APPLIED MATHEMATICS
OVERVIEW
Integration and Sequence & Series dominate this semester of Calculus. From inverse functions, the natural logarithmic exponential function, to general exponential and logarithmic functions with applications of exponential growth and decay, and with a refresh on trigonometry through inverse trigonometric functions Calculus II is all about fields of application. Integration by parts, improper integrals, partial fractions and more all lead to applications of integration. Volumes through the shell method and cross-sectional method are all explored. Lengths of curves and parametric curves, to surface areas, and basic mechanical applications of Work
, through Hook's Law
are explored. Even a brief understanding of Hydrostatic force
is explored. More applications of physics in the areas of Moments
and Center of mass
to the more exotic polar coordinate system are tackled. Sequence and Series dominate the second half of Calculus II from Taylor's formula for polynomial series, to infinite series, geometric series, and how integral tests determine convergence or divergence. Power series
, followed by direction Taylor series
applications are explored in depth. Applications for computer science are throughout Calculus II, including Binomial series
. Near the end, applications for conic sections, ellipses, hyperbolas and rotating axes lead to a unified description of conic sections. A brief exposure to Vectors closes up Calculus II.[1]
