Differential and Integral Calculus 2
COURSE HOME PAGE

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

Course Whatsapp Group

Click here to join the course Whatsapp group
Password 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)

Solution of homework #1

Homework #2

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Solution of homework #2

Homework #3

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

Solution of homework #3

Homework #4

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

Solution of homework #4

Course Problem 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 EXAMPLE

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: \( \newcommand\T{\Rule{0pt}{1em}{.3em}} \) \[ \renewcommand{\arraystretch}{0.9} \begin{array}{|c|c|c|c|c|c|c|c|} \hline m_0 & m_1 & m_2 & m_3 & m_4 & m_5 & m_6 & m_7 \\ \hline 4.0 & 3.0 & 2.0 & 3.0 & 6.0 & 2.0 & 6.0 & 4.0 \\ \hline \end{array} \]