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.


Your course grade for the main 3 credits of Math 231 will be based on: 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.


The required text for this course is:

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:

This book is on reserve in the Math Library in Altgeld Hall.

Homework Assignments

Lecture notes

Here scans of my lecture notes, in PDF format.

  1. Aug 25: Introduction; foundations of integration.
  2. Aug 27: Foundations of integration and the Fundamental Theorem.
  3. Aug 29: Integration by parts.
  4. Sept 3: Trigonometric integrals.
  5. Sept 5: Trig substitution.
  6. Sept 8: Improper integrals.
  7. Sept 10: Improper integrals II.
  8. Sept 12: Improper integrals III; Partial Fractions.
  9. Sept 15: Partial Fractions II; Integration in elementary terms.
  10. Sept 17: Midterm Review.
  11. Sept 22: Differential Equations.
  12. Sept 24: Limits of sequences.
  13. Sept 26: More on sequences.
  14. Sept 29: Convergence of monotone sequences; Intro to series.
  15. Oct 1: Infinite series.
  16. Oct 3: Series with positive terms: the Integral Test.
  17. Oct 6: Comparison and Limit Tests; Alternating series.
  18. Oct 8: Alternating series; Absolute convergence.
  19. Oct 10: Absolute convergence.
  20. Oct 13: Conditional convergence; Intro to power series.
  21. Oct 15: Review for Miderm II.
  22. Oct 20: Power series.
  23. Oct 22: Differentiating and integrating power series.
  24. Oct 24: Taylor series.
  25. Oct 27: Taylor's Theorem.
  26. Oct 29: Applications of Taylor series.
  27. Oct 31: Applications of Taylor series II.
  28. Nov 3: Fourier series.
  29. Nov 5: Fourier series II; intro to Chapter 9.
  30. Nov 7: Plane curves.
  31. Nov 10: Properties of plane curves.
  32. Nov 12: Review for Midterm III.
  33. Nov 17: Polar coordinates.
  34. Nov 19: Properties of curves in polar coordinates.
  35. Nov 21: Conic sections: ellipses.
  36. Dec 1: Conic sections: parabolas and hyperbolas.
  37. Dec 3: Complex numbers.
  38. Dec 5: Complex numbers II.
  39. Dec 8: Miscellaneous.
  40. Dec 10: Final review.

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