repertoire-- Spivak got me in Chapter 1! :-) Trying to find all x that satisfy: x + 3^x < 4 I've tried everything I can think of. Here are a few lines I've run down, to no avail: x + 3^x < 4 \Rightarrow e^{x+3^x} < e^4 \Rightarrow e^x \cdot...
  10. I

    Whats the big deal with spivak?

    I honestly enjoyed using James Stewart (yes heathen) when I did calc I, II, III and now these forums are buzzing with Spivak - as if he's the new Giancoli/Feynman of math textbooks whats the big deal? Oh - and i did check out the Amazon.com reviews - surprisingly the one bad review I read...
  11. J

    Proof of Proposition 2 in Ch.7 Spivak Vol.2: n-Dimensional Distribution?

    Hi. I have a question on proof of proposition 2 in chater 7 Spivak volume2. In the proof, he says that the n-dimensional distribution \Delta_{p}=\bigcap^{n}_{i,j=1}ker\Lambda^{i}_{j}(p) in R^(n+n^2) is integrable. Could anyone explain why it is an n dimensional distribution? Thanks.
  12. B

    Comprehensive intro to diff geometry by Spivak Vol2.

    I am reading a Vol2 of geometry book by Spivak. On page 220-221 he says that: "Notice that the possibility of defining covariant derivatives depends only on the equation..." The equation is some equality involving Christoffel Symbol. If anyone has this book, could you explain why what he...
  13. E

    Apostol or Spivak? Which Math Book?

    I own both volumes of Apostol, but I must confess that when I bought them I had never heard of Spivak's book. I think it's pretty much a toss up for me now. What about you guys?
  14. R

    Proving Differentiability Using Inequalities

    Suppose f(a) = g(a) = h(a) and f(x) <= g(x) <= (x) for all x Prove g(x) is differentible and that f'(a) = g'(a) = h'(a). So.. I need to prove that the following limit exists: lim h -->0 (g(x+h) - g(x)) / h but how can i use the fact that f(x) <= g(x) <= (x) for all x? Thanks
  15. P

    Spivak calculus on manifolds solutions? (someone asked this b4 and got ignored)

    Does anyone know if there's worked out solution to the problems in spivak's calculus on manifolds? It's awfully easy to get stuck in the problems and for some of them I don't even know where to start... Also, if there isn't any, any good problem and 'SOLUTION' source for analysis on manifolds...
  16. K

    (Spivak) - a function with strange behaviour.

    1) Find a function, f(x) which is discontinuous at 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4} ..., but continuous at any other points. Solution (I have come across, probably wrong and a half): f(x) = { 1 for all real x; 0 for 1/x where x is natural numbers. Can anyone tell me the answer to...
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