  
 
{\bf   Calendar for 19A, Winter 2018; post-Midterm:}

{\bf week 6: }

Implicit differentiation,  Mean Value, Intermediate Value, 
Bisection method and Newton's method covered.   
{\bf week 7: }

M Feb 19: HOLIDAY. President's Day.

QUIZ:  from 4.6 

W Feb 21.   Ch. 7 of `to-the-point'.   Areas under curves. Moving sums.
The definite and indefinite integral.  The fundamental theorem of calculus.

Fri. Feb 23 . {\bf  Reading: Chapter 7 and 11 of `to-the-point'.    Hsiang, `Concise Guide...' on   Archimedes etc. . 5.1-5.2 of Rog.}   The problem of area.  Summation notation.  Infinite sums:
$1/2 + 1/4 + 1/8 + 1/16 + \ldots$.  Limits 1.    Riemann integral and limits I. 2.3 of `to-the-point'.   More anti-derivatives. 

 HW from 7.2 of `to-the-point'. 

{\bf week 8: }

QUIZ from  3.8.  of Rog. PLUS  a Writing assignment HW  due in section.  This assignment worth twice the usual quiz. 

M Feb 26  Ch. 11 of `to-the-point'. Ch 5.1- 5.4 of Rog.   More simple sums, infinite and non-infinite.   More integrals.  Tastes of next quarter. 

W Feb 28.  4.5, 8.4, 10.7 of Rog.  Ch. 4.10 of `to-the-point'.   L'H\^opital's rule.  Second order Taylor expansions.  Quotients of Taylor expansions: 


Fr Mar 1.    
   
{\bf week 9 : }

Quiz on  geometric sums or series; OR on  L'H\^opital .  (sums   10.2, p. 526-7 ;  5.1; L'H\^op 4.5)  

M Mar 5:   ch. 2.    From Hsiang.  The real number line. Crisis of irrationality.  Continuity and limits.  Beginnings of the construction
of the real number line.  Irrationality of $\sqrt{2}$. Of the Golden Mean.  Bounded monotonic sequences have limits.  

W Mar 7   ch. 2. And from Hsiang.    Bounded monotonic sequences have limits.
Examples: showing that  $\sqrt{2 +\sqrt{2 + \sqrt{2}}+ \ldots}$ has a limit.   Induction.     Continuity and limits, II.   Transcendental numbers.    

Fr Mar 2.    Fourier series.  Cantor's paradise.     Infinite sums of functions.     Taylor series.  



{\bf week 10:}

Quiz: ch. 2.    

M Mar 12.   Final Review 1.   
 
W  Mar 14.  Why Calculus?    Kepler's laws and  Newton's eqns.  13.6.   


Fri Mar 16:  Grand Finale.    

 

{\bf week 11:}  Finals week.

Wednesday, March 21	12:00 to 3:00 p.m.    {\bf Final.} 
 







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