• Wednesday, 8/22: Issued handouts and course information. No calculator is allowed on quizzes, tests, and the final exams.
  
• Friday, 8/24: We started Chapter 7 Techniques of Integration. You need to learn all formulae on page 469. We did several examples of integration by parts from the book. HW #1 was assigned.
  
• Monday, 8/27: We briefly reviewed integration by parts on examples. We moved on to Section 7.2: Trignometric Integrals. We worked four examples on integrals of the form sin^m x cos^n x and looked at stragegies for evaluating integral of this type.
  
• Wednesday, 8/29:We continued with integrals containing factors sin(nx)sin(mx), sin(nx)cos(mx), cos(nx)cos(mx) - illustrated on one problem each. Moved on to integrals of the form tan^m x sec^n x when (a) n is even, or (b) m is odd with a factor of sec x tan x. We worked out examples integral tan^6 x sec^4 x dx and tan^5 x sec^7 x dx. Several tricks for the remaining case revealed on integrals of tan x, tan^3 x, sec x, sec^3 x. Quiz 1 given. HW #2 was assigned.
  
• Friday, 8/31: We did a brief overview of integrals involving tan x and sec x. Did integral of cot^3 x csc^4 x dx to ilustrate how to develop rules for integrals with cot x and csc x. Started Section 7.3: Trigonometric Substitution. We showed substitutions needed for integrals involving \sqrt{a^2 - x^2}, \sqrt{a^2 + x^2}, \sqrt{x^2 - a^2}. Did one example for each, ending with integral of \sqrt{x^2 - a^2} dx.
  
• Monday, 9/3: Labor Day - no class !
  
• Wednesday, 9/5: We finish integral of \sqrt{x^2 - a^2} dx and did 2 more problems on trigonometric substitutions. Remember that not all integrals which look like ones for trigonometric substituion indeed require it !! Example: integral of x^3/ (4x^2 +9)^{3/2}dx. Started with initial remarks for Section 7.4: Integration of Rational Functions by Partial Fractions. Quiz #2 and HW #3 given.
  
• Friday, 9/7: First three cases (non-repeating linear factors only, repeating linear factors with no quadratic factors, and non-repeating quadratic factors) of integration by partial fractions were discussed. Each ilustrated by an example.
  
• Monday, 9/10: We finished integration by partial fractions by discussing the last case (a power of an irreducible quadratic factor) - did 1 example. Rationalizing substitutions explained on 2 problems. Started with Section 7.5: Strategies for Integration.
  
• Wednesday, 9/12: Finished Section 7.5 with several examples. Started Section 7.8: Improper Integrals. Defined improper integrals ot Type I - integrals with infinity in bounds. Did 4 problems - the most notable one was: integral from 1 to infinity of 1/x^p dx converges for p>1 and diverges otherwise. HW #4 assigned.
  
• Friday, 9/14: Did Comparison Test for integrals of Type I. Defined improper integral of Type 2 - integrand has a discontinuity within the bounds. Several problems presented. Quiz #3 given.
• Friday, 10/26: Had test #2.
• Monday, 10/29: Discussed test problems. Covered Section 8.1 Arc Length. Derived the formula: L = int from a to b of sqrt{1 + (dy/dx)^2} dx. Did 3 problems: length of y=x^{3/2}, x =y^2, and xy =1. The last problem solved using the Simpson Rule.
• Wednesday, 10/31: Covered Section 8.2 Area of a Surface of Revolution. Derived the formula: S = int from a to b of 2\pi f(x) sqrt{1 + (f'(x))^2} dx and some of its variations for rotations about the y-axis. Did a few problems.

Last changed on October 31, 2001.