2
votes
0answers
84 views

Algebraic approach to analysis

Can topics and foundations of real analysis be interpreted and profitably explained in terms of abstract algebraic structures? If so, what papers or books (accessible to undergraduate students) ...
3
votes
1answer
20 views

A pair of integrals of rational powers of sines

I'm currently teaching an introductory calculus course which goes through various "techniques of integration." On the way to showing that we can integrate $$ \int R(x, \sqrt{ax^2 + bx + c})dx $$ for a ...
3
votes
1answer
111 views

Books with collections of unusual and advanced integration techniques

I am searching for some comprehensive books that collect, explain, and provide examples of extremely advanced and/or unusual integration techniques. Can you point out some good references? Note: ...
6
votes
3answers
208 views

Exercise books in analysis

I'm studying Rudin's Principles of mathematical analysis and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as a companion to ...
11
votes
6answers
351 views

Book with novel approaches to analysis

Now I'm studying Rudin's Principles of mathematical analysis, but I'm searching for a book that offers geometric, physical or otherwise non-standard approaches to topics in analysis. Also, I'm looking ...
1
vote
1answer
56 views

Engineer searching for calculus and complex analysis books without limits

I am an engineer and I need to study calculus and complex analysis without too much limits or Riemann sums or proofs. I mean on the differentiation and integration levels and higher (not digging ...
3
votes
0answers
71 views

I have one month preparation. Please suggest some books.

I have one month for my GRE subjective Mathematics test. I am from India. I have learnt $75\%$ of the syllabus in my UG and high school mentioned in the ETS. I am starting today, will I be able to ...
1
vote
0answers
31 views

Finding the source for minimizer of a functional for all $C^2$-curve $x(t_0)=x_0$ and $x(t_1)=x_1$

I am trying to find where this problem comes from and its corresponding proof for my students, but I cannot find the source anywhere. If anyone can find the source of this, or has any ideas where I ...
1
vote
2answers
53 views

Reference Request for calculus self study

I'm wishing to learn calculus in a detailed manner. could any one help me by giving suggestions? I'm looking for books with good illustrative examples and figures.
2
votes
2answers
67 views

Good analysis texts

I'm looking for a good introductory text to analysis, or, more specifically, a text that puts calculus on a much more rigorous ground. I've just finished a year of calculus at my local university, ...
6
votes
0answers
48 views

Who did first use the concept of “supremum”?

Is there one specific person, who first defined the concept of "supremum"? If so: In which work? In my textbooks or by a quick search on the internet, I did not find an answer to my question.
7
votes
2answers
85 views

Modified Hermite interpolation

I asked similar questions here and here, but I tried to formulate this one in a sharper way. Is anyone aware of some literature on polynomial interpolation where we sample the function and its ...
5
votes
1answer
251 views

A question about a mathematical analysis book

I am a newcomer to Analysis. All knowledge I know about "Analysis" are differentials,limit and integration (basically, what we have been taught in high school) I am studying Principles of ...
8
votes
3answers
265 views

Resources for Integrals?

I want to learn to solve integrals of some type, probably definite integrals with results involving various constants such as Catalan's, Euler-Mascheroni,Golden-ratio etc. and involving various ...
2
votes
1answer
61 views

Generalized Logarithmic Integral - reference request

This page at I&S forum defines the Generalized Logarithmic Integral as $$L\left[ \begin{matrix} a,b,c \\ d,e,f \end{matrix};z\right] =\int_0^z \frac{\log^a x \log^b(1-x)\log^c(1+x)}{x^d (1-x)^e ...
2
votes
2answers
85 views

Which book is appropriate for a Chemistry student that needs to learn basics about integrals?

A friend of me who is not studying mathematics now needs to deal with integrals, double integrals and triple integrals within his study of chemistry. He asked me to give him a suggestion for a basic ...
3
votes
1answer
135 views

Single Variable Calculus Reference Recommendations

This question is a generalization of the common question asking for calculus references. It is here to abstract away the repetition, and give a canonical resource for calculus references. I'm ...
5
votes
0answers
117 views

Is there a book only about epsilon delta proofs?

I want to know if there is such book, with beautiful epsilon delta proofs of all kind.
1
vote
1answer
50 views

Approximate Equivalent To Michael Spivak's text, “Calculus” but for Linear Algebra?

Does anyone know of an approximate equivalent To Michael Spivak's text, "Calculus" but for Linear Algebra? I love the way this book is written! It is simultaneously rigorous and thorough without ...
1
vote
1answer
47 views

Pre- calculus and calculus practice questions

I'll be taking pre-calculus this fall, and I am wondering if anyone on here can recommend a good problem solving workbook with lots of questions for practice.Also,any ideas for calculus I and calculus ...
0
votes
0answers
19 views

Where can I read about the techniques for computing areas and volumes before calculus?

I've read the following here: The key insight, however, that earned them this credit, was the fundamental theorem of calculus relating differentiation and integration: this rendered obsolete most ...
2
votes
1answer
91 views

Looking for an identity connecting polylogarithm and polygamma functions of arguments $\frac14$ and $\frac34$

I have a recollection of seeing an identity connecting polylogarithm and polygamma functions of arguments $\frac14$ and $\frac34$. But I don't remember details, and searching my books and the Internet ...
1
vote
1answer
226 views

Gilbert Strang's books on calculus and linear algebra?Are they for math majors?

I would to know what are the best resources to use to teach and learn elementary subjects (calculus,linear algebra),I remember when learning calculus, I used Spivak's book which had wonderful ...
4
votes
1answer
87 views

Proof for and Intuition behind Taylor's Theorem

I notice that multiple versions of a theorem are called Taylor (univariate/multivariate, approximate/exact). But I do not find it trivial to infer proof of one version from the rest. So looking for a ...
-3
votes
1answer
43 views

Books to get started on mathematics

I'm studying grammar and I feel a based mathematics would help me. What you recommend to start considering I'm not familiar with well developed therms and etc?
3
votes
0answers
137 views

Any comments on Lax's “Calculus with Applications, 2e”

There's a new calculus book titled Calculus with Applications by Peter Lax (2nd edition of an old one). I really liked his linear algebra and functional analysis books, and I was wondering if this ...
3
votes
1answer
89 views

Has anyone succeeded in formalizing Leibniz notation in such a way that the chain rule and inversion rule “work”?

The notation $\frac{\partial}{\partial x}$ is ubiquitous and totally useful, but also kind of weird. It seems to be doing the following: Bind $x$ Compute the derivative Evaluate at $x$ To ...
5
votes
1answer
174 views

Where to learn integration techniques?

Is there any book or any website that let you learn integration techniques? I'm not talking about the standard ones like integration by Parts Substitution (trigonometric) Partial fractions Order ...
1
vote
1answer
49 views

Where can I find introductory video lectures about calculus and analysis?

I am having calculus classes that are titled as Calculus for Mathematicians, for the rest of the students who are studying calculus, they use Stewart's book. In our classes, we're having something ...
2
votes
0answers
75 views

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 $\xi_i , \xi_l$ ...
2
votes
1answer
84 views

How to get the domain of $x^x$?

The function $$f(x)=x^x.$$ is defined on $(0,\infty)$ because it is equal to $\exp\left(x\log\left(x\right)\right)$. But what happen when $x\leqslant0$? I tried for example $x=-1$, so ...
3
votes
0answers
86 views

Is Courant's Introduction to Calculus and Analysis still up-to-date?

I just found this marvelous book and I think that it's the best book in this category, but I'm worried that it is not up-to-date. I've heard that Hardy's A Course of Pure Mathematics has some switched ...
7
votes
3answers
162 views

Beginning of Romance

I am a 17-year old student in India, in the standard 12th grade. Recently, I found the fascination in mathematics, and I am eager to dig in further. Currently, the only textbooks I have are the ones ...
1
vote
0answers
28 views

Change of variables to flatten the boundary

It is known that one can perform a change of variables to flatten a $C^2$ domain $\Omega$, that is, for any point $x \in \partial \Omega $, there is a $C^2$ diffeomorphism $\psi$ which maps a ...
0
votes
2answers
74 views

Basic question on complex integration

I have a very basic question on complex integration. How is the definite integral $$ \int_{z_1}^{z_2}{f(z)dz} $$ $z \in \Bbb{C}$ to be interpreted in the absence of a specific path over which ...
0
votes
1answer
43 views

Introduction to bump functions/ mollifiers

I want to introduce a small perturbation into a particular point of a smooth function, and then, use bumo functions to smooth out the perturbed function. Could any of you recommend a good ...
2
votes
1answer
46 views

Is there a general algorithm to solve computable integral equation?

Hilbert's tenth problem ask for the general algorithm(finite number of operation) to solve of all Diophantine problems.Today, it is known that no such algorithm exists in the general case. What ...
2
votes
1answer
119 views

Structured Self-Learning Program for Calculus I & II

I'm interested in a organised program which comprehensively covers the topics of Calculus I and Calculus II. I've recently finished taking my secondary school's university-level Calculus I course, ...
2
votes
1answer
181 views

Sum of two gamma/Erlang random variables $\Gamma(m,\lambda)$ and $\Gamma(n, \mu)$ with integer numbers $m \neq n, \lambda \neq \mu$

The gamma distribution with parameters $m > 0$ and $\lambda > 0$ (denoted $\Gamma(m, \lambda)$) has density function $$f(x) = \frac{\lambda e^{-\lambda x} (\lambda x)^{m - 1}}{\Gamma(m)}, x > ...
2
votes
1answer
109 views

Reference Request - Early Calculus Papers

Question: I am looking for good references on the early calculus papers. Optimally, I want emphasis on the mathematics itself and I want that mathematics to be translated into modern terminology and ...
0
votes
0answers
27 views

What is the radius of convergence of the derivative of a smooth Taylor series?

On this website I found that the derivative of a Taylor series has the same radius of convergence as the Taylor series itselves. However, there is no reference added, and I seem to be unable to find ...
3
votes
0answers
62 views

How to practice applied mathematics calculation skill

As a natural science student in university, you may encounter so many problems that might require a deep understanding in integrating skills and series calculation. But as many of the college students ...
1
vote
2answers
143 views

How can we relate calculus, trigonometry etc in real life

I have always wondered what does trigonometry, calculus, logarithms solve real world problems? Where do they apply in real life? Is there any simple book where I can understand it?
0
votes
2answers
159 views

Need a theoretical textbook for calculus, proof based

The course descriptions is : A theoretical course in calculus; emphasizing proofs and techniques. Trigonometric identities. Limits and continuity; least upper bounds, intermediate and extreme value ...
13
votes
1answer
292 views

l'Hopital's questionable premise?

Historians widely report that l'Hopital's 1696 book Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes contains a questionable premise expressed by an equation of type $x+dx=x$ ...
5
votes
1answer
78 views

eulers original derivation for the Euler–Maclaurin formula?

Please does someone know a good description of how Euler did derive his summation formula? Thank you!
3
votes
1answer
163 views

Errors of Euler interpretation?

To complement the recent post on Euler's errors, I would pose the following question: what common errors of Euler interpetation appear in the literature? What errors are attributed to Euler's work in ...
4
votes
7answers
735 views

Interesting calculus problem advice [closed]

Can someone suggest a really hard calculus problem that can be solved with the knowledge of a high school student ? I would really like to work my brains on something interesting . Thanks a lot !
2
votes
0answers
171 views

Calculus book advice

I'm reading Thomas Calculus now but I don't think it includes Mellin transform or Riemann-Stieltjes integration... Can you recommend an advanced calculus book which includes all of this stuff?
1
vote
2answers
132 views

Choosing a calculus book for self-study

Which one to choose for self-education? What are your recommendations? Calculus - James Stewart or Calculus - Anton, Bivens, Davis Thanks in advance.