M 172M - Calculus II

Credit(s): 5

Prerequisite(s): appropriate placement test score, a grade of “C” or better in M 171, or Math Department consent.
This is the second of three standard courses in calculus. The course includes transcendental functions, applications and techniques of integration, infinite series, parametrized curves, and polar curves. (Spring Semester)

Course Learning Outcomes: Upon completion of the course, students will be able to

Solve problems using mathematical techniques.
Find the area between two curves, surface areas and volumes of revolutions, arc length, moments, centers of mass and hydrostatic pressure, work and the average value of a function using the integral.
Understand integration by direct and trigonometric substitution, parts, and partial fractions and trigonometric integrals.
Understand infinite sequences of real numbers, their monotonicity and boundedness and the Montonic Sequence Theorem.
Understand convergent series of real numbers, geometric series, telescoping series, and the basic test for divergence and use the integral, comparison, limit comparison, and alternating series test for series convergence.
Understand absolute convergence and the ratio and root tests, power series, radius of convergence, and the integration and differentiation of power series.
Understand the Taylor series and Taylor polynomial approximation of functions.
Understand parametrized curves in rectangular and polar coordinates, their derivatives, arch lengths and enclosed areas.