Intereting Posts

continuous map on $\mathbb{R}$ which is the identity on $\mathbb{Q}$ is the identity map, hence Aut$(\mathbb{R}/\mathbb{Q})= 1.$
How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer
Challenge: Demonstrate a Contradiction in Leibniz' differential notation
Strictly convex Inequality in $l^p$
Determine the matrix relative to a given basis
Why Are the Reals Uncountable?
Identity, Bernoulli number
The dual space of $c$ is $\ell^1$
Additive basis of order n: Sets which allow every integer to be expressed as the sum of at most n members of that set.
Radius, diameter and center of graph
Evaluate the series $\sum_{n = 0}^\infty \frac{1}{(2n + 1)^6}$ by examining the real Fourier series of the function $f(x) := x(\pi – |x|)$
Summation of Fibonacci numbers $F_n$ with $n$ odd vs. even
Solution of $\frac{dy}{dx}=\frac{1}{xy(x^2 \sin y^2+1)}$
when does a separate-variable series solution exist for a PDE
Countable set having uncountably many infinite subsets

Can you recommend a good book (with theoretical results with proofs, and with plenty of solved problems and examples) on the topics of improper integrals, (improper) integrals with parameters, special functions (Beta, Gamma, …)?

- Good books on conic section.
- Correct formulation of axiom of choice
- Proof of Existence of Algebraic Closure: Too simple to be true?
- Intuition in algebra?
- The notations change as we grow up
- Striking applications of integration by parts
- Generating Sets for Subgroups of $(\Bbb Z^n,+)$.
- Small primes attract large primes
- The definition of metric space,topological space
- Every partial order can be extended to a linear ordering

You may have a look at the affordable and accessible Schaum’s Outline of Advanced Calculus. Not too much advanced ðŸ™‚

I like Hildebrand’s ‘Advanced Calculus for Applications’. It has many applications of special functions for differential equations and shows how to use them to solve problems.

- How to find the quotient group $Z_{1023}^*/\langle 2\rangle$?
- Proving $\frac2\pi x \le \sin x \le x$ for $x\in $
- Learning Complex Geometry – Textbook Recommendation Request
- What are the interesting applications of hyperbolic geometry?
- How $a^{\log_b x} = x^{\log_b a}$?
- What are some algebraically closed fields?
- Without Stokes's Theorem – Calculate $\iint_S \operatorname{curl} \mathbf{F} \cdot\; d\mathbf{S}$ for $\mathbf{F} = yz^2\mathbf{i}$ – 2013 10C
- Prove (or disprove) that $ \sum_{n=1}^\infty \frac{4(-1)^n}{1-4n^2} x^n = \frac{2(x+1) \tan^{-1}(\sqrt x)}{\sqrt x} – 2 $ for $ 0<x\leq1$
- Proof if $I+AB$ invertible then $I+BA$ invertible and $(I+BA)^{-1}=I-B(I+AB)^{-1}A$
- Solving a Nonlinear Recursion
- Convolution of an integrable function of compact support with a bump function.
- For a set of symmetric matrices $A_i$ of order p, show that if the sum of their ranks is p, $A_iA_j=0$
- Taylor Series of $\tan x$
- How to use a Rhumb Line?
- On the canonical isomorphism between $V$ and $V^{**}$