# Tagged Questions

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### A proof of a theorem of Liouville

I need some reference for the proof of the following theorem attributed to Liouville: Theorem: Let $f(x):\Omega\longrightarrow \mathbb R^n$ a $C^2$ function where $\Omega$ is an open subset of ...
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### Fréchet Derivative Bibliography

Good night, I'm new studying the Frechet Derivative. I still don't understand the concept of it. My question is...do you have some bibliography about it you can recommend me? I'd really appreciate ...
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### A question on generalization of the concept of derivative

I am looking for some material to understand the process of generalization of the concept of derivative. I would not like to just read and apply the definition of the concept of differentiation in ...
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### Show $\partial _x \int_{(x_0, y_0)}^{(x,y)}P(s,t)ds + Q(s,t)dt = P(x,y)$

There is a theorem from advanced calculus that I'm trying to prove. Suppose $P(x,y)$, $Q(x,y) \in C^2$ on a simply connected domain $D$, and suppose that $P_y = Q_x$ (i.e. $\omega = Pdx + Qdy$ is ...
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### Second Text for Multivariable Calculus

I took a rather disappointing multivariable calculus course this semester -- the (visiting) professor was not demanding at all. We didn't get to what is in most standard calculus III curriculum. What ...
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### What does it mean by piecewise smooth boundary?

I will be highly obliged if anyone can give me any reference where i can get the definition of domain (in $\mathbb{R^n}$) with piecewise smooth boundary. My question is when a domain in ...
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### Reference for an integral's convergence on an $n$-ball when $n>2$.

I was searching for a reference of a standard result from calculus. Unfortunately I couldn't find it. I think that's mostly due to I am not familiar with any english calculus book. So I am ...
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### Notes about evaluating double and triple integrals

I'm searching notes and exercises about multiple integrals to calculate volume of functions, but the information I find in internet is very bad. Can someone recommend me a book, pdf, videos, ...
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### Calculus book for people who know limits

I have the probably slightly unusual background of being quite comfortable with real numbers, functions, limits, sequences, series, etc, but having no knowledge of calculus beyond the definitions of ...
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### Algorithm to calculate multiple integral.

One of the major difficulties of student in advanced calculus (including myself when student) is to obtain the extremes of repeated integrals to calculate the volume integral in $R^n$ i.e. transform ...
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### A sequel for Elementary Analysis by Ross?

I've been learning real analysis from this book: Elementary Analysis, K.A. Ross I really liked the style of this book. It is quite old, and sometimes very difficult, but I guess I liked the way it ...
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### Divergence Theorem and Mean Curvature as applied to Tension in a Membrane

I'm reading a paper on tension in a membrane and am currently stuck at this part. The paper so far reads: We consider a portion $S^M$ of a membrane $\Omega^M$, where $\hat k$ denotes the unit ...
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### Continuity of multivariable functions when “component functions” are continuous

Given topological spaces $X_1, X_2, \dotsc, X_n, Y$, consider a multivariable function $f : \prod_{i = 1}^nX_i \to Y$ such that for any $(x_1, x_2, \dotsc, x_n) \in \prod_{i = 1}^nX_i$, the functions ...
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### Reference books or any sources advice for my advanced calculus course

My course outline: Differentiation of functions of several variables: partial derivatives, differential, differentiability, inverse function theorem, implicit function theorem, free extremum ...
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### the usual examples for multi-variable integrals

well sadly in our exam our tutor is going to ask us to calculate different integrals etc. Well we're studying maths and not "being a good calculator" but in contrast to give exercises about simple ...
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### Multivariable Calculus books similar to “Advanced Calculus of Several Variables” by C.H. Edwards

I am currently trying to teach myself multivariable calculus using C.H. Edwards' "Advanced Calculus of Several Variables", but the text unfortunately doesn't have very many problems with solutions. ...
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### Calculus 3 Explained

I am trying to learn some calculus 3 and I understand HOW to do the problems but I just don't understand WHY I'm doing what I'm doing. So does anyone have any good recommendations on books that are ...
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### Good introductory book for matrix calculus

Hi I am an electronics graduate and working on image processing for the past one year...I have a basic exposure to linear algebra(thanks to Gilbert Strang..!!!). Now I am facing problems with matrix ...
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### A rigorous book (or preferrably set of notes) on classic multivariable calculus-analysis?

This is different to (Theoretical) Multivariable Calculus Textbooks as I want a classical treatment of line and surface integrals without the notion of a differential form. Prerequisites: Paths, ...
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### Practise with Smooth Functions and Manifolds

I'm trying to get an intuition for smooth manifolds, and in particular the smoothness of transition functions. I haven't done that much calculus on $\mathbb{R}^n$ before, and would like to practice ...
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### Multivariable Product Rule, Integration by Parts, Derivative, etc.

I am searching for a book on multi-variable calculus that explains multi-variable product, multi-variable integration by parts, etc. As an example, here's a simple problem that I would like to be ...
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### about a good book - Vector Calculus[by Jerold E. Marsden, Anthony J. Tromba ]

I start reading Vector Calculus by Jerold E. Marsden, Anthony J. Tromba and I want to know if there is a book with the answers of the exercises. I like a lot this book, it seems to be made for a ...
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### Free PDF for MV Calculus

I was looking for a free PDF from which I can review MV calculus. Specifically: MV Limits, Continuity, Differentiation. Differentiation of vector and scalar fields Surface/Multiple Integrals A ...
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### Spivak's “Calculus on Manifolds” :: A good relearning of MV Calculus?

A friend of mine gifted me his copy of Spivak's Calculus on Manifolds. I was looking out for a good book to relearn MV Calculus to the extent of : Multivariable Limits, Continuity and Differentiation ...
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### Multivariable Calculus Book Reference

I am looking for a multivariable calculus book that is really physics oriented. Anyone know of any? EDIT: My wife is looking to brush up on multivariable at the same time she needs to brush up on ...
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### Reference for multivariable calculus

I'm looking for a book to learn multivariable calculus that is rigorous, but not overly technical, and also provides meaningful insight. Standard calculus texts like Stewart and Thomas are too ...
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### Formulae for PDEs : Commuting derivatives and/or integrals

Many times I come across some new formula being used to work with and/or reduce partial differentials. As kleingordon said, these things are mysteriously not taught anywhere(atleast in physics ...
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### Computing the derivative of a quadratic form and matrix chain rule

I'm working on using the Generalized Method of Moments to analyze some yogurt purchase data, and in the course of trying to implement the standard Hansen method (i.e. not an empirical likelihood ...
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### Interval Algorithm for Gradient Descent Method

Are there any references discussing an interval algorithm for the vanilla gradient descent method given a function $f \colon \mathbb{R}^n \to \mathbb{R}$? Edit: In particular, I am searching for an ...
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### Computing Gradient and Hessian of a vector function

I'm wondering how to compute gradient and hessian for this function $$f(\textbf{x}) = ||\textbf{x}||_2^p$$, where $\textbf{x}$ is a vector and $p$ is a constant and $p>1$. This is a homework ...
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### Are there any places to get highly graphical/visual math videos, specifically for calculus?

I love watching National Geographic and Discovery channel pieces on the universe/outer space because they are so visually appealing, but if I had to read about the topics, I wouldn't have much ...
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### Need Help: Any good textbook in undergrad multi-variable analysis/calculus?

This semester, I will be taking a senior undergrad course in advanced calculus "real analysis of several variables", and we will be covering topics like: -Differentiability. -Open mapping theorem. ...
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### geometric meaning behind line integrals

What are some geometric meanings behind line integrals? I know if you have a curve on the xy plane and you are given a function $f(x,y)$ then the geometric meaning is a "curtain drawn" from the ...
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### When did Fubini's name get applied to the theorem without measures?

Fubini's theorem, from 1907, expresses integration with respect to a product measure in terms of iterated integrals. The simpler version of this theorem for multiple Riemann integrals was used long ...
Let $X,Y$ be Banach spaces over $\mathbb{C}$ and let $U \subset X$ be open. If $f:U \to Y$ is Fréchet differentiable at every point of $U$, can we locally expand $f$ as a "power series"? To be more ...