MATH 122-01, Calculus II, Fall 2010

Abstract

We will cover the following material from the text. Chapter 5, Sections 3 – 5: Review of the fundamental theorem of calculus and integration by substitution, both of which you should have seen in Calculus I. Numerical integration. The natural logarithm as an integral. Integrals involving inverse trigonometric functions. Chapter 6, Sections 1 – 5: Applications of integration, including area between curves, volumes by several techniques, work, and average value of a function. Chapter 7, Sections 1 – 4, 7, 8: Techniques for integration, including integration by parts, trigonometric integrals and substitution, and partial fractions. Numerical integration and improper integrals. Chapter 8, Sections 1 – 5: More applications of integration, including arc length, area of surfaces of revolution, applications to physics, engineering, biology, and economics, and probability. Chapter 9, Sections 1 – 6: Differential equations. Modeling, direction fields, some solution techniques. Chapter 11, Sections 1 – 11: Infinite sequences and series. Tests for convergence, power series and their use in representing functions, Taylor and Maclaurin series.