Math 231/249, Honors Calculus II
Fall 2008
Course Description:
A second course in calculus, focusing on sequences and series, but
also covering techniques of integration, parametric equations, polar
coordinates, and complex numbers. While covering the same basic
material as the standard sections, this honors class does so in
more detail, including some additional topics. As such, it is for
those students who, regardless of their major, are particularly
interested in, and excited by, mathematics. In addition, a score of 5 on
the AP Calculus AB exam, or a grade of "A" in Math 220 or 221 is
required for enrollment. Students who enroll in this course must also
register for Math 249 Q1H, the "honors supplement", with CRN 32044.
Grading:
Your course grade for the main 3 credits of Math 231 will be based on:
- Weekly Homework (15%). Homework will be assigned during
each lecture and due at the beginning of class each
Wednesday. No late homework will be accepted; however, your lowest
homework grade will be dropped so you are effectively allowed one
infinitely late assignment. Collaboration on homework is permitted,
nay encouraged. However, you must write up your solutions individually
and understand them completely. You may use a computer or calculator
on the HW for experimentation and to check your answers, but may not
refer to it directly in the solution, e.g. "by Mathematica" is not an
acceptable justification for deriving one equation from
another. (Also, computers and calculators will not be allowed on the
exams, so it's best not to get too dependent on them.)
- Three in-class exams (20% each). These will be closed-book,
calculator-free exams, though you will be allowed to bring one piece
of paper with handwritten formulas. They will be on Fridays, in
particular, September 19, October 17, and November 14.
- A final exam (25%) Our final exam is scheduled for Friday, December 12 from 1:30-4:30 pm.
The grade for the additional 1 credit of Math 249 will be determined
by your grade on the the extra "honors problems". Overall, the
grading policy of this course is designed so that you are not
penalized for selecting an honors section.
Textbook
The required text for this course is:
- Smith and Minton, Calculus: Early Transcendental
Functions, 3rd edition, McGraw Hill, 2006 or 2007.
We will be covering Chapters 6-9, so either the "Single Variable" or
"Full" version of this book is fine. As to the future value of the
longer version for those planning on taking Math 241 (Calculus III),
the honors sections of that course do not use this text, though
some, but not all, of the standard sections do.
A change of perspective is often helpful to clear up
confusion. A good informal supplement to our text is:
- Adams, Thompson, and Hass, How to ace the rest of calculus, the
streetwise guide, Freeman, 2001.
This book is on reserve in the Math Library in Altgeld Hall.
Homework Assignments
- HW #1: Due Friday, August 29. Read Chapter 4
of the text, and find two or three things that you are uncomfortable or
unfamiliar with. For each one, write a couple of sentences
explaining exactly what you don't understand.
- HW #2: Due Wednesday, September 3.
- Section 6.1: 41, 44, 45.
- Section 6.2: 7, 10, 19, 33, 37, 38.
- HW #3: Due Wednesday, September 10.
- Section 6.2: 40, 59, 60.
- Section 6.3: 5, 8, 15, 16, 17, 20, 23, 26.
- Section 6.6: 7, 8.
- HW #4: Due Wednesday, September 17.
- Section 6.4: 5, 6, 13, 31, 37.
- Section 6.6: 11, 18, 25, 35, 39, 40, 41, 45, 46, 54, 55, 56.
- Honors #1: Due Wednesday, September 24. Download here as a PDF file.
- HW #5: Due Wednesday, October 1.
- Section 7.1: 5, 15, 21, 32.
- Section 8.1: 4, 11, 13, 21, 24, 33, 36, 40, 41, 45.
- HW #6: Due Wednesday, October 8.
- Section 8.2: 1, 7, 8, 16, 19, 20, 35.
- Section 8.3: 7, 8, 9, 15, 21, 25, 26, 31, 34, 43, 49.
- HW #7: Due Wednesday, October 15.
- Section 8.4: 5, 6, 19, 24, 29, 37.
- Section 8.5: 5, 6, 11, 17, 18, 24, 27, 33, 36.
- Honors #2: Due Wednesday, October 22. Download here as a PDF file.
- HW #8: Due Wednesday, October 29.
- Section 8.6: 2, 5, 6, 9, 12, 13, 15, 17, 25, 26, 34, 35, 37.
- Section 8.7: 1, 2, 5, 12, 13, 15.
- HW #9: Due Wednesday, Nov 5.
- Section 8.7: 22, 25, 28, 32, 35, 41, 47.
- Section 8.8: 1, 4, 7, 10, 12, 15, 25, 26, 27.
- Section 8.9: 1.
- HW #10: Due Wednesday, Nov 12.
- Section 8.9: 6, 11, 21, 22, 29, 35, 36, 37.
- Section 9.1: 3, 6, 9, 25-30, 33, 36.
- Section 9.2: 2, 3, 12, 13, 21, 26.
- Section 9.3: 5, 7.
- Honors #3: Due Wednesday, November 19. Download here as a PDF file.
- HW #11: Due Wednesday, December 3.
- Section 9.4: 11, 13, 19, 23, 29, 38, 48, 62.
- Section 9.5: 9, 13, 15, 20, 39.
- Section 9.6: 3, 7, 9, 32, 35, 42.
- HW #12 and Honors #4: Due Wednesday, December 10. Download here as a PDF file.
- Review problems for the final Not to be turned in.
- Chapter 6 Review problems.
- True-False: All.
- Exercises: #1-50, 61-68, 70, 71.
- Chapter 8 Review problems.
- True-False: #1-15.
- Exercises: #1-82, except 15.
- Section 8.5: #1-38.
- Section 8.9: Additional problems similar to HW.
- Chapter 9 Review problems.
- True-False: #1-6, 8.
- Exercises: #1-26, 29-60.
Lecture notes
Here scans of my lecture notes, in PDF format.
- Aug 25: Introduction; foundations of integration.
- Aug 27: Foundations of integration and the Fundamental Theorem.
- Aug 29: Integration by parts.
- Sept 3: Trigonometric integrals.
- Sept 5: Trig substitution.
- Sept 8: Improper integrals.
- Sept 10: Improper integrals II.
- Sept 12: Improper integrals III; Partial Fractions.
- Sept 15: Partial Fractions II; Integration in elementary terms.
- Sept 17: Midterm Review.
- Sept 22: Differential Equations.
- Sept 24: Limits of sequences.
- Sept 26: More on sequences.
- Sept 29: Convergence of monotone sequences; Intro to series.
- Oct 1: Infinite series.
- Oct 3: Series with positive terms: the Integral Test.
- Oct 6: Comparison and Limit Tests; Alternating series.
- Oct 8: Alternating series; Absolute convergence.
- Oct 10: Absolute convergence.
- Oct 13: Conditional convergence; Intro to power series.
- Oct 15: Review for Miderm II.
- Oct 20: Power series.
- Oct 22: Differentiating and integrating power series.
- Oct 24: Taylor series.
- Oct 27: Taylor's Theorem.
- Oct 29: Applications of Taylor series.
- Oct 31: Applications of Taylor series II.
- Nov 3: Fourier series.
- Nov 5: Fourier series II; intro to Chapter 9.
- Nov 7: Plane curves.
- Nov 10: Properties of plane curves.
- Nov 12: Review for Midterm III.
- Nov 17: Polar coordinates.
- Nov 19: Properties of curves in polar coordinates.
- Nov 21: Conic sections: ellipses.
- Dec 1: Conic sections: parabolas and hyperbolas.
- Dec 3: Complex numbers.
- Dec 5: Complex numbers II.
- Dec 8: Miscellaneous.
- Dec 10: Final review.