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).
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...
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...
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...
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...
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...
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...
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!
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...
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...
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...
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...
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...
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...
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...
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...
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?
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...
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?
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!
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...
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...
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...
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...
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
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...
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...
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...
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...
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...
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...
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...
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.
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.
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.
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...
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...
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...
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...
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...
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...