# Differential and Integral Calculus 2T (104013)

Department of Mathematics

Lecturer: Samy Zafrany
Email: samyz@technion.ac.il

## Lecture Notes

Corrections and improvement suggestions are most welcome (send to email above).

## Youtube videos for Course Topics

This is an extended Spherical Harmonics 3D surface with 12 varying parameters

$r = \sin^{m_1}(m_0\phi) + \cos^{m_3}(m_2\phi) + \sin^{m_5}(m_4\theta) + \cos^{m_7}(m_6\theta) + \sin^{m_9}(m_8\theta) + \cos^{m_{11}}(m_{10}\theta) \\$

The Python code for generating this movie can be obtained from here.

## Classic Spherical Harmonic 3D surface (moving perspectives)

This is the classical Spherical Harmonics 3D surface with 8 static parameters

$r = \sin^{m_1}(m_0\phi) + \cos^{m_3}(m_2\phi) + \sin^{m_5}(m_4\theta) + \cos^{m_7}(m_6\theta) \\$

The Python code for generating this movie can be obtained from here.

## Conic Section 3D Animation

The Cartesian equation of the Conic Section surface is given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = \frac{z^2}{c^2}$

## 3D Two-Sheeted Hyperboloid with a tangent plane

The Cartesian equation of the Hyperoloid surface is given by $x^2 - y^2 - z^2 = 4$ The tangent plane is $3x - 2y - z - 4 = 0$ The tangent point is $(3,2,1)$.