Math 2242   (Dr. J. S. Zheng)


Office: Math-Phys 3306
Phone: 8 1338
E-mail: szheng at GeorgiaSouthern

   


Thy word is sweeter than honey. (Psalm:119:103)


We are what we repeatedly do.  Excellence, then, is not an act, but a habit. (Aristotle)


Interactive Integration

Integration by parts    \(\int_{a}^{b} u \, dv = [uv]_{a}^{b} - \int_{a}^{b} v \, du\)

Geometric series \begin{align*} S_{N}:=&\sum_{n=0}^N ar^n=\frac{a(1-r^{N})}{1-r}{=}\frac{a(r^{N}-1)}{r-1}\Rightarrow\\ \sum_{n=0}^\infty ar^n=&\frac{a}{1-r}\quad\text{converges to \(\frac{\text{leading term}}{1-\text{ratio}}\) if \(|r|<1\)} \end{align*}



Taylor series

\(f(x)=\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!} (x-a)^n\)

Exponential function: \(e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots\)
Sine Function: \(\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \dots\)
Cosine Function: \(\cos(x) = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \dots \)



MathML with \(\LaTeX\) input

Zouleaf Spectrum of multiscale: simulations tool online
✓ [MathJax Html]
✓ [Python]


   
    		Green's formulas, which I call fundamental theorem in higher dimensions


To know the way ahead, ask those coming back.

The journey is the reward. (Taoism)

There is no difference between living and learning. (John Holt)




What Calculus can do

COSM Undergraduate Student Research
NASA STEM OPPORTUNITIES
NASA Undergraduate Student Research Project (USRP)

Schedule of the class
Class schedule by chapters/sections (tentative)
Transcendental Functions 7.1 - 7.8
Techniques of Integration 8.1 - 8.8
Exam 1   Chap.7 and part of Chap.8
Infinite Sequences and Series 10.1 - 10.10*
Exam 2   part of Chap.8 and Chap.10
Conic Sections and Polar Coordinates 11.1 - 11.7*
Cumulative Final Exam Chapters 7,8,10, 11



Homework assignments    MyMathLab (ask Instructor for course code)

Zoom hours: Tuesday/Thursday 2:30-3:30 or other times by appointment only


Important Calendar/Dates


Review   Exam     Date  
Review Exam I    Exam I
Review Exam II Exam II
Review Exam III    Exam III  
Review Final      Final Exam  

Riemann zeta function \(\zeta(s)=1+\frac{1}{2^s}+\frac{1}{3^s}+\cdots+\frac{1}{n^s}+\cdots \)

Euler (1737): \( \sum_{n=1}^\infty\frac{1}{n^s}=\prod_{p\; prime}\frac{1}{1-p^{-s}} \)




MASTER Virtual Tutoring   Academic Success SMART Center 

Computing Lab