Calculus II Assignments

MTH 112: Calculus with Analytic Geometry II
Dr. Elmer K. Hayashi
Fall 2001
Assignments

Aug 29-31	Sep 3-7	Sep 10-14	Sep 17-21	Sep 24-28
Oct 1-5	Oct 8-12	Oct 15-19	Oct 22-26	Oct 29-Nov 2
Nov 5-9	Nov 12-16	Nov 19-23	Nov 26-30	Dec 3-7

Textbook: Stewart, Calculus, Fourth Edition
Graduate Teaching Assistant: Becky Ellington
Help Sessions, Wednesday 11:30-12:30, Calloway 338.

Wed, 08/29/2001. Sequences.: Read section 12.1 on sequences and make sure you understand what it means for a sequence to converge or diverge, and how to find the limit of a sequence. On page 736, know how to do problems 1-24. Write up problems 10, 12, 14, 18, 20, 22 on page 736 to turn in on Friday.
Working with Sequences in Maple

Fri, 08/31/2001. Limits of Sequences.: Review examples 1-10 in section 4.4 and examples 1-5 in section 7.7. Read section 12.1 on using the limit theorems and the Squeeze theorem. Practice on problems 25-48 on page 736.
Examples of sequences
Sequence Examples in a Maple 6 worksheet

Mon, 09/03/2001. Monotone Convergence Theorem.: Read material in section 12.1 on Monotone and Bounded sequences. In particular, study example 11 on page 735. Make sure you know how to do problems 52-62 on page 736.
Write up problems 54 and 60 on page 736 to turn in on Wednesday.

Tue, 09/04/2001. Review.: Review of limit strategies: factoring highest powers, difference of squares, taking absolute values, inverse functions, looking at logarithm of each term, dealing with factorials.
Review section 12.1 and problems at the end of the section.

Wed, 09/05/2001. Infinite Series.: Read section 12.2 on series and series convergence, geometric series, Divergence test, and Series properties or rules.
practice problems, page 745-746: odd probs 11-33, 41, 49.
Write up problems 16, 20, 28, 30, 50 on pages 745-746 to turn in on Friday.
Series Examples discussed in class.
Maple 6 worksheet of Examples discussed in class
There will be a help session at 11 a.m. in Calloway 338, today.

Fri, 09/07/2001. Harmonic Series.: Review sections 12.1 and 12.2., and read ahead in section 12.3.
For practice look at problem 61 on page 737,
problems 6, 7, 23, 26, 33, and 35 on page 745,
problems 58, 60-63 on page 747.
Challenge Problem: page 747, problem 68 (you may submit this for extra credit).

Mon, 09/10/2001. Integral Test.: Read section 12.3 on Integral Test. Make sure to know how to draw pictures similar to those used in the proof of the Integral Test.
Write up problems 2, 4, 8 on page 754 to turn in on Wednesday.

Tue, 09/11/2001. Error estimates using Integral Test.: Review section 12.3 on Integral Test, approximation of a series using a partial sum, and estimates of the error in doing so.
Practice problems 3, 5, 7, 9, 10, 11, 15, 17, 19, 21, 25, 29, 31, 33, 35a on pages 754-755.

Wed, 09/12/2001.: Read section 12.4 on the Comparison Test and Limit Comparison Test.
Write up problems 30 and 32 on page 755 and problem 36 on page 760 to turn in on Monday.
Look at problems 15, 33, and 35 on page 760 to be discussed on Friday. Other problems to practice on pages 759-760: 1, 3, 5, 7, 9, 11, 13, 21, 23, 25, 27.

Fri, 09/14/2001. Estimating Error using a Geometric Series.: Review Divergence Test, Geometric Series Test, P-series Test, Integral Test, Comparison Test, Limit Comparison. Know them precisely, and know how and when each is applicable. Review estimation of errors using Integration or Geometric Series Sum. Read ahead in section 12.5 about the Alternating Series Test, and estimating the sum of an alternating series.

Mon, 09/17/2001. Alternating Series Test.: Read section 12.4 on the alternating series test, and how to estimate the sum of a series converging by the alternating series test.
For practice do problems 2, 3, 7, 9, 12, 13, 14, 15, 21, 23.
Review problems on hour exam from Spring 2001

Tue, 09/18/2001. Absolute Convergence.: Review Section 12.5 on error estimation of series that converge by the Alternating Series Test. Begin reading Section 12.6 on absolute and conditional convergence.
Do problems 26 and 30 on page 765 and problems 10 and 18 on pages 770-771 to turn in on Friday.
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Wed, 09/19/2001. Ratio Test.: Read Section 12.6 on the Ratio Test.
Do odd problems 3-21, and 33 on pages 770-771 for practice.
Help Session today from 11:30 a.m. to 12:30 p.m.

Fri, 09/21/2001. Root Test.: Read section 12.6 on the Root Test.
Do problems 22-26 on page 771.

Mon, 09/24/2001. Power Series.: Review of convergence tests, and error estimates for sum approximations. A brief introduction to power series.
Help Session today from 11:30 a.m. to 12:30 p.m. and 3:00 to 4:00 p.m.

Tue, 09/25/2001.

Wed, 09/26/2001. First Hour Exam: The exam will cover sections 1-7 in Chapter 12. There will be a take home portion that will be due on Friday, September 28, 2001.

Fri, 09/28/2001. Power Series: Read sections 12.8 on radius of convergence and interval of convergence for power series. Begin reading section 12.9 on the representation of functions as power series.
On page 778: do 3, 5, 7, 9, 11, 13, 19, 21, and 27 for practice.
On page 783-784: do 3, 5, 7, and 9 for practice.

Mon, 10/01/2001. Differentiation of Power Series.: Read about differentiation of power series in section 12.9.
On page 778, do problems 20 and 30, and on page 784, do problem 22 to turn in on Wednesday.
Look at problems 10-24 on pages 783-784 for practice.

Tue, 10/02/2001. Integration of Power Series.: Read about integration of power series in section 12.9.
For practice, do problems 1, 2, 21, 23, 25, 27 on pages 783-784.

Wed, 10/03/2001. Approximation of Definite Integrals using Infinite Series.: Study examples 8 and 9 in section 12.9.
Do problems 18,30,32 on page 784 to turn in on Friday.
For more practice, do problems 29, 31, 37, 39 on page 784.

Fri, 10/05/2001. Maclaurin's Series.: Read the definition of Maclaurin's Series in section 12.10.
On pages 794-795, do problems 1-6, 21, 23, 25, 27 for practice.

Mon, 10/08/2001. Finding Power Series for functions.: Review section 12.10. Study examples 3, 6, 7, and 8.
On page 795, for practice, do problems 31, 33, 35, 37, 39.

Tue, 10/09/2001. Finding limits using Maclaurin's Series.: Review section 12.10. Study examples 8 and 9.
Do problems 36, 44, 46 on page 795 to turn in on Friday.
Do problems 41, 43, 45, 47, 48 on page 795 for practice.

Wed, 10/10/2001. Taylor's Formula with remainder.: Do practice problems 9-18 on page 794.
See Taylor Polynomials in Maple
See proof that the Taylor's Series of exp(x) converges to exp(x)
See derivation of Taylor's Formula

Fri, 10/12/2001. Application of Taylor's Inequality.: Read section 12.12 on the application of Taylor's Inequality. In particular, study examples 1 and 2 on pages801-804.
On pages 806-807, do problems 10, 16, 21, and 24 to turn in next Tuesday.
See Accuracy of Taylor Approximations

Mon,10/15/2001. Distance Formual in Three Space.: Read about rectangular coordinates in three space, and the distance formual in three space.
On page 821, look at problems 1, 3, 7, 10, 11, and 13.
To review power series, look at problem 49-58 on page 795, problems 1-28 on pages 806-807, and problems 30-57 on pages 810-811.
See Cartesian Coordinates in 3-Space

Tue, 10/16/2001.: Review Section 13.1 Cartesian Coordinates and distance formula, and begin reading Section 13.2 on vectors.
do problems 9, 15, 17, 27, 29, 31, 33 on page 821 and 1, 3, 5 on page 829 for practice.
See Graphing Cylindrical Surfaces

Wed, 10/17/2001. Parametric Equations of a Line.: Begin reading section 13.5 on the parametric equations of a line.
For practice look at the odd numbered problems from 7-29 on page 829, problems 3,7 on pages 852-853.

Fri, 10/19/2001. Fall Break.: No Class.

Mon, 10/22/2001. Equations of Lines.: Review vector, parametric, and symmetric equations of lines in section 13.5.
Do problems 2, 8, 16, 18 on pages 852-853 to turn in on Wednesday.
Look at problems 2-9, 15-18 on pages 852-853 for more practice.

Tue, 10/23/2001. Dot Product and Equation of a Plane.: Read about dot product and angle between two vectors in section 3.2. Study example 4 on page 849.
For practice, look at problems 5, 7, 9, 11, 25, 27 on page 836, and problems 19-26 and 35-38 on page 853.

Wed, 10/24/2001. Cross Product and Equation of a Plane.: Study examples 5 and 7 on page 849-851.
For practice, do problems 10, 14, 27, 29, 31, 33, 41, 43, 45, 47, 49 on pages 853-854.

Fri, 10/26/2001. Distance from a Point to a Line or Plane.: Read about scalar and vector projections on pages 834-835. Study examples 8 and 9 on pages 851-852.
Do problem 53 on page 837 and problems 59, 61, 63, and 65 on page 854 for practice.

Mon, 10/29/2001. Areas and Volumes.: Read about direction angles and cosines on page 833, area of a parallelogram on page 840, and volume of a parallelepiped on page 842.
Extra Credit: Do Discovery Project, questions 1, 2, 3 on page 845.
Review problems on Exam 2 from Spring 2001

Tue, 10/30/2001. Hour Exam: Hour exam will cover sections 12.8 - 13.5. There will be a take home portion counting about 20 per cent and due at the beginning of class on Wednesday.

Wed, 10/31/2001. Functions of two variables.: Review conic sections in section 11.6, and polar coordinates earlier in Chapter 11 if necessary. Begin reading section 15.1 on functions of two and three variables with particular attention to domains, ranges, and graphs.
See Graphing with plot3d
For practice, look at odd problems 7-19 on page 918.

Fri, 11/02/2001. Level Curves: Review direction cosines in section 13.3, and read about level curves and level sets in section 15.1
See Graphing Level Sets with Maple
on page 836, do 33, 37, 38, and on page 919 do 35-42 for practice.
Write up problems 30, 51-56 on pages 919-921 to turn in next Tuesday. Concentrate on finding good reasons for justifying your choices.

Mon, 11/05/2001. Limits and Continuity.: Read about limits and continuity in section 15.2
On page 929, look at problems 25-36 for practice.

Tue, 11/06/2001.: Review section 15.2 on how to show that a limit does not exist, and on how to show that certain limits are 0. Look at contour maps of the functions, and know how to determine from the contour maps which functions have limits, or to determine what paths to use to show the limit does not exist.
See Analyzing Limits using Contour Maps
On page 928, do problems 6, 8, 12,14, 21, 22 to turn in on Friday.

Wed, 11/07/2001. Review Properties of Graphs.: Review sections 15.1-15.2

Fri, 11/09/2001.: Read about partial derivatives in section 15.3.
Do problems 5, 7, 9, 15, 19, 21, 33, 35, 37, 57, 59 on page 940 for practice.
See Graphs of Partial Derivatives

Mon, 11/12/2001. Implicit Differentiation.: Review sections 15.2 and 15.3.
Do problems 10, 16, 28, 34 on page 928 and problems 52 and 56 on page 941 to turn in Wednesday.
Look at problems 39, 41, 53, 59, 67 on pages 940-941 for practice.

Tue, 11/13/2001. Equation of Tangent Planes found explicitly.: Begin reading section 15.4 about tangent planes and linearizations.
Look at problems 1, 3, 5, 7, 9, 11 on page 950 for practice.
See Computing and Graphing Linearizations of a function of two variables.

Wed, 11/14/2001. Linear Approximations of Functions.: Review section 15.4 and learn how to compute dz and delta z. Note that using differentials is nothing more than linear approximation.
On pages 950-951, Do at least the odd problems 11-19, 29-37 for practice.

Fri, 11/16/2001. Double Integrals and Iterated Integrals.: Begin reading sections 16.1 and 16.2.
On pages 1008-1009, look at problems 5, 9, 12, 15, and pages 1014-1015, look at problems 3, 11, 15, 16.
See Numerical Approximation of a Double Integral.

Mon, 11/19/2001. Volume and Integration over more general regions.: Read section 16.2 on volume, and section 16.3 on type I and type II regions.
On pages 1014-1015, look at problems 27, 29.
On pages 1022, look at problems 1, 3, 5, 8, 9, 18, 19, 20, 33, 35, 37, 39.
See Graphs of Type I and II Regions.

Tue, 11/20/2001. Average value and review.: Review sections 16.1-16.3.
On page 1015, look at problems 33, 34 on average value.

Wed, 11/21/2001. Thanksgiving Vacation.: No Class.

Mon, 11/26/2001. Double Integral Rules.: Review 15.1-15.4 and 16.1-16.3 for exam on Wednesday.
On page 1023, look at problems 47 and 48.
Review problems on Exam 3 from Spring 2001
PDF Format Exam 3 from Spring 2001

Tue, 11/27/2001.

Wed, 11/28/2001.: Hour Exam covering sections 15.1-15.4, 16.1-16.3.

Fri, 11/30/2001. Double Integrals in Polar Coordinates.: Double integrals over circular regions can be evaluated more easily by using polar coordinates. Read section 16.4.
On page 1028, do problems 1,3, 6, 7, 9, 11, 19, 21, 23 for practice.
See Graphs over circular regions.

Mon, 12/03/2001. Total Mass and Center of Mass.: Read section 16.5 on total mass, moments about each axis, and center of mass.
On page 1028-1029, do problems 8, 26, 30, and on page 1038, problem 12 to turn in on Wednesday.

Tue, 12/04/2001. Areas enclosed by Polar Curves.: On page 1028-1029, look at problem 15-18, and 33.
See Graphing Polar Curves using polarplot

Wed, 12/05/2001. Review.: Review when to use polar coordinates and when to use rectangular coordinates. Review the method of drawing the regions of integration.
On pages page 1038, look at problems 3, 7, 9, and on pages 1069-1070, look at problems 9, 11, 13, 21, 41.

Fri, 12/07/2001. Review.: Study Guides for the final exam are available for $4.00 each in Calloway 302. Each study guide contains an outline of the main topics in the course, practice problems including problems from the final exam given in Spring 2001, and the solutions to the practice problems. The final exam will cover sections 12.1-12.10, 12.12, 13.1-13.5, 15.1-15.4, 16.1-16.5.

Wednesday, 12/12/2001. Final Examination.: 9:00 a.m.-12:00 p.m.
308 Greene Hall

Created 05/31/2001. Last modified 11/19/2001. Email to ekh@wfu.edu