Intereting Posts

The ideal generated by a non-compact operator
Is there a chain rule for integration?
Is a non-repeating and non-terminating decimal always an irrational?
Second derivative of class $C^2$ expressed as limit
Find the Area of the ellipse
Number of elements which are cubes/higher powers in a finite field.
A question about associativity in monoids.
$A \subset \mathbb{R^n}$, $n \geq 2$, such that $A$ is homeomorphic to $\mathbb{R^n} \setminus A$, and $A$ is connected
How to design/shape a polyhedron to be nearly spherically symmetrical, but not a platonic solid?
On integral of a function over a simplex
How can Busy beaver($10 \uparrow \uparrow 10$) have no provable upper bound?
k-Cells are Connected
A(nother ignorant) question on phantom maps
evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$
Explain $\iint \mathrm dx\,\mathrm dy = \iint r \,\mathrm \,d\alpha\,\mathrm dr$

I tried to do euler’s method with this problem:

$$\frac{dw}{dt} = (3-w)(w+1),\quad w(0) = 0,\quad \text{and }t\in [0,5].\quad \Delta t = 0.5.$$

But am getting weird results like for $y_2 = 5.25$, $y_3= -15.84375$;

but checked against the book but this is not correct. Can you please work out some iterations?

$y_2 = 1.5 + (3-1.5)(1.5+1)(1) = 5.25$, for example

- Toward “integrals of rational functions along an algebraic curve”
- Weird and difficult integral: $\sqrt{1+\frac{1}{3x}} \, dx$
- Improper integral of $\frac{x}{e^{x}+1}$
- If the derivative approaches zero then the limit exists
- Inequality $\sum\limits_{1\le k\le n}\frac{\sin kx}{k}\ge 0$ (Fejer-Jackson)
- Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$

- Continued fraction estimation of error in Leibniz series for $\pi$.
- Symmetry functions and integration
- smooth functions or continuous
- Phase plots of solutions for repeated eigenvalues
- What does the derivative of area with respect to length signify?
- Solving Wave Equation with Initial Values
- Evaluating $\int_{0}^{\infty} \left ^{-1}\mathrm{d}x$
- Integral $\int_0^{\pi/2} \theta^2 \log ^4(2\cos \theta) d\theta =\frac{33\pi^7}{4480}+\frac{3\pi}{2}\zeta^2(3)$
- Differentials Definition
- Prove that $\lim_{x\to 2}x^2=4$ using $\epsilon-\delta$ definition.

Euler’s method in this case is

$

y_{k+1} = y_k + \Delta t \cdot (3-y_k)(y_k+1)

$, $y_0=0$. This gives $y_2 = 3.375$ and $y_3=2.555$. Note that $\Delta t = 0.5$.

- Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
- What does “if and only if” mean in definitions?
- Continuous Collatz Conjecture
- Proof of Stirling's Formula using Trapezoid rule and Wallis Product
- For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
- Fiboncacci theorem: Proof by induction that $F_{n} \cdot F_{n+1} – F_{n-2}\cdot F_{n-1}=F_{2n-1}$
- Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
- Bochner Integral vs. Riemann Integral
- Linear Transformation and Change of Basis
- Hyperbolic metric geodesically complete
- When is the sum of two squares the sum of two cubes
- Proving that a natural number made entirely of 6's and 0's is not a square.
- Why is the cartesian product so categorically robust?
- Upper semi continuous, lower semi continuous
- an intriguing integral $I=\int\limits_{0}^{4} \frac{dx}{4+2^x} $