What is Advanced calculus: Definition and 64 Discussions

Analysis is the branch of mathematics dealing with limits
and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis.
Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).

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  1. A

    Calculus Advanced Calculus with Applications in Statistics

    Is someone has already heard about this book wrote by Andre I. Khuri (Professor emeritus in science at university of Florida) ? By the table of contents the book seems to cover a lot of things in calculus/multivariable calculus and in a rigourous way according to the preface (they argue that...
  2. yucheng

    Prove the lower bound for a sequence (Buck, Advanced Calculus)

    Clearly, ##x_{n+1}>x_n \because x_n + \sqrt{x_n} > x_n## $$ \begin{align*} x_{n+1} &= x_n+ \sqrt{x_n} \\ &= x_1 + \sqrt{x_1} + \sqrt{x_2} + \cdots \sqrt{x_n} \\ &>n+1 \end{align*} $$ ##\because \sqrt{x_n}>\sqrt{x_1}=1## In fact, $$x_{n+1} > 1+ \sqrt{1} + \sqrt{2}+ \sqrt{3} + \cdots \sqrt{n}$$...
  3. torito_verdejo

    Calculus Recommended book for advanced calculus

    I'm looking for recommendations about advanced calculus books. I'm interested in going further and deeper than nth-order linear differential equations, but overall as a Physics student I'm deeply interested in being very, very comfortable dealing with line, surface and volume integration...
  4. WMDhamnekar

    MHB Using advanced calculus for finding values

    It is possible to find positive integers $A,B, C, D, E$ such that $\displaystyle\int_0^{\frac{2a}{a^2+1}} sin^{-1}\big(\frac{|1-ax|}{\sqrt{1-x^2}}\big)dx=\frac{A}{\sqrt{a^2+1}}sin^{-1}\big(\frac{1}{a^B}\big ) - C sin^{-1} \big(\frac{1}{a^D}\big) + \frac {Ea\pi}{a^2+1}$ for all real numbers $ a...
  5. gibberingmouther

    I A rigorous definition of a limit and advanced calculus

    i'm trying to review calculus and look a little deeper into proofs/derivations/etc. I'm doing this both for fun and to review before i go back to school. am i the only one who has difficulty understanding the "rigorous" definition of the limit? i found this web page...
  6. Maddiefayee

    Finding a convergent subsequence of the given sequence

    Homework Statement For some background, this is an advanced calculus 1 course. This was an assignment from a quiz back early in the semester. Any hints or a similar problem to guide me through this is greatly appreciated! Here is the problem: Find a convergent subsequence of the sequence...
  7. P

    Textbook for advanced calculus

    Oh wait, I am not supposed to ask questions here, sorry. I can't find where i should post questions though
  8. F

    Analysis Choose Best Book to Learn Advanced Calculus: Callahan or Fleming?

    I have a knowledge of Calculus, Differential Equations, and Linear Algebra, I want to learn advanced calculus, but I'm wondering what book is the best choice, I want to learn it rigorously "enough" but not to the point where someone would call me a mathematician i.e. Calculus by Lang vs Calculus...
  9. J

    Applied Books like J. Callahan's Advanced Calculus: A geometric view

    Hello, do you know of any books similar in style to Callahan's Advanced Calculus book(a book that explains the geometrical intuition behind the math)? This goes for any subject in mathematics(but especially for subjects like vector calculus, differential geometry, topology). Thanks in advance!
  10. D

    Calculus Advanced Calculus textbooks that are useful for Cal BC

    Hi everyone, I will be junior next year in my high school and take Calculus BC. However, I also take Calculus 1&2 Honor in the community college which is known as Orange Coast College ( If anyone has studied here before, please tell me the difference between the content of this course and...
  11. B

    Analysis How is "Advanced Calculus" by Loomis/Sternberg?

    Dear Physics Forum friends, my old friend recently gave me a book called "Advanced Calculus" by Loomis/Sternberg, published by the World Scientific. I had taken a look at that book, and it seems to be that the book treats the vector calculus, linear algebra, and some topics on the mathematical...
  12. R

    Summer Upper Level Math Courses Online?

    Econ Major here. I plan to graduate in spring 2016 and from there apply to economics grad programs. I still need to take Advanced Math and Advanced Calculus, and Real Analysis, all of which are not available during the summer at my uni (Florida International University). Anyone know of any...
  13. Andreol263

    Advanced Calculus is usable in physics?

    I was searching in amazon, where i found a book which have very good comments about him, called Loomis & Sternberg's Advanced Calculus, I'm already reading this book, and from what i seen, i liked :), this book will help me in physics, or will be desnecessary, that basic calculus is good??, and...
  14. YogiBear

    Show that w is solenoidal having spherical polar coordinates

    Homework Statement The gradient, divergence and curl in spherical polar coordinates r, ∅, Ψ are nablaΨ = ∂Φ/∂r * er + ∂Φ/∂∅ * e∅ 1/r + ∂Φ/∂Ψ * eΨ * 1/(r*sin(∅)) nabla * a = 1/r * ∂/∂r(r2*ar) + 1/(r*sin(∅)*∂/∂∅[sin(∅)a∅] + 1/r*sin(∅) * ∂aΨ/∂Ψ nabla x a = |er r*e∅ r*sin(∅)*eΨ | |∂/∂r ∂/∂∅...
  15. Q

    Intro Math Rigorous math/physics self teaching material?

    Hi guys, So, I'm a high school senior about to graduate, and because of reasons, I most likely will not be attending a college next year. However, I will apply to colleges next year for a Physics major. In the meantime, I would like to use my time wisely, and I was thinking that the smart thing...
  16. A

    Textbook Suggestions for Self-Studyng Advanced Calculus

    Hi I am studying engineering, as you know the maximum level of calculus reached in engineering is Multivariable Calculus and some vectorial calculus (Im not including courses like Differential Equations or others where there is also applied calculus) so i plan to self study more advanced...
  17. KevinMWHM

    Advanced Calculus Extra Credit Suggestions

    I have an opportunity to present an extra credit project for my advanced calc class. Basically it's calc 4 with a focus on generalizing everything calc 1-3 to R^n. I've never been presented with this kind of opportunity so I'm clueless as to possibilities. I'm not looking to stun or dazzle the...
  18. Alxb577

    Studying What I have to learn to be able to understand this textbook

    I have been given the opportunity to work with a phd student to do research. He said that something that he would like to work on with me is a topic on Convex Optimization. He gave me this paper to read chapters 1-6 which I will link here...
  19. B

    MHB Advanced Calculus - Differentiable and Converging Polynomials

    I could really use some help on this problem as well! Thanks!
  20. B

    MHB Advanced Calculus - Continuous Functions

    I'm really stumped on how to do these proofs… I would really appreciate any help or insight!
  21. W

    Advanced calculus like Sternberg's but less abstract

    I've read Spivak 's calculus so I tried Sternberg 's book,IT IS kind of hard,because the abstraction is put upfront,I know of his other book with Bamberg, but a review on amazon deterred me from buying it,was I right in doing so? Any adv.Calculus book that have some physics in it like Sternberg's?
  22. T

    Loomis "Advanced Calculus" and Baby Rudin

    Hello everybody! I was wondering how the two compare? Thank you everybody :)
  23. T

    Prerequisites to Advanced Calculus by Loomis

    Does Spivak and Artin or Hoffman/Kuzne suffice?
  24. S

    Nice Resource to learn Advanced Calculus

    Greetings everyone, I know this is not the right place for this post but I cannot post in the science education subforum so I post my question here. I need a good resource - textbook, online resource, video lecture etc.- that explains the multivariate calculus really well; the topics I want...
  25. K

    Advanced Calculus: Proving x=cosx for x in (0,π/2)

    Homework Statement Show that x=cosx, for some xε(0,∏/2). Homework Equations The Attempt at a Solution Define f(x)=x-cosx, i want to show that for some aε(0,∏/2), limx→af(x)=0. is this correct?
  26. M

    Advanced Calculus Sequence Convergence

    Homework Statement Prove that the sequence {a_n} converges to A if and only if lim n--->∞ (a_n-A)=0. Homework Equations The Attempt at a Solution It's an if and only if proof, but I'm not sure how to prove it. Please help!
  27. M

    Limit of n^2/n! and Using Limit Properties for Advanced Calculus Sequences

    Homework Statement Determine whether the given limit exists and find their values. Give clear explanations using limit properties. Homework Equations lim n--->∞ (n^2)/n! The Attempt at a Solution I know that the limit is 0, but I don't know how to show it in detailed steps...
  28. T

    Is Fitzpatrick's Advanced Calculus the Best Book for Multivariable Analysis?

    I realize the term 'Advanced Calculus' is rather vague, so to be more specific I'm looking for a textbook covering multivariable analysis. I've taken a look at Shifrin's Multivariable Mathematics and Hubbard and Hubbard's Vector Calculus, Linear Algebra, and Differential Forms, and these seem...
  29. S

    Preparation for Advanced Calculus?

    I'm signed up to take Advanced Calculus 1 for the Fall semester, I think it's the equivalent of an intro Real Analysis course. I want to prepare ahead of time, especially because I heard it's challenging, does anyone know any books I can use to get a feel for the topic? I'm not too good with...
  30. T

    Understanding ds in Advanced Calculus

    Homework Statement My question is not specific to any particular problem but is rather of a conceptual nature. In my advanced calculus class this semester, the notation ds appears often, for line integrals, surface integrals, and arc length. In all honestly, I don't really understand what ds...
  31. M

    Recommendation for an Advanced Calculus text

    Lookin' for a good text on Advanced Calculus for self-study. Thanks.
  32. M

    Recommendation for an Advanced Calculus text

    As the title suggests, I'm looking for a good text on Advanced Calculus for self-study. Thanks.
  33. C

    Advanced Calculus - Taylor errors

    This might be a weird quest and in the wrong section but does anyone know of a list with errors and corrections for the book "Advanced Calculus" by Taylor & Mann 3rd ed? Thanks
  34. M

    Advanced calculus proof involving mean value theorem

    Homework Statement If f is strictly decreasing and differentiable on R, then f '(x) ≤ 0 for all x. Homework Equations Mean value theorem The Attempt at a Solution if f is strictly decreasing, then for any a,b\inℝ such that a<b, f(b)<f(a) or f(b)-f(a)<0. By the MVT, there exists a...
  35. R

    Supplement to Advanced Calculus

    Hello, Things have gone pretty well, I changed my major to math (used to be physics) and I am starting third semester in 10 days. Ill be taking Linear Algebra 2, Abstract Algebra 1 and Multivariable Calculus, plus 2 courses in Literature and one on Nietzsche and Foucault. So, I am studyng Mike...
  36. A

    Need a really advanced Calculus book

    I'm looking for an advanced Calculus book that explains special (non-elementary) functions and their properties and applications (like Lambert W function, elliptic functions, error function, Ei and other special functions). I'd also like it to contain different methods of integration like...
  37. J

    Advanced Calculus Infinite Series

    Homework Statement Suppose that {an} is a monotone decreasing sequence of positive numbers. Show that if the series an converges, then the lim(nan)=0. Homework Equations The Attempt at a Solution I started the proof with the fact that since I know the sequence is monotone decreasing and the...
  38. W

    About Advanced Calculus by Loomis and Sternberg

    Hey, I found a copy of this book at my school library and I've been looking through it; I've been brought under the impression that this book is more geared towards a physicists audience versus being a "pure math" book. But other than the final chapter on mechanics, I've so far thought that the...
  39. M

    Edwards Advanced Calculus of Several Variables

    Edwards "Advanced Calculus of Several Variables" We have been using some chapters from this textbook (1995 edition, ISBN: 978-0070602281) in my Advanced Calculus class, but our professor just gave us photocopies of the chapters we were covering (2 and 3 I think). I wanted to try to do some of...
  40. MathWarrior

    What exactly is Advanced Calculus?

    What exactly is "Advanced Calculus?" My school lists this class with the description of: Advanced Calculus I "real numbers, completeness, continuity, sequences/series, uniform theorems, derivative, pointwise/uniform convergence, Riemann integral, Taylor's theorem." as the description...
  41. D

    Solution for y in Advanced Calculus - x,y,z

    Near what points (x,y,z) does e^{yz}-x^2 zln{y}=\pi have a solution for y in terms of x and z
  42. M

    Proving Symmetric Continuity of a Function at X0

    A function f is said to be symmetrically continuous at X0 if lim [f(X0 + h) - f(X0 - h)]= 0 h-> 0 Show that if f is continuous at X0, it is symmetrically continuous there but not conversely.
  43. N

    What Makes Apostol's Advanced Calculus Text Stand Out?

    im looking for an advanced calculus text somthing with more difficult problems than stewart. not an analytical style text but somthing with a good number of exercises covering topics in integral and differential calculus.
  44. N

    What are some good textbooks for advanced calculus with challenging exercises?

    im looking for a textbook with an advanced level of dificulty in the problems somthing harder than stewart. not an analytical style text but some with a good number of exercises.
  45. I

    Book Recommendation Advanced Calculus?

    Could someone recommend a good book to review Calculus leading up to Advanced Calculus. I have Advanced Calculus next semester and want to get a jump on it. It has been a couple of years since I had Calc II. and I am reviewing the Stewart Book. I am looking for something a little more concise...
  46. Z

    Sternberg's Advanced Calculus and math education

    There are several reactions that one can have upon seeing the text Advanced Calculus by Sternberg and Loomis. (Those unfamiliar with this book can find it online here: http://www.math.harvard.edu/~shlomo/) My reaction was simply to be surprised at the extreme discrepancy between the material...
  47. A

    Advanced calculus proof

    Homework Statement let L(x)= integral from 1 to x: 1/t dt. Show that L:]0,infinity[--->R is continuously differentiable. show that L(xy)=L(x)+L(y) for all x,y in ]0,infinity[. hint: let L1(x)=L(xy) and compute L'1(x) you don't have to solve it for me, just lead me in the right...
  48. F

    I underestimated the difficulty of Widder's Advanced Calculus

    I somehow managed to get Bs in two calculus courses and was pretty confident that in a pinch I was capable of doing work involving lagrange multipliers, Green's theorem, convergences of improper integrals, and such. My textbook was multivariable calculus by Larson and Edwards which I was sold...
  49. E

    Advanced calculus proof- oscillating sequences

    Homework Statement For the sequence defined recursively as follows: a_1 = 2, and a_(n+1) = 1/ (a_n)^2 for all n from N. Homework Equations So, we are supposed to use induction to first fidn if the sequence increases or decreases, and then use induction again to show if it...
  50. E

    Advanced Calculus Proof-limit of a sequence.

    Homework Statement Suppose that the sequence {a_n} converges to A. Define the sequence {b_n} by: b_n = (a_n +a_(n+1) )/2 Does the sequence {b_n} converge? If so, specify the limit and prove your conclusion. Otherwise, give an example when this is not true. Homework Equations...
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