# Tagged Questions

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### Typed version of Newton's Principia Mathematica

I need a typed pdf version of Newton's Principia. Is it available for free online? And I also need the proof of universal law of gravity and the elliptical orbits of planets(If there's no typed ...
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### Reference Request: Fubini's theorem for non-negative functions

I have never seen this (1st page) formulation of Fubini's theorem in the literature. Does anyone know where I can find it? In every calculus book (e.g. Apostol, Courant, etc.) I looked, the authors ...
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### Simplifying a Vector Integral

While reading the book - Cercignani, Theory and Applications of Boltzmann Transport Equation (I am not a math student), I found this integral which I am unable to understand. Note that $\xi_i , \xi_l$ ...
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### Multivariable calculus and real analysis in one semester. What is the best way to study for such course?

I am in my first year of EECS and planning on taking a lot of maths classes. I have already taken single variable calculus and linear algebra and did well in them and decided to take multivariable ...
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### Less Terse alternative to Advanced Calculus by Folland.

I am currently in an advanced calculus class in university. We use Advanced Calculus by Folland. When I try to follow along the book I find that it is not verbose enough, and has too few examples. I ...
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### Nature of Hessian of a function of a matrix

If input to a differentiable function is a matrix, what is the nature of Hessian of the function? Is it a tensor or something? This is a simple question, but I guess I am not sure where refer to, to ...
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### Best Book or Source for learning Multivariable Calculus!

I urgently need some sources for learning multivariable calculus in an efficient way, without too much intuition. I'd like it to be explained in a clear and concise way and with a number of worked ...
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### Best book for learning multiple integrals, line integrals, greens theorem etc..

I've been searching for a book that teaches multiple integrals and such in a way that I can understand, I need to learn it quickly, so I don't need too much of the intuition, I just need to be able to ...
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I'm a 12th grade student and I've recently developed a passion for mathematics . Currently my knowledge in this particular area is comprised by : single-variable calculus , trigonometry , geometry , ...
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### Video lectures and reference book Multivariable calculus

I am in a particular situation that I am doing Master's in a Computer Science related degree, and I would like to take the course on Convex Optimisation which is taught by the Machine Learning ...
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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 ...