**
Mon Jan 12: ** Intro. How to find the area under a parabola.
**
Tue Jan 13: ** Area under parabola; sums of squares;
Def of Riemann sum started: * Hwk pblm 1 due Fri*
**
Wed Jan 14: ** Def' of Riemann integral, with illustrations.
Examples how integrable and non-integrable functions may look.
* Hwk pblm 2 (only 1st line) due Fri. Think a bit of the 2nd line
of pblm 2; we'll discuss this informally in class*
**
Fri Jan 16: ** Guided discovery of set additivity, linearity and
order properties of the integral.
* Hwk pblm 3 and 4 due for hand-in and classroom presentation on Tue.
Also think about pblm 5a-d and be prepared to ask questions if you don't
understand something there.*
**
Mon Jan 19: ** MLK DAY
**
Tue Jan 20: ** Mainly discussed hwk.
Results for Hwk 3 and 4
**
Wed Jan 21: ** Fundamental theorem of calculus; * Hwk pblm 5a-d due
on Monday *
**
Fri Jan 23: ** indefinite integral, antiderivatives; evaluation of some
simple integrals. More Hwk available now at link above:
*6,7 due Mon, 8 due Tue;
more to come; look at the other ones already in case you want to work ahead
or have questions* (5e will come only after we have all come up with the
same numerics from 5d)
**
Mon Jan 26: ** chain rule and substitution (indefinite & definite
integrals). * Problems 9-12 due Friday *
**
Tue Jan 27: ** training in integrals (substitution):
sheet of integrals
**
Wed Jan 28: ** Discussion of Hwk #5cd; inverse functions;
barely started repetition (or new?) inverse trigs
(arcsin, arccos, arctan) and their derivatives.
**
Fri Jan 30: ** Inverse trigs
(arcsin, arccos, arctan) and their derivatives.
* Hwk 13,14 due Monday; Hwk 15 due Friday *
**
Mon Feb 02: ** Some discussion on the Simpson rule hwk;
The natural logarithm.
**
Tue Feb 03: ** Discussion of Hwk pblm 13, and of 8.
**
Wed Feb 04: ** Exponential function, and hyperbolic functions,
and their derivatives and antiderivatives
* Hwk 16,18 due Monday; Hwk 19 due Friday next week *
**
Fri Feb 06: ** Equivalence of two def's of e.
Exponential function as a model for growth and radioactive decay.
**
Mon Feb 09: ** Certain volumes can be eval'd as integrals.
Arclengths can be eval'd as integrals.
Areas of rotational surfaces can be evaluated as integrals
* Hwk for presentation tomorrow: calculate the volume of a torus,
as sketched in class today. *
**
Tue Feb 10: ** discussed shell method for volumes; volume of torus
* Hwk 22-24 for discussion on Wed *

---> I am posting sample solutions for the integration hwk
here; links may be dead yet; they'll
become active
when we have discussed the problem
**
Wed Feb 11: ** * Hwk 19,20,21, 25 (surface area only) due Friday *
**
Fri Feb 13: ** Discussion and presentation of integration, volume,
surface, arclength problems.
**
Mon Feb 16: **Discussion and presentation of integration, volume,
surface, arclength problems.
**
Tue Feb 17: **Discussion and presentation of integration, volume,
surface, arclength problems.
**
Wed Feb 18: ** ** First Exam Thursday Feb 19, 7pm **
**
Fri Feb 20: ** Class cancelled since previous day's exam
was out of class time: I'll however be around for questions at this time.
**
Mon Feb 23: ** Discussion of exam;
*Hwk 30, 29 for presentation tomorrow*
--- * Written hwk: 32a by Wed; 32b1,b2 by Fri; 33 by Mon *
**
Tue Feb 24: ** Pblm 30: hanging chain; Newton's method revisited
**
Wed Feb 25: ** Pblm 32a; Integration by parts.
**
Fri Feb 27: ** Pblm 32b; more examples on integration by parts
*Use sheet of training integrals for integration by parts.
Written Hwk for Monday: 34,35. By Wednesday 40,41,42 *
**
Mon Mar 01: ** Discussion of Pblm 39
**
Tue Mar 02: ** Discussion of Pblm 39, and for 36:
how to get formulas for area and length in polar coordinates
* Written Hwk for Friday: 36 *
**
Wed Mar 03: ** Partial Fraction Decomposition; Basics
**
Fri Mar 05: ** Partial Fraction Decomposition; Cover-up method
**
Mon Mar 08: ** SPRING BREAK
**
Tue Mar 09: ** SPRING BREAK
**
Wed Mar 10: ** SPRING BREAK
**
Fri Mar 12: ** SPRING BREAK
**
Mon Mar 15: ** Partial Fraction Decomposition; using complex numbers
in the cover-up method for quadratic terms; philosophy of PFD: looking
exactly at the points where the rational function goes to infinity gives
the crucial information most effectively. More hints for a hidden connection
between exponentials and trigs.
**
Tue Mar 16: ** Training PFD
**
Wed Mar 17: ** Training PFD; integral dx/x may be ln(-x); separating
fractions in quadratic terms
**
Fri Mar 19: ** The power series of sin and cos and exp, obtained through
integration. (Convergence without proof so far). Euler's formula.
Complex numbers come out of the electric AC outlet.
**
Mon Mar 22: ** PFD for integral from Hwk#33; some remarks
on trigs and hyps on the way *Hwk 43-46 due Friday*
**
Tue Mar 23: ** Factoring (x^4+1), and finding the antiderivative of
1/(x^4+1)
**
Wed Mar 24: ** Overview over integration methods; in particular:
which type of substitutions for which type of integrals; trig' and hyp'
substitutions
**--->
Solutions to #36-46 posted now;
(some to become readable only later) **
**
Fri Mar 26: ** Integrals: Training problems
**
Mon Mar 29: ** Integrals: Training problems
**
Tue Mar 30: ** Integrals: Training problems;
included: sqrt(linear/linear) is as good or bad as sqrt(quadratic)
**
Wed Mar 31: ** Integrals: Training problems; included: quick evaluation of polynomials;
the complex trick for integrating exponentials times trigs

--> **
As requested, solutions for training problems now posted here**
They should be ok, but I haven't checked'em for typos yet, so don't treat'em as
divinely inspired ;-)
**
Thu Apr 01: ** **EXAM APRIL 1, 7PM.** -- Friday class canceled in compensation for the
off-day exam.
**
Mon Apr 05: ** Exam back, and discussion
**
Tue Apr 06: ** Series: convergence and basic examples; comparison test,
Leibniz criterion
**
Wed Apr 07: ** Series: conditional vs absolute convergence.
Termwise addition of series, and multiplication with numbers; rearrangement
of absolutely convergent sereis.
**
Fri Apr 09: ** GOOD FRIDAY
**
Mon Apr 12: ** Rearrangement of conditionally convergent series can
give any value, or divergence. The geometric series in detail.
**
Tue Apr 13: ** Power series; radius (and disc) of convergence; smoothness
inside disc of convergence; basic idea: comparison with geometric series.
* non-numeric part of 47, and 48, tomorrow; all of 47, and 49, by Friday;
*
**
Wed Apr 14: ** Addition, multiplication, and division of power series,
and what we know about the radius of convergence of the resulting series.
*Hwk: 47-51 by Friday*
**
Fri Apr 16: ** Understanding the radius of convergence in terms of the
represented function, or in terms of the coefficients.
**
Mon Apr 19: ** Taylor series of a function; it may or may not represent
the function.
**
Tue Apr 20: ** Discussion of pblms 54-56; including intro to the
binomial series
**
Wed Apr 21: ** Discussion of the series for 1/(1-x-x^2) from all aspects
**
Fri Apr 23: ** ** THIRD EXAM THURSDAY APR 22, 7PM**
(Instead of Friday class)
**
Mon Apr 26: **
**
Tue Apr 27: **
**
Wed Apr 28: **
**
Fri Apr 30: ** STUDY PERIOD
**
Mon May 03: ** 12:30-02:30 FINAL EXAM