January 28: How Archimedes solved a calculus problem without calculus.
January 30: Course mechanics.
January 31: Approximating areas with lots of skinny rectangles.
February 1: Riemann sums for computing areas and distances.
February 4: The definite integral. Integrable and nonintegrable functions.
February 6: Basic properties of the integral.
February 7: More properties of the integral.
February 8: Even more properties of the integral. The Evaluation Theorem for integrals.
February 11: A proof of the Evaluation Theorem for integrals.
February 13: Integrability reconsidered: All about (Adam and) Eve.
February 14: Indefinite integrals. The Net Change Theorem.
February 15: Riemann sums reconsidered. Areas without Riemann sums. Notational niceties.
February 19: The Fundamental Theorem of the Calculus. Averages.
February 20: The Mean Value Theorem for Integrals. The Substitution Rule
February 21: The Substitution Rule (continued).
February 22: The Substitution Rule (continued). See also Extra Reading #1 and the answer to the question it raises.
February 25: The Fundamental Theorem of the Calculus: the fine print. See also Extra Reading #2 and the answer to the question it raises.
February 27: The Substitution Rule for Definite Integrals.
February 28: Integration by Parts.
February 29: Integration by Parts (concluded). Integration by Partial Fractions.
March 3: Integration by Partial Fractions (concluded). Integrating with Computer Algebra Systems.
March 5: Numerical integration.
March 6: Numerical integration (continued).
March 7: Numerical integration (continued).
March 10: Numerical integration (concluded).
March 12: Improper integrals.
March 13: Review.
March 26: Area between curves. Area under parametrized curves. March 27: Volumes (by disks).
March 28: Volumes (by disks and cylindrical shells).
March 31: Volumes (by cylindrical shells).
April 2: Arc length of parametrized curves. Force and work.
April 3: Hydrostatic pressure. Centers of mass and moments.
April 4: Centers of mass and moments (concluded). Differential equations.
April 7: Sequences.
April 9: Sequences (continued).
April 10: Sequences (concluded). Series.
April 11: The Integral, Comparison, and Limit Comparison Tests.
April 14: The Integral and Limit Comparison Tests (concluded). Alternating Series.
April 17: Power Series. Interval of Convergence. Adding Power Series.
April 18: Multiplying Power Series. Differentiating and Integrating Power Series.
April 23: Taylor Series.
April 24: Newton's Binomial Theorem. Taylor Polynomials.
April 28: Parametric Curves.
April 30: Polar Coordinates.
May 1: Areas in Polar Coordinates.
May 2: Arc Length and Conic Sections in Polar Coordinates.
May 5: Limits and Derivatives. Continuity and Differentiability.
May 7: Continuity and Differentiability (contluded). Lies My Calculator Told Me.
May 12: Proof of the Irrationality of e. Click here for the answers to the True/False questions from chapters 6, 8, and 9.