1.Importance of Visualization

2. Geogebra and its capability

4. Applets for Visualizing 1D and 2D functions

5. Applets for Activity based Learning

6. Conclusion

3. Funny and Motivating Example

Taylor series is a way of approximating any continuously differentiable function $\mathscr{f(x)}$ using polynomials of degree $n$. The higher the degree the better the approximation!.

 $\mathscr{f}(x)=\mathscr{f}(p)+\frac{\mathscr{f'}(p)}{1!}(x-p)+\frac{\mathscr{f''}(p)}{2!}(x-p)^2+\frac{\mathscr{f'''}(p)}{3!}(x-p)^3+ \cdots$

$\eta \in (0,1)$ is a parameter to adjust the gradient value to obtain a better approximation around point $p$

Try with different $f(x)$ such as $x^2,exp(x),sin(x),x^3 \cdots$ and see how closely taylor series approximate the function at the point $x = X$ and around its neighbour $\epsilon$

You can drag the point on the sliders

You can increase/decrease Polynomial

Degree by clicking +/- symbol