Calculus 2 at Lycoming College is a continuation of Calculus 2, and the two courses share a common description in the catalog. The two-course sequence covers the traditional topics of a 1-variable calculus sequence, namely the basics of limits, integration, differentiation, and their applications to essential problems in physics and geometry.
Calculus 2 specifically --at the present time, and this division depends on the text we happen to be using-- continues with
Applications of integration, including
areas in the planes, volumes of solids of revolution, areas of surfaces of revolution, lengths of arcs, and possibly centers of mass, hydrostatic pressure and work.
Differential equations of first order, including separable and first order linear equations.
Differentiation and integration using exponential, logarithmic, and trigonometric and inverse-trigonometric functions.
The calculus of the hyperbolic functions.
Systematic integration theory, including integration by parts, partial fractions, trigonometric substitution, and the use of reduction formulae.
Improper integrals, and the general idea of convergence.
Numerical Integration, using trapezoidal and Simpson rules.
Convergence of series, including tests for convergence such as comparison test, integral test, ratio test, and Geometric series.
Power series, intervals of convergence, and representation of functions by their series,
the Taylor polynomial.
Polar coordinates, including graphing in polar coordinates, and finding areas in polar coordinates.
A computer algebra system such as Maple or Mathematica is an important part of the course, and there have been computer labs every week as part of the course design since 1986.