The exact course schedule will depend on the semester in which the course is offered, and the course coordinator. However, a rough outline of the time that we spend on each of the different mathematical topics in the course is given by the following (times are based on a 14 week semester, excluding a week of finals). Below this, we include some sample course materials to illustrate the type of work expected of students.
- Week 1: Review of Velocity and Distance, Riemann Sums, the Definite Integral, the First Fundamental Theorem of Calculus, Antiderivatives and Indefinite Integrals
- Week 2: The Second Fundamental Theorem of Calculus, Integration by Substitution and Parts
- Week 3: Partial Fractions, MID and TRAP rules for Integral Estimation, Areas and Volume using Integrals
- Week 4: Washer Method and Shell Method for Volumes of Revolution, Other Applications of Integration to Geometry, Density and Center of Mass
- Week 5: Applications of Integration to Physics (Work)
- Week 6: Midterm 1, L’Hospital’s Rule, Improper Integrals
- Week 7: More on Improper Integrals, including the Comparison Test
- Week 8: Applications of Improper Integrals to Probability, including Probability Density and Cumulative Distribution Functions, Means and Medians; Introduction to Sequences
- Week 9: Geometric Series, Series Convergence including Power Series, Integral Test, Comparison and Limit Comparison Tests
- Week 10: More on Series, including Ratio Test, Alternating Series, Absolute and Conditional Convergence, Power Series including Radius and Interval of Convergence
- Week 11: Midterm 2, Taylor Polynomials and Series
- Week 12: More on Taylor Series
- Week 13: Parametric Equations and Calculus, including Speed and Arc Length
- Week 14: Polar Coordinates and Calculus, including Area and Arc Length
Course Materials
Sample course materials will be added here shortly.
