Welcome, please note that the offical syllabus is linked here. Please note this webpage is where test solutions and further assignments are to be posted. For your convenience, I have provided a few links to points further down this page.

- I. Course Contact Information
- II. Useful Materials and Links:
- III. Additional Examples:
- IV. Test Reviews and Solutions:
- V. Course Notes:
- VI. Bonus Point Policy:
- VII. Required Homework List:

- Instructor: Dr. James S. Cook
- Office: Applied Science 105
- Office Hours: M-T-W-R-F from 11:00am-12:00pm
- Email: jcook4@liberty.edu
- Office Phone: 434-582-2476
- Lectures and tests are in Science Hall 134
- Lecture Times: MWF 8:50 am - 9:40 am, and TR 9:15 am - 10:30 am

I'll probably post Mathematica templates and small notes about particular lectures here if need be.

- Course Syllabus
- My NCSU webpage (you'll find the old ed. of my notes in the ma 241 course).
- Notes concerning the basics of complex variables
- Yet more notes on the complex exponential:
- Concerning rearrangement of power series. Domain changing algebra.
- Select solutions to a few arclength and average problems

If you surf through these documents you'll find over a dozen old tests, numerous quiz solutions and just plain old solved homework problems. There are solved problems like your homework for most of the sections we cover. Exceptions to this rule are the material in my Chapter 13 and 14 this semester. I am attempting to organize these so you can find the sort of problem you are working on without too much searching. Unfortunately there are some irrelevant problems, but those should be fairly obvious and I certainly don't mind if you email to ask if a given problem has anything to do with your homework or not... On the other hand, there is more than likely a number of solved homework problems in the mix. This is not on purpose. It's just the inevitable consequence of Stewart's Calculus never changing it's problems from edition to edition or decade to decade if I had to speculate...

- Test I solution
- Test I solution
- Test one solution
- Test one solution
- U-subst. , 7-3-07
- U-subst. in-class exercise, 1-10-06
- U-substitution, 1-13-06
- Trig-subst./Partial Fractions , 7-6-07
- Trig-subst. in-class exercise, 1-17-06
- trig. substitution, 1-20-06
- IBP(5.6), 1-23-06
- partial fractions, 1-26-06
- Partial fractions make-up quiz (add's maximum of 5+1 points to test one)
- Final Exam and solution
- Solution to old extra credit project
- Older extra credit project Solutions by Ginny. Warning, she's my wife so she doesn't have to show all her work. You do not have this privilige on the tests. Please ask me if you don't understand some step she made since her work is very concise.
- quizzes integration, differential equations, series ( best of collection)

- first order ODEs
- separation of variables, 3-15(?)-06
- homogeneous 2nd order ODEs with constant coefficients, 3-20-06
- Test III solution
- Test III solution
- Test three solution
- Test three solution
- Final Exam and solution
- quizzes integration, differential equations, series ( best of collection)
- Test three solution
- Test I solution from DEQns course, much overlap.

- series convergence and divergence(8.1-8.4)
- convergence/divergence test guidewith box to put in an example of your own
- convergence/divergence test guidewith box filled with the wise guidance of a fellow TA and a warning about what my focus is on for our section of ma 241.
- Sequences and series, basics
- Test IV solution
- Test IV practice test and solution
- Test IV solution
- Test four solution
- Test four solution

- Power Series, Interval of Convergence and Geometric Series Techniques
- geometric series trick chart my graphical representation of how to use the geometric series indirectly. This trick should be combined with some common sense to solve problems in section 8.6. Of course some problems are just plain-old geometric series, so try that first when attacking 8.6 questions.
- a selection of homework problems worked I work out a few of your homework problems. I deal with the endpoints for an example or two, but then focus on the main part which is the open interval of convergence. That just requires careful application of the ratio test. The endpoints require more thought sometimes.
- a selection of homework problems worked mostly even numbered problems, I hope these help you understand how to get started. These sort of problems reflect what I think is the most important element of power series. This is the part that you can use in other courses ( convergence and divergence is fine and all but if you can't calculate the power series representation of a function then the question of where it converges seems somewhat pointless ). Also the fact we can integrate almost anything with power series is just fantastic.
- power series extra examples ( E6 thru E13 relevant to ma241-006 )
- Test IV solution
- Test IV practice test and solution
- Test IV solution
- Test four solution
- Test four solution
- Final Exam and solution
- quizzes integration, differential equations, series ( best of collection)

- arclengths, 2-20-06
- averages, 2-21-06
- probability and center of mass, 2-24-06
- Test II solution
- Test II solution (has arclength and probability problem)
- Test two solution
- Test two solution

I will post reviews and solutions for our course here once it's time.

- Review for Test 1
- Review for Test 2
- Review for Test 3
- Supplemental Review Problems for Test 3
- Review for Test 4
- Bonus Project to help prepare for Final Exam

Lectures often closely follow these notes (I expect you to have a copy with you in lecture). Sometimes there is not time to say everything during class, I try to stick to the most important parts in lecture. We start with Chapter 9 in calculus II.

- Chapter 1: Introduction
- Chapter 2: Functions and Algebra
- Chapter 3: Limits and Continuity
- Chapter 4: Derivatives
- Chapter 5: Applications of Derivatives
- Chapter 6: Integral Calculus
- Chapter 7: Applications of the Integral
- Chapter 8: L'Hopital's Rule
- Chapter 9: Integration Techniques
- Chapter 10: Introduction to Differential Equations
- Chapter 11: Sequences and Series
- Chapter 12: Basics of Power Series
- Chapter 13: Power Series Techniques
- Chapter 14: Geometry and Coordinates
- Chapter 15: Parametrized Curves and Geometry
- Chapter 16: Further Applications of Calculus

It is possible to earn bonus points by asking particularly good questions or suggesting corrections to errors in notes and materials on the course website. This does not include spelling or grammatical errors, those are provided for your amusement. Once I notify the class of the error you may no longer ask for that point.

I also provide a little bonus project from time to time. These are not required. It is entirely possible to earn an A without completing these. If you scan through the notes you'll find a number of bonus opportunities already available. In contrast to previous semesters I will not offer bonus points on the in-class portion of the test. Instead, you have the choice to do them outside class at your leisure. I will usually be able to take these as late as the final exam day, just ask.

It is important to both complete and understand the homework. I encourage you to form study groups, however, it is very important that in the end you come to an understanding of the material for yourself. You will most likely find the homework in this course challenging at times, so it is important to begin early and give yourself a chance to talk to others (for example me) before the due date. You may also email me reasonable questions.

It is not enough to find the answer - you must be able to justify each step. Imagine that you are writing the solution for a person who doesn't know calculus. On our tests I will expect you to explain your work since presentation and proper notation are arguably as important as the answer itself. In my lectures I strive to present calculations in a coherent and logical manner and I will expect you to do the same. So, take some time to notice what the notation means and don't just scribble the bare amount to get the answer. It's a bad habit and it will most likely knock a letter grade or two off of your tests.

I am always happy to look over your derivations of homework during office hours. Additionally, most days (time permitting), I'll answer a question about the homework. I try to give you all the tools you need to do the homework, but it is you who must put those tools to work.

The homework is posted below. Notice I have indicated which portion of my lecture notes as well as which part of the textbook is most relevant to the assigment. Beware, sometimes the homework is not exactly matched up with the lecture notes link, sometimes you need to look at the next few pages. The pdf's of my lecture notes are chopped up Chapter by Chapter, usually you can find what you need somewhere in that chapter. If you are lost send me an email, I'll try to point you in the right direction. I expect you to print out a copy of the lecture notes - you will find them helpful for certain homework problems.

Section # |
My Notes |
Due Date |
Assignment |
Description |

Sec. 7.6 | . | Jan. 16 | 63, 64 | u-substitution |

Sec. 7.7 | Ch. 9 | Jan. 16 | 9, 30, 31, 57, 58, 60, 63, 64 | calculus of hyperbolic functions. |

Sec. 8.2 | Ch. 9 | Jan. 16 | 2, 7, 8, 16, 20, 25, 41, 43, 44 | integrals of trig functions |

Sec. 8.3 | Ch. 9 | Jan. 23 | 1, 2, 3, 10, 18, 24, 31, 32, 38 | trig substitution |

Sec. 8.1 | Ch. 9 | Jan. 23 | 3, 4, 7, 8, 10, 12, 17, 33 | Integration By Parts (IBP) |

Sec. 8.1 | Ch. 9 | Jan. 30 | 34, 49, 62*, 64 | Integration By Parts (IBP) |

Sec. 8.4 | Ch. 9 | Jan. 30 | 2, 4, 6, 7, 8, 10, 13, 19, 20, 29, 34, 35, 48, 51, 57*, 69 | partial fractions |

Sec. 8.8 | Ch. 9 | Jan. 30 | 2, 6, 9, 16, 17, 18, 27, 31, 35, 38, 71*, 78 | improper integration |

Test I | . | Feb. 5 | Test I covers most of chapter 9 in my notes | integration, improper integration |

Sec. 8.7 | Ch. 9 | Feb. 9 | 5, 22, 40 (use Mathematica to calculate finite sums for each of these.) | numerical integration and error |

Sec. 10.1 | Ch. 10 | Feb. 13 | 7, | basic concepts for differential equations |

Sec. 10.3 | Ch. 10 | Feb. 13 | 1, 2, 8, 11, 12, 16, 22, 30, 48* | separation of variables |

Sec. 10.5 | Ch. 10 | Feb. 13 | 8, 10, 17, 18, 23, 26, 27, 29, 35*, 36* | integrating factor method |

Sec. 10.4 | Ch. 10 | Feb. 20 | 7*, 8* | population growth |

Supplemental Stewart Sec. | Ch. 10 | Feb. 20 | Click Here for the Problems (2, 4, 6, 7, 9, 10, 18, 21, 22, 34) | homogeneous 2nd order constant coefficient ODEs |

Sec. 12.1 | Chap. 11 | Feb. 20 | 5, 15, 22, 25, 30, 33, 62, 64 | sequences, limits of sequence |

Appendix E | Chap. 11 | Feb. 20 | 11, 12 | sigma notation |

Sec. 12.2 | Chap. 11 | Feb. 20 | 10, 15, 31, 34, 42, 48, 56, 60, 67, 68, 70 | geometric series, n-th term test. |

Sec. 12.3 | Chap. 11 | Feb. 27 | 7, 12, 17, 31, 34 | p-series and integral test |

Sec. 12.4 | Chap. 11 | Feb. 27 | 3, 5, 8, 12, 13, 16, 28, 30 | limit and direct comparison tests |

Sec. 12.5 | Chap. 11 | Feb. 27 | 5, 7, 12, 19, 28, 35* | alternating series test and error |

Sec. 12.6 | Chap. 11 | Feb. 27 | 2, 3, 6, 12, 14, 18, 29, 38 | absolute convergence, ratio test |

Test II | . | Mar. 3 | covers Chapters 10 and 11 of my notes | differential equations, sequences, conv/div tests |

Event | . | Mar. 9-13 | no lectures, spring break | The "Hollidays" |

Sec. 12.8 | Chap. 12 | Mar. 20 | 4, 6, 12, 25, 30, 32, 38, 41 | power series |

Sec. 12.9 | Chap. 12 | Mar. 20 | 4, 9, 10, 11, 17, 18, 23, 26, 28, 32 | power series expansions via geometric series tricks |

Sec. 12.10 | Chap. 13 | Mar. 27 | 9, 11, 15, 25, 28, 29, 33, 36, 39, 41, 47, 50, 59 | Taylor Series |

Sec. 12.11 | Chap. 13 | Mar. 27 | 4, 8, 28, 35* | Taylor Polynomials |

Test III | . | Mar. 31 | chapter 12 and 13 of my notes | power series representation of functions, IOC and ROC, Taylor Polynomials |

Sec. 11.5 | Chap. 14 | Apr. 10 | 6, 12, 20, Prove Theorems 14.1.1, 14.1.2, 14.1.3 (worth 6 problems) | Conic Sections |

Sec. 11.3 | Chap. 14 | Apr. 10 | 4, 6, 8, 10, 15, 16, 18, 20, 22, 24, 26, 30, 36, 40, 44, 48 | Polar Coordinates |

Sec. 11.1 | Chap. 15 | Apr. 17 | 2, 4, 6, 8, 12, 14, 18, 34, 35, 46 | Parametric Curves |

Sec. 11.2 | Chap. 15 | Apr. 24 | 1, 42, 44, 48, 52, 69*, 70*, 72* | Arclength |

Sec. 9.1 | Chap. 15 | Apr. 24 | 9, 12, 38, 40 | Arclength |

Sec. 9.2 | see Stewart. | Apr. 24 | 5, 6, 12, 14, 15 | Area of a surface of revolution |

Sec. 9.5 | Chap. 16 | Apr. 24 | 5, 6 | Probability |

Sec. 6.5 | Chap. 16 | Apr. 24 | 2, 7, 8, 20, | Averages |

Sec. 6.4 | Chap. 16 | Apr. 29 | 14*, 22* | Work, Force, Physics |

Sec. 9.3 | Chap. 16 | Apr. 29 | 6*, 9* | Hydrostatic Force |

Test IV | . | Apr. 28 | parts of chapters 14, 15 and 16 of my notes | coordinates, conic sections, parametric curves, arclength, surface area, averages, probability density definition |

Final | . | May 6 | comprehensive | 8-10am, Wed. May 6, usual room. |

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Last Modified: 4-29-09