2
votes
1answer
46 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
68 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 ...
1
vote
0answers
18 views

3-Point Shoot using Quadratic Equation [on hold]

This is my assignment. The question is "In what part of the three-point line can a player do best the three-point shoot to gain 3 point but using quadratic equation." There are no data given but we ...
3
votes
1answer
97 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
100 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
39 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
44 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
18 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
75 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
164 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
83 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
37 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
133 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
87 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 ...
4
votes
1answer
127 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
43 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
67 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
82 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
71 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
141 views

Beginning of Romance

I am a 17 guy from India. The fascination of maths has struck me recently, while I am in standard 12th. But all the resources I have, is some school textbooks. M.L Agrawal's of 11th and 12th. I don't ...
1
vote
0answers
23 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
72 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
37 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
40 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
100 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
144 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
105 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
61 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
99 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
127 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
284 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
73 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
687 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
149 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
103 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.
0
votes
2answers
83 views

Comprehensive, rigorous calculus book with a small number of exercises?

I'm looking for a calculus book that (1) is comprehensive and rigorous enough for Calculus I-III (but pre-Spivak/Apostol in terms of rigor -- they can come later perhaps) (2) has only a small number ...
1
vote
0answers
51 views

Integral asymptotics

Is there some kind of a variation of the Laplace's method or some other formula for the asymptotics of integrals of a type $$\int_a^bf(x)e^{mp(x)}\cos(mq(x)+x/2)dx, \ m\to\infty.$$ Here $f,p,q$ are ...
0
votes
1answer
38 views

Reference request: Limits and Derivatives

Could you recommend/suggest a good E-book about Limits and Derivatives with exercise solutions What do you think about that book Limits and Derivatives Made Easy ? looks good but it's not available ...
10
votes
3answers
183 views

Computing $\int_0^\pi \sin(x) \; dx$ using the definition.

A colleague of mine and I, in the course of teaching integral calculus for the umpteenth time, were wondering if we could expand the class of examples that our students are exposed to when computing ...
4
votes
2answers
149 views

Works on Calculus by Newton and Leibniz (primary sources)

I'm trying to find PDFs or hard copies of the following works from the dawn of calculus. Does anyone know where I could find English translations of them? Newton - De analysi per aequationes numero ...
0
votes
0answers
34 views

Reference for power series

I would need some references for power series, Taylors series of elementary functions, derivation and integration of power series, convergence of sequences of functions and series of functions. The ...
0
votes
2answers
49 views

What is list of common integral that have no closed form?

What is list of common integral that have no closed form? It's diffucult for me to google it for some reason.
3
votes
1answer
110 views

Multivariable matrix calculus textbook?

I study a multivariable calculus course, and the lecturer is using matrix calculus notation, which I'm not familiar with. The notes that come with the course aren't sufficient in understanding this ...
0
votes
0answers
43 views

Calculus book with different definition of derivative

I am looking for a calculus book which defines derivative as a linear approximation and not as a rate of change. Then it generalizes this notion to derivatives from $\mathbb{R^n}$ to $\mathbb{R}^m$. ...
0
votes
1answer
90 views

learn math, again

I am an international student. I am going to apply for a MA program in economics but before doing that, I want to refresh all my math knowledge. I have to take the GRE so I need to re-learn ...
1
vote
2answers
60 views

References for probability using Calculus

I have to teach a Calculus class (details on the syllabus below) and I want to add some applications to other sciences. But I would like to avoid the classical physics examples, because the physics ...
3
votes
1answer
72 views

The best place to excercise Linear Algebra or Calculus?

Could anyone tell me some good website for excercising Linear Algebra or Calculus? Thank you very much for every advice :)
1
vote
6answers
76 views

Noncircular construction of $e$ and $\ln$ for the real line

Could anyone direct me to (or possibly detail) a construction of $e$ and $\ln$ along the reals? For example, they can define $e=\lim_{n\rightarrow\infty}(1+\frac{1}{n})^n$ but from this definition ...