Spivak Definition and 161 Threads

Hello. I'm not sure if I'm making the topic in the right place but I'd like to have the fourth edition of Calculus (Spivak). I've got the 3rd one which is quite good but I'd like to see the 4th one. If anyone has it or knows where I can download it from it would be much appreciated if you can...

I have realized that almost everyone on this forum talks about the calculus by spivak, and from the arguments in it's favour make it unbeatable, it seems that nobody can learn analysis without reading that book. I am studying ONLINE at Paul's notes and Calculus by James Stewart, is my...

Hey guys, I'm an electrical engineering student on my first year. I'm from Canada and I think our first year of University is the equivalent of 2nd year in the USA. I've taken calc I, II and III (multi-variable calculus, PDE's...), statistics and linear algebra. I've also learned some discrete...

Homework Statement In problem 1.18.b of Calculus, he says: . (Bold mine). I assume that is supposed to say in fact x2+bx+c>0 ? However, I am having trouble proving that for all choices of b and c. If I complete the square on x2+bx+c>0 I get x2+bx+c = (x+b/2)2 + k > 0 => k > 0. So I...

Homework Statement Prove that if 0≤x<y then xn < ynHomework Equations 12 properties of numbers.The Attempt at a Solution For the case: 0 =x < y is trivial. So now we just need y > x > 0 : Now, I am having a bit of trouble with this. Take the case where n=2: x < y so x*x < x*y AND x*y...

Homework Statement Find all x for which \frac{x-1}{x+1}>0 \qquad(1)Homework Equations (2) AB > 0 if A,B >0 OR A,B < 0 (3) 1/Z > 0 => Z > 0 The Attempt at a Solution Since (1) holds if: (x-1) > 0 \text{ and } (x+1) > 0 \qquad x\ne -1 then we must have x>1 AND x>-1 and since (1) also...

Homework Statement I am doing the HW in Spivak's calculus (problem 4 (ii) ) on inequalities. The problem statement is: find all x for which 5-x2 > 8The Attempt at a Solution I know this is a simple problem, but bear with me for a moment. I want someone who is familiar with Spivak to tell...

Homework Statement Prove that if x2 = y2 then x=y or x = -y Homework Equations The 12 Properties of numbers The Attempt at a Solution I think I should do this case-wise: Case (a) if x=y then x2 = x*x=y*y=y2. Simple enough. Case (b) if x = -y then x2 = x*x=(-y)*(-y)...

Question if a < b, then -b < -a proof if a < b then a-b<0 and b-a>0 so a-b<0<b-a so -b<-a Question if a<b & c<0, then ab>bc proof if ac<ab then ab>bc then ac<ab>bc then ac>bc Question if a>1 then a^2>a proof a*a > 1*a lemma 1: a*a = a^2...

I am having a really difficult time doing these proofs and want to know how i need to confront them and if there is a good strategy to solving these. I am in first year university. I understood the problem the prof went over but when i try to do on my own, I am just not able to prove them. I...

Hello all :smile: I have started the problem set for Chapter one (basic properties of numbers) in Spivak's Calculus (self study). I think I am doing these right, but I have some questions. As a solid example, problem 1-(iv) says to prove the following: x^3 - y^3 =...

Hello all! :smile: I am (painfully) going through the first chapter of Spivak's Calculus. At one point he introduces the property: if a, b, and c are any numbers, then a\cdot(b+c) = a\cdot b +a\cdot c. He then uses this property in an example in which he shows that the only time that a - b =...

Homework Statement 1b) Prove by induction: 1^{3}+...+n^{3}=(1+...+n)^{2} 2a) Find a formula for: \sum^{n}_{i=1}(2i-1) Homework Equations There's a Hint for 2a): 'What to this expression have to do with 1+2+3+...+2n?' The Attempt at a Solution In 2a) I've got near the answer...

Homework Statement d) Show that \left|x-y\right| \leq \left|x\right|+\left|y\right| e) Show that \left|x\right|-\left|y\right| \leq \left|x-y\right| The Attempt at a Solution For item d) I've tried some approaches but none was promising. For item e), I tried squaring...

Homework Statement This is from Spivak, Vol. 4 Page 102-103 Given |x-x_0| < 1, |x-x0| < Epsilon/(2(|y_0|+1)) Also given |y-y_0| < Epsilon/(2(|x_0| + 1)) Prove |xy-x_0y_0| < Epsilon Homework Equations See above The Attempt at a Solution The proof proceeds clearly enough...

Where can I get a copy of Spivak (new) for <= 50$ as I have a gift card for $50?

Using the fact that the Arithmetic Mean of n numbers is greater than the Geometric Mean of those n numbers when n=2, prove by induction on k that the Arithmetic Mean is greater than the Geometric Mean for n=2^k. I know how to prove the AM-GM inequality in general, but I can't figure out how...

Hi everyone, been away for a while I got bogged down with my classes so didn't have time to work on this book and haven't been on the forums much. Was getting caught back up to where I was before in here and I ran into a problem that I can't figure out the notation on. I am only looking for...

Hey all, I'm going to be reading a calculus book after I finish my book on Trig. Problem is, i can't decide which book I want to read. I'm wondering if anyone has any insight on either book, or could recommend a better book. I want to use my time the most effectively so any input will be a big...

I have been trying to find them all over the place, but have had no such luck. Does anybody have the skinny on this book? I just got through ch. 1, and I am hooked! Spivak is a bad mamajamma, and I want to verify my answers. Thanks.

Spivak "Calculus" 3rd Ed. or 2nd Ed.? I've found a pretty interesting price for the 3rd Ed. of Spivak "Calculus". I'm wondering if you suggest me to buy it or to look for the second edition. My concern is related to the fact that almost every scientific textbook is watered down edition...

1. Spivak 4th Edition Problem 1 (i) Chapter 1 If ax = a for some a not equal to 0, then x = 1. 2. P7 where a*a^-1=a^-1*a=1 3. Using P7 Then (x^-1)ax=a then (X^-1 * x)a=a then 1*a=a then x=1 Am I approaching this correct or am I supposed to prove P7 as well or prove this a whole different...

I hope this is not the wrong place to ask this... Can anybody tell me if it is possible to find "Spivak calculus on manifolds" on line (a PDF copy for example) Thanks

Homework Statement Prove that a/b=c/d if and only if ad=bc Homework Equations Multiplicative inverse property: (a)(a^1) = 1 Commutativity: ab = ba Associativity: (ab)c = a(bc) Transitivity: If a = b and b = c then a = c The Attempt at a Solution a/b=c/d=ab^1= cd^1. Multiplying both sides by...

Hi I'm doing the first chapter of Spivak's Calculus and just a little concerned about a particular thing he does in the chapter. He is talking about the trichotomy axiom and that if a > b then a - b, this can be understood as expressing (a - b) > 0 and then the axiom can be interpreted...

Heard many people say that there are three good cal textbooks: the ones by Apostol, Spivak, and Courant. I own Apostol's and Spivak's. The major difference between the two is the degree of rigor and logical order, in which Apostol's apparently beats Spivak's, although Spivak's is far better than...

Homework Statement Let A and B be two nonempty sets of numbers which are bounded above, and let A+B denote the set of all numbers x+y with x in A and y in B. Prove that sup(A+B) = sup(A) + sup(B). Hint: The inequality sup(A+B) <= sup(A) + sup(B) is easy. To prove that sup(A) + sup(B)<=...

I'm currently studying Euclid's Elements and Elements of Algebra by Euler. I'd like to know what others recommend I study before Spivak/Apostol. I've been researching a lot, and have had major difficulty in discerning proper texts.

http://planetmath.org/?op=getobj&from=objects&id=4370 that's pretty much the proof of Stolkes Theorem given in Spivak but I'm having a lot of difficulty understanding the details specifically...when the piecewise function is defined for j>1 the integral is 0 and for j=1 the integral is...

Homework Statement |x + y + z| \le |x| + |y| + |z|. Indicate when the equality holds, and prove your statement. Homework Equations Answer in the books says it hold only when x, y, and z are all of the same sign. The Attempt at a Solution The value on the rhs of the eq will keep...

Is Michael Spivak Wrong!? My text says, In general, if ε > 0, to ensure that |x²sin(1/x)| < ε, we need only require that |x| < ε and x ≠ 0, provided that ε ≤ 1. If we are given an ε which is greater than 1 (it might be, even thought it is "small" ε's which are of interest), then it does not...

I've been trying to learn introductory physics for about a month now from a copy of Halliday 6th ed with some supplements from MITs 8.01 and an electronic copy of Feynman's lectures (I'm at about chapter/lecture 10 give or take in all of them) and I'm finding the presentation in Halliday rather...

Hey guys. Seeing that the Calculus textbooks of Apostol and Spivak have been mentioned and recommended numerous times in this forum, I was wondering which one is better? Currently, I am senior taking calculus. I feel that my calculus class is too easy and will not help me in college where I...

Hi, I've gotten Spivak's calculus and I have a question on the second proof in the first chapter What is wrong with the following "proof"? suppose x=y 1. x² = xy 2. x² - y²= xy - y² 3. (x + y)(x - y)=y(x - y) 4...

On p. 36 of "Calculus on Manifolds" Spivak writes: "If the theorem is true for (\lambda^{-1})\circf , it is clearly true for f." This far I understand. However, he next says: "Therefore we may assume at the outset that \lambda is the identity." I don't understand how this follows...

Homework Statement In Spivak's Calculus 4e, he defines absolute value as: |a|= a,\qquad a\ge 0 \qquad \text{ and } \qquad -a,\qquad a \le 0 Did he really mean to include the '\le ' and not just '<' ? I know it does not affect the answer, but I didn't think that you could...

Homework Statement Prove the following: xn-yn= (x-y)(xn-1+xn-2y+ … + xyn-2+yn-1) The Attempt at a Solution What do the 3 full stops (...) mean? I didnt know where to start, so I tried to subsitute a number for n, I said n=5, I then multiplied out the brackets and removed terms that...

Homework Statement Suppose A_n is, for all natural numbers n, some finite set of numbers in [0,1] and A_n intersect A_m={ } if m!=n Define f as follows: f(x) = 1/n if x is in A_n and 0 if x is not in A_n for all n. Prove that the limit as x goes to a of f(x) = 0 for all a in [0,1]...

Homework Statement http://img3.imageshack.us/i/0902091724.jpg/ http://img3.imageshack.us/i/0902091724.jpg/Homework Equations The Attempt at a Solution My problem is that I don't even know where to start on this! My first problem is always forgetting what I can and can't use, because we can...

Let me further specify: Which of the following texts would be the best for understanding REAL WORLD applications of calculus, and approaching it in a practical manner? Okay, so maybe Spivak and Apostol can be removed from the list as they are a rigorous theoretical approach. How about the rest...

Last year I took ap calculus ab, and I am taking ap calculus bc next year. So i decided to refresh my memory this summer and went through The Calculus Lifesaver by Adrian Banner, and thoroughly enjoyed it since i didn't get the depth that it went into in class. Now i know there are more "in...

In his proof of the IFT, on p. 36 of "Calculus on Manifolds," Spivak states: "If the theorem is true for \lambda^{-1} \circf, it is clearly true for f. Therefore we may assume at the outset that \lambda is the identity. I don't understand why we may assume that. thanks for your help...

Homework Statement Prove: $\left(ab^{-1}\right)\left(cd^{-1}\right)^{-1}=\left(ad\right)\left(cb\right)^{-1}$. I know how to distribute exponents to get both sides to look identical... Homework Equations ...but a step in the solution requires distributing exponents. But how do...

Working my way through Spivak "Calculus on Manifolds." On p. 34, problem 2-33, the problem asks "show that the continuity of D1f^{i} at a can be eliminated from the hypothesis of Theorem 2-8. Is this a typo? Is he saying that there is no need for continuity of ONE partial derivative, or...

Hi, I got a 5 on the AP Calculus (BC?) exam, so I have a basic knowledge of calculus (probably on the level that a Stewart book would teach). However, I'm planning to major in mathematics and computer engineering/science, so I'm looking for a rigorous introduction to Calculus. I've read the...

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...

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...

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...

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)...

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...