Calculus II |
Course Outline (subject to minor rescheduling)
Week One Chapters 6, 7, and 8 to section 8.1 |
Geometric applications of the integral: finding area, volume, arclength. Physical applications of the integral: work. Techniques for evaluating integrals (parts, trigonometric substitution, partial fractions, tables, computer algebra systems, and numerical). Improper integrals. Arclength. |
Week Two Chapters 8, 9 and 10 to section 10.2 |
Arc Length. Surface Area. Applications of the Integral to physics, engineering, and probability: hydrostatic pressure, probability density functions, mean and median. Differential Equations: Various models for population growth, predator/prey systems. Parametric Equations. Cycloids. Tangents. |
Week Three Chapters 10 and 11 |
Polar Coordinates. Conic Sections. Sequences, Series. Tests for convergence: The Integral Test, The Comparison Test, The Ratio and Root Test. Power Series. |
Week Four | More on Power Series, including the Taylor, McLaurin and binomial series. Applications. |