## MAT 142 Honors Calculus II Fall 1998 - Homework

Text: Thomas/Finney, Calculus 9th Ed.
Homework will be discussed at the recitation meeting of the following week: make sure you are prepared!
[Exercises in brackets are optional]

```Week of:   Section:	Homework exercises

August 31  5.1          1,3,7,11,17,25,33,37,43,51
5.2          1,3,7,11

Sept 7     5.3          3,9,13,21,29,41
5.4          1,3
5.5          3,13,19
5.6          3,9,19
Hand in 9/16: Derive from first
geometric principles the formula
("2 pi times slant length times
average radius") for the area of
a frustrum of a cone.

Sept 14    5.7          1,3,9,15,29,31
5.8          1,3,11,13,21,25
5.9          1,3,9,13,17
5.10         11,13,21,23
Hand in 9/23: Moments, Problem 27.

Sept 21    7.1          1-21 odd,37,49,55,67
7.2          1-11 odd,25,29,31,35,41

Sept 28    7.3          1,3,15,17,25
4.9          1,3,13,27,32
Friday October 2: Midterm I (on Chapter 5) in class.

Oct 5      8.1          1,3,7,11,15,19,25,27,29,31,33,35,39,40,55, [68]
8.2          1,5,11,17,25,33,45,65
Hand in 10/12: the curves y=4x(1-x)
and  y=sin(pix) both define arches
from (0,0) to (1,0) passing through (1/2,1). Which
arch is longer? Use your calculators to estimate
the two lengths. Is there a way to settle the
question without calculating the lengths?

Oct 12    8.3           1,3,5,9,23,27,29,35,41,47,51,61,73,77,[78]
8.4           1,3,9,31,33
8.5           1,3,5,7,13,39

Oct 19    8.6           13,3,5,13,27
8.7           3,5,13,23,45,51,59
8.8           1,3,7,13,23,33,39,41

Oct 26    8.9           1,3,5,9,13,21,29,33,35
8.10          1,3,7,13,19,21,23,31,39,[44],49,51,54,55,56
Hand in 11/2: 1. Find a power series which only
converges when x=0.
2. Graph the sum of the first 3, the first 4
and the first 5 terms of the power series for
sin(x), and compare with the graph of sin(x).

Nov  2    8.11          1,41,47
Review for Midterm
Hand in 11/9: Use power series to solve the
d.e. y'' = y2 with y(0) = 1, y'(0)=0.
Calculate the coefficients a0,...,a6.
Friday November 6: Midterm II, part 1 (in class).
This part will cover methods of integration (7.1 7.2 7.3) and
numerical calculation of integrals, with error estimates (4.9).

Nov  9    Note: this week there will be two lectures on
Monday (the second during recitation time)
4.2           1,5,17,31,33,35,39,47,49
6.11          1,3,7,9, 19,35, 47, 49,51,55
Friday November 13: Midterm II, part 2 (in class).
This part will cover sequences and series (8.1 through 8.10). One
20-point question will be: give the correct definition of this statement:
"The limit of the sequence a1,a2,a3,... is L."

Nov 16	  6.12          1,3,11-14,15
A3            1,3,7,11,19,23,25,27
Hand in: Consider the differential equation y' = sin(x+y).
1. Sketch the slope field for -2 < x < 6, -3 < y < 3. (Note that
slopes are constant along the lines x + y = C; use this fact for
C = 0, pi/2, pi, etc. to make the job easier.)
2. Let y=f(x) be the solution with initial value y(0)=0. Use your
slope field to sketch f and to estimate the first x > 0
with f(x)=0.
3. Use your Euler's method program to check the accuracy of your
estimate, and then to calculate x with 2 decimal places of accuracy.
Run the program with small n to get near the right x, and then
increase n to get a more accurate answer.

Nov 23	 Second order differential equations (from notes)

Nov 30	  6.6           1,7,43,57,59
6.7           1,3,5,9

Dec  7    7.6

Dec 14    (Monday) Last Day of Classes
Dec 16    (Wednesday) 8:30-11:30AM FINAL EXAMINATION
```

Anthony Phillips
Math Dept SUNY Stony Brook
tony@math.sunysb.edu
November 18 1998