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

- Course Planner test dates, homework assigned, etc... (I have a Recommended Homework list document in Blackboard)
- You Tube Playlist for review course of Math 131 (under construction this summer, will announce when significant progress made)
- You Tube Playlist for Fall Semester of 2016 (section 3), to be linked in due time

- You Tube Playlist from Spring Semester of 2016: You Tube Playlist for the later section (9:20-10:10 M-W-F, 9:45-11:00 T-TH)
- My NCSU webpage (you'll find the old ed. of my notes in the ma 241 course).
- Concerning rearrangement of power series. Domain changing algebra.
- Link to page with Numerical Integration Java Applet. does midpoint, left, right, trapezoid and Simpson's. Use this to do homework if you like. (or make Mathematica code if your Mathematica skills are impressive)

My lectures tend to follow these notes, however, sometimes I go deeper than classtime affords us time. Also, I do write these notes with an exceptional student in mind. I believe we are called to excellence not mediocrity. Of course, not everybody needs to understand the entirety of my notes. I just want you to do your best. Notice that I have only been able to put the first 40% or so of the notes into the LaTeX format. The last 60% are in my older, inferior, Word-based format (the whole 2nd-ed. of my notes is posted further down, and if you are really really curious you can find the first edition somewhere on this website...).

- Chapter 9: Integration Techniques
- Chapter 10: Numerical Techniques
- Chapter 11: Improper Integrals
- Chapter 12: Curves
- Chapter 13: Calculus of Parametrized Curves
- Chapter 14: Further Application of Integral Calculus
- Chapter 15: Geometry and Coordinates
- Chapter 16: Introduction to Differential Equations
- Chapter 17: Sequences and Series
- Chapter 18: Basics of Power Series
- Chapter 19: Taylor Series and Techniques

Posted below are problems and some solutions to problems I assigned in previous semesters. These were originally assigned in the Spring 2011 Semester:

- Problem Set 1:

on integration techniques and its solution - Problem Set 2:

on parametric geometry, polar coordinates and applications and its solution - Problem Set 3:

on differential equations and convergence theory and its solution - Problem Set 4:

on power series and applications and its solution - Problem Set 5:

on trouble spots and the missing parts plus the selected select topic and its solution

The problems below were taken from Stewart's Calculus. The qualifier "prereq" means that I don't plan a specific lecture devoted to this topic. It is probably spread over many other lectures. I include these solutions specifically to help those of you who had a lackluster preparation before this course. OK, I hope the reason these solutions are posted here is clear enough.

Section # |
My Notes |
Lecture Date |
Assignment Label and content |
Description |

Sec. 7.8 | . | prereq. | H40 = 5, 11, 13, 15, 19, 21, 25, 27, 43 | L'Hopital's Rule (p. 478) |

Sec. 7.8 | . | prereq. | H41 = 49, 55, 59, 63, 85, 93, 94 | L'Hopital's Rule (p. 478) |

Sec. 7.6 | . | prereq. | H1 = 63, 64 | u-substitution |

Sec. 7.7 | Ch. 9 | prereq. | H2 = 9, 30, 31, 57, 58, 60, 63, 64 | calculus of hyperbolic functions. |

Sec. 8.1 | Ch. 9 | Jan. 24 | H5 = 3, 4, 7, 8, 10, 12, 17, 33 | Integration By Parts (IBP) |

Sec. 8.1 | Ch. 9 | Jan. 24 | H6 = 34, 49, 64 | Integration By Parts (IBP) |

Sec. 8.2 | Ch. 9 | Jan. 25 | H3 = 2, 7, 8, 16, 20, 25, 41, 43, 44 | integrals of trig functions |

Sec. 8.3 | Ch. 9 | Jan. 26 | H4 = 1, 2, 3, 10, 18, 24, 31, 32, 38 | trig substitution |

Sec. 8.4 | Ch. 9 | Jan. 28 | H7 = 2, 4, 6, 7, 8, 10, 13, 19, 20, 29, 34, 35, 48, 51, 69 | partial fractions |

Sec. 8.7 | Ch. 10 | Feb. 2 | H9 = 5, 22, 40 (use Mathematica to calculate finite sums for each of these.) | numerical integration and error |

Sec. 8.8 | Ch. 11 | Feb. 4 | H8 = 2, 6, 9, 16, 17, 18, 27, 31, 35, 38, 78 | improper integration |

Test I | . | Feb. 10 | Test I covers Chapters 9, 10 and 11 of my notes. | integration, improper and numerical integration |

Sec. 11.1 | Ch. 12 | Feb. 11 | H29 = 2, 4, 6, 8, 12, 14, 18, 34, 35, 46 | Parametric Curves |

Sec. 11.2 | Ch. 14 | Feb. 15 | H30 = 1, 42, 44, 48, 52 | Arclength |

Sec. 9.1 | Ch. 14 | Feb. 15 | H31 = 9, 12, 38, 40 | Arclength |

Sec. 9.2 | Ch. 14 | Feb. 17 | H32 = 5, 6, 12, 14, 15 | Area of a surface of revolution |

Sec. 9.3 | Ch. 14 | Feb. 21 | TBA (nothing to post here, but you ought to work some of these) | Calculus in Physics |

Sec. 9.5 | . | . | H33 = 5, 6 | Probability*(optional topic) |

Sec. 11.3 | Ch. 15 | Feb. 23 | H28 = 4, 6, 8, 10, 15, 16, 18, 20, 22, 24, 26, 30, 36, 40, 44, 48 | Polar Coordinates |

Sec. 11.4 | Ch. 14 | Feb. 24 | TBA (nothing to post here, but you ought to work some of these) | polar coordinate calculus |

Sec. 11.5 | Ch. 15 | Feb. 28 | H27 = 2,4,12,16,20,24,26,30,40,48, 55 | Basics of Conic Sections |

Test II | . | Mar. 3 | Test II covers Chapters 12, 13, 14 and 15 of my notes. | parametric curves, physics, two-dimensional motion, polar coordinate calculus, surface area, conic sections. |

Sec. 10.1 | Ch. 16 | Mar. 4 | H10 = 7 | basic concepts for differential equations |

Sec. 10.3 | Ch. 16 | Mar. 7 | H11 = 1, 2, 8, 11, 12, 16, 22, 30 | separation of variables |

Sec. 10.5 | Ch. 16 | Mar. 9 | H12 = 8, 10, 17, 18, 23, 26, 27, 29 | integrating factor method |

Sec. 10.4 | Ch. 16 | . | H13 = 7, 8 | population growth*(optional topic) |

Supplemental Stewart Sec. | Ch. 16 | . | H14 = Click Here for the Problems (2, 4, 6, 7, 9, 10, 18, 21, 22, 34) | homogeneous 2nd order constant coefficient ODEs*(optional topic) |

Sec. 12.1 | Ch. 17 | Mar. 11 | H15 = 5, 15, 22, 25, 30, 33, 62, 64 | sequences, limits of sequence |

Event | . | Mar. 14-18 | . | Spring Break (The Holidays) |

Appendix E | Ch. 17 | Mar. 22 | H16 = 11, 12 | sigma notation |

Sec. 12.2 | Ch. 17 | Mar. 22 | H17 = 10, 15, 31, 34, 42, 48, 56, 60, 67, 68, 70 | geometric series, n-th term test. |

Sec. 12.3 | Ch. 17 | Mar. 24 | H18 = 7, 12, 17, 31, 34 | p-series and integral test |

Sec. 12.4 | Ch. 17 | Mar. 25 | H19 = 3, 5, 8, 12, 13, 16, 28, 30 | limit and direct comparison tests |

Sec. 12.5 | Ch. 17 | Mar. 28 | H20 = 5, 7, 12, 19, 28 | alternating series test and error |

Sec. 12.6 | Ch. 17 | Mar. 29 | H21 = 2, 3, 6, 12, 14, 18, 29, 38 | absolute convergence, ratio test |

Test III | . | April 5 | chapter 16 and 17 of my notes | differential equations and convergence theory for series. |

Sec. 12.8 | Ch. 18 | Apr. 6 | H22 = 4, 6, 12, 25, 30, 32, 38, 41 | power series |

Sec. 12.9 | Ch. 18 | Apr. 7 | H23 = 4, 9, 10, 11, 17, 18, 23, 26, 28, 32 | power series expansions via geometric series tricks |

Sec. 12.10 | Ch. 19 | Apr. 8 | H24 = 9, 11, 15, 25, 28, 29, 33, 36, 39, 41, 47, 50, 59 | Taylor Series |

Event | . | Apr. 13 | . | Assessment Day Party |

Sec. 12.11 | Ch. 19 | Apr. 15 | H25 = 4, 8, 28 | Taylor Polynomials (also, see my Section 6.5) |

N/A | Fourier Section | . | H26 = 1, 4, 7, 11, 13, 15, 17 (from the linked pdf) | Fourier Series*(optional topic) |

Sec. 6.5 | . | . | H34 = 2, 7, 8, 20, | Averages*(optional topic) |

Test IV | . | Apr. 28 | chapters 18 and 19 as well as section 6.5 of my notes. | power series techniques and applications. |

Final | . | T.B.A. | comprehensive | LU-officially scheduled time, usual room. |

These give you some idea of the difficulty of the course. Also, while tests change from semester to semester these show you certain things you might expect.

- Solution to Test 1 (posted now, the solution for 1b is only correct if you make all the limits right limits)
- Solution to Test 2
- Solution to Test 3
- Solution to Test 4

We start with Chapter 9 in calculus II. You do not need to print these. These are not the notes for this semester. That said, my approach in these notes is less formal than the approach I am currently applying to the calculus sequence. I expect more of my students in the current edition of my notes.

- 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
- Stewart Add-on: Fourier Series
- Chapter 14: Geometry and Coordinates
- Chapter 15: Parametrized Curves and Geometry
- Chapter 16: Further Applications of Calculus

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.

- 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

Modified 6-30-2016

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