## What is Weierstrass equation?

A Weierstrass equation or Weierstrass model over a field k is a plane curve E of the form y 2 + a 1 x y + a 3 y = x 3 + a 2 x 2 + a 4 x + a 6 , y^2 + a_1xy + a_3y = x^3 + a_2 x^2 + a_4 x + a_6, y2+a1xy+a3y=x3+a2x2+a4x+a6, with a 1 , a 2 , a 3 , a 4 , a 6 ∈ k a_1, a_2, a_3, a_4, a_6 \in k a1,a2,a3,a4,a6∈k.

**What is a non differentiable function?**

A function is non-differentiable when there is a cusp or a corner point in its graph. For example consider the function f(x)=|x| , it has a cusp at x=0 hence it is not differentiable at x=0 .

### Why is the Weierstrass function important?

Weierstrass’s work was very influential and formed a solid foundation for analysis for decades to come. He shocked the mathematical world by coming up with a function which is continuous everywhere but differentiable nowhere!

**Is the Weierstrass function periodic?**

It is periodic with period 2π. You can see it’s pretty bumpy. So bumpy, in fact, that it’s not differentiable anywhere.

## Why is weierstrass function not differentiable?

The higher-order terms create the smaller oscillations. With b carefully chosen as in the theorem, the graph becomes so jagged that there is no reasonable choice for a tangent line at any point; that is, the function is nowhere differentiable.

**Why is Weierstrass function not differentiable?**

### What are the examples of non differentiable functions?

A function which jumps is not differentiable at the jump nor is one which has a cusp, like |x| has at x = 0. Generally the most common forms of non-differentiable behavior involve a function going to infinity at x, or having a jump or cusp at x.

**When was the Weierstrass function first used?**

1872

The Weierstrass function has historically served the role of a pathological function, being the first published example (1872) specifically concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points.

## What was Karl weierstrass known for?

Known as the father of modern analysis, Weierstrass devised tests for the convergence of series and contributed to the theory of periodic functions, functions of real variables, elliptic functions, Abelian functions, converging infinite products, and the calculus of variations.

**Is Weierstrass function uniformly continuous?**

Is it still uniformly continuous? Yes.

### Where is the Weierstrass function continuous?

In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve.

**Who is father of mathematical analysis?**

Karl Theodor Wilhelm Weierstrass

Karl Theodor Wilhelm Weierstrass (German: Weierstraß [ˈvaɪɐʃtʁaːs]; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the “father of modern analysis”….

Karl Weierstrass | |
---|---|

Nationality | German |

Alma mater | University of Bonn Münster Academy |

## What is Weierstrass a theorem?

A theorem obtained and originally formulated by K. Weierstrass in 1860 as a preparation lemma, used in the proofs of the existence and analytic nature of the implicit function of a complex variable defined by an equation $ f ( z, w) = 0 $ whose left-hand side is a holomorphic function of two complex variables.

**What is Weierstrass’theorem on the approximation of functions?**

Weierstrass’ theorem on the approximation of functions: For any continuous real-valued function $ f ( x) $ on the interval $ [ a, b] $ there exists a sequence of algebraic polynomials $ P _ {0} ( x), P _ {1} ( x) \\dots $ which converges uniformly on $ [ a, b] $ to the function $ f ( x) $; established by K. Weierstrass .

### What is the Weierstrass function?

In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function.

**What does the Weierstrass plot look like?**

Plot of Weierstrass function over the interval. Like some fractals, the function exhibits self-similarity: every zoom (red circle) is similar to the plot as a whole.