January 22: Sequences and the Constant Sequence Principle.

January 23: The Constant Sequence Principle, mathematical induction, and summation formulas.

January 24: More about sequences and induction.

January 27: Estimating areas. Computing areas as limits. Velocity, time, and distance.

January 29: Riemann sums. The definition of the definite integral.

January 30: The definition of the definite integral. Properties of the definite integral.

January 31: Properties of the definite integral.

February 3: More properties of the definite integral. The Evaluation Theorem.

February 5: Proof of the Evaluation Theorem. Indefinite integrals. The Net Change Theorem. See also the BrainShark version of this lecture.

February 6: More on the Evaluation Theorem. Lead-in to the Fundamental Theorem of Calculus.

February 7: The Fundamental Theorem of Calculus. Averages.

February 10: The Fundamental Theorem of Calculus (concluded). The Substitution Rule.

February 12: The Substitution Rule for definite integrals.

February 13: The Substitution Rule for indefinite integrals.

Feburary 14: The Substitution Rule (concluded).

February 18: True-False Quiz for Chapter 5. A challenge problem for tomorrow.

February 19: True-False Quiz for Chapter 5 (concluded). Integration by parts.

February 20: Integration by parts (concluded).

February 21: Integration by partial fractions.

February 24: Integration with computer algebra systems. See also a Mathematica notebook on this topic; if you don't have a Mathematica viewer, you can view the PDF.

February 26: Improper Integrals.

February 27: Improper Integrals (continued).

February 28: Improper Integrals (concluded). True/False Quiz for Chapter 6.

March 3: True/False Quiz for Chapter 6 (continued).

March 5: True/False Quiz for Chapter 6 (concluded). Area between two curves.

March 6: MIDTERM EXAM

March 7: MIDTERM EXAM

March 10: Volume.

March 12: Volume by disks.

March 13: Volume by cylindrical shells.

March 14: Arc length and surface area.

March 24: Work and force. Hydrostatic pressure.

March 26: Centers of mass and moments.

March 27: Differential equations.

March 28: Differential equations.

March 31: Sequences.

April 2: The Monotonic Sequence Theorem. Series.

April 3: Integral and Comparison Tests.

April 4: Other convergence tests.

April 7: Power series.

April 9: Representing functions as power series.

April 10: Taylor series.

April 11: Taylor polynomials and the Taylor remainder theorem.

April 14: Parametric curves.

April 16: Polar coordinates.

April 17: Polar coordinates (concluded).

April 18: True/False Quiz for Chapter 8.

April 23: True/False Quiz for Chapter 8 (continued).

April 24: True/False Quiz for Chapter 8 (concluded).

April 25: True/False Quiz for Chapter 9.

April 28: Lies My Calculator and Computer Told Me.

April 30: Odds and ends.