#
Differential and Integral Calculus 2

COURSE HOME PAGE

**
ORANIM ACADEMIC COLLEGE OF EDUCATION
School of Mathematics, Computer Science, and Physics
**

**
Lecturer:
Samy Zafrany
**

## Course Whatsapp Group

Click here to join the course Whatsapp groupPassword should be given at the first lecture or can be obtained from me (Samy)

## Course Program

Course Program: sylabus, grading policy, bibliography, etc.

# Lecture Notes

Full lecture notes can be downloaded from the link above or by parts from the links below. Corrections and improvement suggestions are most welcome (send to email above).[Infinite series chapters have been moved to Appendix A-C at the end of the booklet]

## Homework #1

Download Homework #1 (Last modified: December 30, 2017, 23:21:48)## Homework #2

Download Homework #2 (Last modified: December 30, 2017, 23:21:48)## Homework #3

Download Homework #3 (Last modified: December 30, 2017, 23:21:48)## Homework #4

Download Homework #4 (Last modified: January 09, 2018, 19:33:12)## Course Promlem Set

A list of exercises for the whole semester.Make sure to solve as many problems as you can before the final exam (best way to prepare).

(Last modified: March 10, 2018, 23:01:37)

## Course Summary (sikum)

A summary of the main course theorems, definitions, and formulas.(Last modified: March 10, 2018, 23:01:42)

This documnet can be used in the final exam (in printed form), but please make sure you do not add any hand written notes on it!

## Quizes

We will have 3 short quizes during the course. Here is an example (with detailed explanation) on how it looks
** QUIZ #3 (Final home quiz covering all semester material) **

## Final Exam 1 - Solution

Solution of final exam given on February 07, 2018...

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## Future Topics in Calculus 2 - Parametric 3D surfaces

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 parametric equations are:
\[
\begin{cases}
x &= r \sin(\phi) \cos(\theta) \\[0.5em]
y &= r \cos(\phi) \\[0.5em]
z &= r \sin(\phi) \sin(\theta)
\end{cases}
\]
Initial values of the twelve parameters are:
\(
\newcommand\T{\Rule{0pt}{1em}{.3em}}
\)
\[
\renewcommand{\arraystretch}{0.9}
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
m_0 & m_1 & m_2 & m_3 & m_4 & m_5 & m_6 & m_7 & m_8 & m_9 & m_{10} & m_{11} \\
\hline
4.0 & 3.0 & 2.0 & 3.0 & 6.0 & 2.0 & 6.0 & 4.0 & 8.0 & 4.0 & 6.0 & 8.0 \\
\hline
\end{array}
\]

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 parametric equations are:
\[
\begin{cases}
x &= r \sin(\phi) \cos(\theta) \\[0.5em]
y &= r \cos(\phi) \\[0.5em]
z &= r \sin(\phi) \sin(\theta)
\end{cases}
\]
Static values of the eight parameters are:
\(
\newcommand\T{\Rule{0pt}{1em}{.3em}}
\)
\[
\renewcommand{\arraystretch}{0.9}
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
m_0 & m_1 & m_2 & m_3 & m_4 & m_5 & m_6 & m_7 \\
\hline
4.0 & 3.0 & 2.0 & 3.0 & 6.0 & 2.0 & 6.0 & 4.0 \\
\hline
\end{array}
\]

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 \((3,2,1)\).

And of course, let's not forget all the great people who made this possible ...

(page 339 from a soon to be published book ... stay tuned :-)