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 1,3,13,27,32Friday 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 curvesy=4x(1-x) andy=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 whenx=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''=y^{2}withy(0) = 1,y'(0)=0. Calculate the coefficientsa_{0},...,a_{6}.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, 49,51,55Friday 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 sequencea_{1},a_{2},a_{3},... isL." Nov 16 6.12 1,3,11-14,15 A3 1,3,7,11,19,23,25,27 Hand in: Consider the differential equationy'= sin(x+y). 1. Sketch the slope field for -2 <x< 6, -3 <y< 3. (Note that slopes are constant along the linesx+y=C; use this fact forC= 0, pi/2, pi, etc. to make the job easier.) 2. Lety=f(x) be the solution with initial valuey(0)=0. Use your slope field to sketchfand to estimate the firstx> 0 withf(x)=0. 3. Use your Euler's method program to check the accuracy of your estimate, and then to calculatexwith 2 decimal places of accuracy. Run the program with smallnto get near the rightx, and then increasento 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

Math Dept SUNY Stony Brook

tony@math.sunysb.edu